AMC 12 Problems
1300 problems · 2000–2025 · AI-classified
Loading…
1300 problems · 2000–2025 · AI-classified
1300 of 1300 problems
| Description | Topic | |||
|---|---|---|---|---|
| 2025 AMC 12A | Two cyclists leave from the same point at different times and speeds; find when they are equidistant from the start. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2025 AMC 12A | Two nut mixes with different percentages are combined; find the pounds of cashews in the final mix. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2025 AMC 12A | Ash joins student or teacher teams, changing their average ages; find Ash's age. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2025 AMC 12A | Four statements about truth/false counts are given; determine how many are false. | Algebra | Logic & Truth Values | 4 |
| 2025 AMC 12A | An infinite pattern of nested squares with alternating shading; find the side-length ratio k. | Algebra | Sequences & Series | 5 |
| 2025 AMC 12A | Six chairs around a round table; find probability that two students and two teachers sit in adjacent pairs. | Combinatorics | Probability | 6 |
| 2025 AMC 12A | Given log equations relating running speed to toes and eyes, find the sum of constants k, a, b. | Algebra | Logarithms & Exponents | 7 |
| 2025 AMC 12A | Pentagon inscribed in a circle with given angles and side lengths; find the length BF. | Geometry | Triangles & Polygons | 8 |
| 2025 AMC 12A | Find the real number r such that r, w, and w^2 are collinear in the complex plane. | Algebra | Complex Numbers | 9 |
| 2025 AMC 12A | Two concentric arcs and segments of length 2π; find the distance from the center to point A. | Geometry | Circular Geometry | 10 |
| 2025 AMC 12A | Given coordinates of triangle vertices, find the sum of the coordinates of the orthocenter. | Geometry | Coordinate Geometry | 11 |
| 2025 AMC 12A | Find the harmonic mean of all real roots of a product of 2025 quadratics. | Algebra | Polynomials | 12 |
| 2025 AMC 12A | Find the probability that a maximal subset of {1,...,13} with no five consecutive integers is chosen. | Combinatorics | Probability | 13 |
| 2025 AMC 12A | Two ellipses with same eccentricity, one internally tangent to the other; find the eccentricity e. | Geometry | Conic Sections | 14 |
| 2025 AMC 12A | Find the maximum size of a sum-free subset of {1, 2, ..., 20}. | Combinatorics | Counting | 15 |
| 2025 AMC 12A | Triangle with given side lengths; find the length from vertex B to intersection of angle bisector and altitude. | Geometry | Triangles & Polygons | 16 |
| 2025 AMC 12A | Find the area of the triangle formed by the three roots of a given cubic polynomial. | Algebra | Complex Numbers | 17 |
| 2025 AMC 12A | Count ordered triples of distinct integers from 1 to 8 satisfying xy > z, xz > y, yz > x. | Combinatorics | Counting | 18 |
| 2025 AMC 12A | Given roots a, b, c of x^3 + kx + 1, find the value of a symmetric sum expression. | Algebra | Polynomials | 19 |
| 2025 AMC 12A | Find the volume of a pentahedron with a rectangular base and given lateral faces. | Geometry | 3D Geometry & Solids | 20 |
| 2025 AMC 12A | Solve for nonnegative integers a, k, m in a geometric series ratio equation equal to 964. | Algebra | Sequences & Series | 21 |
| 2025 AMC 12A | Three random numbers in [0,1]; find probability the greatest exceeds twice each of the others. | Combinatorics | Probability | 22 |
| 2025 AMC 12A | Count positive integers with no repeated digits, no 0s, and no digit adjacent to two greater digits. | Combinatorics | Counting | 23 |
| 2025 AMC 12A | A central circle is surrounded by 12 unit circles; find the radius r of the central circle. | Geometry | Circular Geometry | 24 |
| 2025 AMC 12A | Count ordered pairs of monic cubic polynomials with roots in {1,...,5} such that f(x) ≤ 0 on [a,b]∪(c,d). | Algebra | Polynomials | 25 |
| 2025 AMC 12B | Find max number of 20-gram coffee mugs from a 350-gram bag | Algebra | Rates, Mixtures, & Averages | 1 |
| 2025 AMC 12B | Sum of ones digits of first 2025 positive squares. | Number Theory | Modular Arithmetic | 2 |
| 2025 AMC 12B | Value of i(i-1)(i-2)(i-3) where i = sqrt(-1). | Algebra | Complex Numbers | 3 |
| 2025 AMC 12B | Two-digit numbers in base 7 and base 9 are equal; find a+b. | Algebra | Systems & Algebraic Manipulation | 4 |
| 2025 AMC 12B | Positive integers x,y satisfy 57x+22y=400; minimize x+y. | Number Theory | Factors, Multiples & Divisibility | 5 |
| 2025 AMC 12B | Total cost ABB.BA is divisible by 36; find A+B. | Number Theory | Factors, Multiples & Divisibility | 6 |
| 2025 AMC 12B | Sum of a telescoping series with logarithms from n=2 to 255. | Algebra | Logarithms & Exponents | 7 |
| 2025 AMC 12B | Polynomial x^3-5x^2+ax+b has root 4+sqrt(5); find a+b. | Algebra | Polynomials | 8 |
| 2025 AMC 12B | Tens digit of 6^(6^6). | Number Theory | Modular Arithmetic | 9 |
| 2025 AMC 12B | Ratio x/(x+y) on altitude of 30-60-90 triangle divided by median. | Geometry | Triangles & Polygons | 10 |
| 2025 AMC 12B | Probability that the three tallest athletes are group captains. | Combinatorics | Probability | 11 |
| 2025 AMC 12B | Area cleaned by a windshield wiper sweeping a 60-degree arc. | Geometry | Circular Geometry | 12 |
| 2025 AMC 12B | Number of colorings of 6 sectors with 2 each of red, green, blue, no adjacent same. | Combinatorics | Counting | 13 |
| 2025 AMC 12B | Greatest n for decreasing sequence with given average conditions. | Algebra | Sequences & Series | 14 |
| 2025 AMC 12B | Time to fill remainder of a truncated pyramid container. | Geometry | 3D Geometry & Solids | 15 |
| 2025 AMC 12B | Tangent of acute angle between hour and minute hand after 2025 minutes. | Geometry | Trigonometry | 16 |
| 2025 AMC 12B | Number of 3x3 grid colorings with red-blue-yellow adjacency constraints. | Combinatorics | Counting | 17 |
| 2025 AMC 12B | Expected number of games until at least one win and one loss. | Combinatorics | Probability | 18 |
| 2025 AMC 12B | Number of squares with same number in horizontal and vertical fillings. | Number Theory | Factors, Multiples & Divisibility | 19 |
| 2025 AMC 12B | Probability frog reaches 4 on number line with given transition rules. | Combinatorics | Probability | 20 |
| 2025 AMC 12B | Sum of integer third sides of two non-congruent triangles with sides 8,9 and equal area. | Geometry | Triangles & Polygons | 21 |
| 2025 AMC 12B | Greatest area of triangle with vertices 2z, (1+i)z, (1-i)z given |4z-2|=1. | Algebra | Complex Numbers | 22 |
| 2025 AMC 12B | Sum of integers z>1 such that remainders of 2025x mod z increase with x. | Number Theory | Modular Arithmetic | 23 |
| 2025 AMC 12B | Number of real solutions to sin(20πx) = log_20(x). | Algebra | Functions | 24 |
| 2025 AMC 12B | Side length squared of equilateral triangle with vertices on concentric circles radii 1,2,3. | Geometry | Triangles & Polygons | 25 |
| 2024 AMC 12A | Evaluate 9901*101 - 99*10101. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2024 AMC 12A | Find hiking time given linear model T=aL+bG with two data points. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2024 AMC 12A | Least number of two-digit numbers summing to 2024. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2024 AMC 12A | Least n such that n! is a multiple of 2024. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2024 AMC 12A | Find how many 6s were in a data set given means. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2024 AMC 12A | Least possible positive sum of three integers with product 60. | Number Theory | Factors, Multiples & Divisibility | 6 |
| 2024 AMC 12A | Find the length of the sum of vectors from a vertex to points on the hypotenuse. | Geometry | Triangles & Polygons | 7 |
| 2024 AMC 12A | Find the number of angles theta satisfying a logarithmic equation. | Algebra | Logarithms & Exponents | 8 |
| 2024 AMC 12A | Units digit of greatest M such that M+1213 and M+3773 are perfect squares. | Number Theory | Factors, Multiples & Divisibility | 9 |
| 2024 AMC 12A | Express the smallest angle of a 7-24-25 triangle in terms of that of a 3-4-5 triangle. | Geometry | Trigonometry | 10 |
| 2024 AMC 12A | Count bases b between 5 and 2024 where 2024_b is divisible by 16. | Number Theory | Modular Arithmetic | 11 |
| 2024 AMC 12A | Sum of digits of least b in geometric sequence a, 720, b with a<720<b. | Algebra | Sequences & Series | 12 |
| 2024 AMC 12A | Find the reflection of a point over the axis of symmetry of a graph. | Algebra | Functions | 13 |
| 2024 AMC 12A | Find entry (1,2) in 5x5 grid with arithmetic progressions in rows and columns. | Algebra | Sequences & Series | 14 |
| 2024 AMC 12A | Evaluate an expression involving the roots of a cubic polynomial. | Algebra | Polynomials | 15 |
| 2024 AMC 12A | Find the probability that each player gets specific colored tokens. | Combinatorics | Probability | 16 |
| 2024 AMC 12A | Find ab+bc+ca given ab+c=100, bc+a=87, ca+b=60. | Algebra | Systems & Algebraic Manipulation | 17 |
| 2024 AMC 12A | Find how many cards are needed until a vertex lands on a given point. | Geometry | Triangles & Polygons | 18 |
| 2024 AMC 12A | Find the length of the shorter diagonal of a cyclic quadrilateral. | Geometry | Circular Geometry | 19 |
| 2024 AMC 12A | Find the probability that triangle area is less than half the total area. | Combinatorics | Probability | 20 |
| 2024 AMC 12A | Find the greatest integer less than or equal to a sum of squares from a recurrence. | Algebra | Sequences & Series | 21 |
| 2024 AMC 12A | Number of ways to place toothpicks forming a closed loop on an 8x3 grid with numbered cells. | Combinatorics | Counting | 22 |
| 2024 AMC 12A | Find the value of a trigonometric expression involving tangent squares. | Geometry | Trigonometry | 23 |
| 2024 AMC 12A | Find the least total surface area of a disphenoid with integer side lengths. | Geometry | 3D Geometry & Solids | 24 |
| 2024 AMC 12A | Count quadruples of integers making a rational function symmetric about y=x. | Algebra | Functions | 25 |
| 2024 AMC 12B | Find total people given 1013th from left and 1010th from right. | Algebra | Logic & Truth Values | 1 |
| 2024 AMC 12B | Evaluate 10! - 7! * 6!. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2024 AMC 12B | Count integer x satisfying |2x| ≤ 7π. | Algebra | Inequalities | 3 |
| 2024 AMC 12B | Find bin for ball 2024 in a triangular deposit pattern. | Number Theory | Modular Arithmetic | 4 |
| 2024 AMC 12B | Minimize sign flips to make sum of odds negative. | Algebra | Inequalities | 5 |
| 2024 AMC 12B | Find number of base-5 digits of 5×10^13. | Algebra | Logarithms & Exponents | 6 |
| 2024 AMC 12B | Find area of right triangle WMA in a rectangle. | Geometry | Triangles & Polygons | 7 |
| 2024 AMC 12B | Solve equation with log_2 x and log_3 x. | Algebra | Logarithms & Exponents | 8 |
| 2024 AMC 12B | Probability dart lands in annular region of a square. | Geometry | Coordinate Geometry | 9 |
| 2024 AMC 12B | Count ordered triples (x,y,z) given range, mean, median constraints. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2024 AMC 12B | Find mean of sin^2(1°) through sin^2(90°). | Geometry | Trigonometry | 11 |
| 2024 AMC 12B | Find imaginary part of z given |z|=2 and quadrilateral area 15. | Algebra | Complex Numbers | 12 |
| 2024 AMC 12B | Minimize h+k given two circle equations in x and y. | Algebra | Systems & Algebraic Manipulation | 13 |
| 2024 AMC 12B | Number of remainders of n^100 mod 125. | Number Theory | Modular Arithmetic | 14 |
| 2024 AMC 12B | Area of triangle with vertices at log points. | Geometry | Coordinate Geometry | 15 |
| 2024 AMC 12B | Find exponent of 3 in number of committee assignments. | Combinatorics | Counting | 16 |
| 2024 AMC 12B | Probability cubic has 3 distinct integer roots. | Combinatorics | Probability | 17 |
| 2024 AMC 12B | Sum of ratios of Fibonacci numbers F_{2n}/F_n. | Algebra | Sequences & Series | 18 |
| 2024 AMC 12B | Find tanθ given area of hexagon from rotated equilateral triangle. | Geometry | Trigonometry | 19 |
| 2024 AMC 12B | Find p+q+r+s for median length function of triangle. | Geometry | Triangles & Polygons | 20 |
| 2024 AMC 12B | Perimeter of third primitive triple with angles summing to 90°. | Geometry | Trigonometry | 21 |
| 2024 AMC 12B | Least perimeter of triangle with angle B = 2A and integer sides. | Geometry | Triangles & Polygons | 22 |
| 2024 AMC 12B | Square of height of pyramid with regular octagon base. | Geometry | 3D Geometry & Solids | 23 |
| 2024 AMC 12B | Count triples of altitudes giving integer inradius. | Geometry | Triangles & Polygons | 24 |
| 2024 AMC 12B | Probability color and pattern are independent for selected ball. | Combinatorics | Probability | 25 |
| 2023 AMC 12A | Alicia and Beth bike toward each other from cities 45 miles apart; find meeting distance from Alicia's city. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2023 AMC 12A | Find weight of a large pizza given equal weights of pizza fractions and orange slices. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2023 AMC 12A | Count positive perfect squares less than 2023 that are divisible by 5. | Number Theory | Factors, Multiples & Divisibility | 3 |
| 2023 AMC 12A | Find number of digits in base-ten representation of 8^5 * 5^10 * 15^5. | Algebra | Logarithms & Exponents | 4 |
| 2023 AMC 12A | Probability that running total of 4 die rolls equals 3 at some point. | Combinatorics | Probability | 5 |
| 2023 AMC 12A | Points A and B on y=log2(x) have midpoint (6,2); find positive difference of x-coordinates. | Algebra | Logarithms & Exponents | 6 |
| 2023 AMC 12A | Count 2023 dates where each digit appears an even number of times in 8-digit display. | Combinatorics | Counting | 7 |
| 2023 AMC 12A | Find current mean quiz score given effect of one or three additional 11s. | Algebra | Rates, Mixtures, & Averages | 8 |
| 2023 AMC 12A | Find ratio of shorter to longer leg in right triangle formed by inscribed squares. | Geometry | Triangles & Polygons | 9 |
| 2023 AMC 12A | Positive reals x,y satisfy y^3=x^2 and (y-x)^2=4y^2; find x+y. | Algebra | Systems & Algebraic Manipulation | 10 |
| 2023 AMC 12A | Find acute angle between lines with slopes 2 and 1/3. | Geometry | Trigonometry | 11 |
| 2023 AMC 12A | Evaluate alternating sum of cubes from 1^3 to 18^3. | Algebra | Sequences & Series | 12 |
| 2023 AMC 12A | Find total games in round-robin tournament given left-handed win 40% more than right-handed. | Algebra | Systems & Algebraic Manipulation | 13 |
| 2023 AMC 12A | Count complex numbers z satisfying z^5 = conjugate(z). | Algebra | Complex Numbers | 14 |
| 2023 AMC 12A | Find angle theta so zigzag path across 100x30 field has total length 120 meters. | Geometry | Trigonometry | 15 |
| 2023 AMC 12A | Maximize imaginary part of z given |1+z+z^2|=4; express as sqrt(m)/n. | Algebra | Complex Numbers | 16 |
| 2023 AMC 12A | Probability frog starting at 0 eventually lands at 10 with jump distances geometric. | Combinatorics | Probability | 17 |
| 2023 AMC 12A | Find radius of circle internally tangent to two unit circles and externally tangent to another. | Geometry | Circular Geometry | 18 |
| 2023 AMC 12A | Find product of all solutions to logarithmic equation with variable bases. | Algebra | Logarithms & Exponents | 19 |
| 2023 AMC 12A | Find units digit of sum of 2023 numbers in 2023rd row of triangular array. | Algebra | Sequences & Series | 20 |
| 2023 AMC 12A | Probability d(Q,R) > d(R,S) for three random vertices of regular icosahedron. | Combinatorics | Probability | 21 |
| 2023 AMC 12A | Find f(2023) for function on positive integers with sum over divisors condition. | Number Theory | Factors, Multiples & Divisibility | 22 |
| 2023 AMC 12A | Count ordered pairs of positive reals (a,b) satisfying (1+2a)(2+2b)(2a+b)=32ab. | Algebra | Inequalities | 23 |
| 2023 AMC 12A | Count sequences of nested subsets of {1,...,10} with length at most 10. | Combinatorics | Counting | 24 |
| 2023 AMC 12A | Find coefficient a_{2023} in tangent multiple-angle formula for tan(2023x). | Geometry | Trigonometry | 25 |
| 2023 AMC 12B | Pour juice from full glasses into a partial glass to equalize amounts. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2023 AMC 12B | Find original price given discount, tax, and maximum budget. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2023 AMC 12B | Find ratio of areas of circles circumscribing 3-4-5 and 5-12-13 right triangles. | Geometry | Circular Geometry | 3 |
| 2023 AMC 12B | Convert millimeters and meters to find area in square centimeters. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2023 AMC 12B | Find minimum guesses to guarantee finding a hidden 2x1 rectangle on a 3x3 grid. | Combinatorics | Counting | 5 |
| 2023 AMC 12B | Count intervals where polynomial with repeated roots is positive. | Algebra | Polynomials | 6 |
| 2023 AMC 12B | Find integer n for which a log expression is real. | Algebra | Logarithms & Exponents | 7 |
| 2023 AMC 12B | Count subsets where the number of elements equals the least element. | Combinatorics | Counting | 8 |
| 2023 AMC 12B | Find area of region defined by nested absolute value inequality. | Geometry | Coordinate Geometry | 9 |
| 2023 AMC 12B | Find slope of line through intersection points of two tangent circles. | Geometry | Coordinate Geometry | 10 |
| 2023 AMC 12B | Maximize area of isosceles trapezoid with legs 1 and bases in ratio 2:1. | Geometry | Triangles & Polygons | 11 |
| 2023 AMC 12B | Find modulus of complex number z given a custom binary operation. | Algebra | Complex Numbers | 12 |
| 2023 AMC 12B | Find space diagonal of rectangular box given edge sum, surface area, volume. | Algebra | Systems & Algebraic Manipulation | 13 |
| 2023 AMC 12B | Count integer pairs (a,b) so cubic has three distinct integer roots. | Algebra | Polynomials | 14 |
| 2023 AMC 12B | Determine which statements about gcd are true given a linear Diophantine equation. | Number Theory | Factors, Multiples & Divisibility | 15 |
| 2023 AMC 12B | Find largest non-representable value using 6, 10, 15 cent coins. | Number Theory | Modular Arithmetic | 16 |
| 2023 AMC 12B | Find area of triangle with sides in arithmetic progression and a 120° angle. | Geometry | Trigonometry | 17 |
| 2023 AMC 12B | Determine which statement about yearly quiz averages cannot be true. | Algebra | Rates, Mixtures, & Averages | 18 |
| 2023 AMC 12B | Find probability each of 3 bins gets an odd number of 2023 balls. | Combinatorics | Probability | 19 |
| 2023 AMC 12B | Find probability frog lands within 1 unit after two 2-unit jumps. | Geometry | Trigonometry | 20 |
| 2023 AMC 12B | Find shortest path on frustum surface from bottom to farthest top point. | Geometry | 3D Geometry & Solids | 21 |
| 2023 AMC 12B | Find which value of f(1) is impossible given a functional equation. | Algebra | Functions | 22 |
| 2023 AMC 12B | Find n such that product of n dice rolls has 936 possible values. | Combinatorics | Counting | 23 |
| 2023 AMC 12B | Find gcd of four numbers given product and pairwise lcm relations. | Number Theory | Factors, Multiples & Divisibility | 24 |
| 2023 AMC 12B | Find area of smaller pentagon formed by folding vertices of a regular pentagon. | Geometry | Triangles & Polygons | 25 |
| 2022 AMC 12A | Evaluate the continued fraction 3 + 1/(3 + 1/(3 + 1/3)). | Algebra | Systems & Algebraic Manipulation | 1 |
| 2022 AMC 12A | Find the absolute difference between the first and second numbers given sum and relationships. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2022 AMC 12A | Identify the middle rectangle in a square arrangement. | Geometry | Triangles & Polygons | 3 |
| 2022 AMC 12A | Find the sum of digits of n given LCM(n,18)=180 and GCD(n,45)=15. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2022 AMC 12A | Count lattice points with taxicab distance at most 20 from origin. | Combinatorics | Counting | 5 |
| 2022 AMC 12A | Find the sum of all positive X such that the mean of the data set equals a value in the set. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2022 AMC 12A | Count colorings of five regions in a rectangle so touching regions differ. | Combinatorics | Counting | 7 |
| 2022 AMC 12A | Evaluate an infinite product of nested cube roots of 10. | Algebra | Sequences & Series | 8 |
| 2022 AMC 12A | Determine how many pieces of candy truth-tellers received based on yes/no answers. | Algebra | Logic & Truth Values | 9 |
| 2022 AMC 12A | Count ways to pair numbers 1-14 so each pair's larger is at least double the smaller. | Combinatorics | Counting | 10 |
| 2022 AMC 12A | Find the product of all x satisfying a logarithmic distance equation. | Algebra | Logarithms & Exponents | 11 |
| 2022 AMC 12A | Find the cosine of angle CMD in a regular tetrahedron. | Geometry | 3D Geometry & Solids | 12 |
| 2022 AMC 12A | Find the area of a region in the complex plane defined by a Minkowski sum. | Geometry | Coordinate Geometry | 13 |
| 2022 AMC 12A | Evaluate an expression involving base-10 logarithms. | Algebra | Logarithms & Exponents | 14 |
| 2022 AMC 12A | Find the volume of a box formed by adding 2 to each edge of a box with given polynomial roots. | Algebra | Polynomials | 15 |
| 2022 AMC 12A | Find the sum of digits of the fourth triangular number that is a perfect square. | Number Theory | Factors, Multiples & Divisibility | 16 |
| 2022 AMC 12A | Find p+q+r for the set of a where a trig equation has more than one solution. | Geometry | Trigonometry | 17 |
| 2022 AMC 12A | Find the least n so that applying T_1 through T_n returns (1,0) to itself. | Geometry | Coordinate Geometry | 18 |
| 2022 AMC 12A | Count orderings of cards 1-13 that are picked up in exactly two passes. | Combinatorics | Counting | 19 |
| 2022 AMC 12A | Find BC/AD in an isosceles trapezoid given distances from point P to vertices. | Geometry | Triangles & Polygons | 20 |
| 2022 AMC 12A | Identify which polynomial is a factor of x^2022 + x^1011 + 1. | Algebra | Polynomials | 21 |
| 2022 AMC 12A | Find c when the area of a quadrilateral formed by roots and their reciprocals is maximized. | Algebra | Complex Numbers | 22 |
| 2022 AMC 12A | Count n up to 22 where the denominator of the harmonic sum is less than LCM(1..n). | Number Theory | Modular Arithmetic | 23 |
| 2022 AMC 12A | Count 5-digit strings from 0-4 where at least j digits are less than j for j=1..4. | Combinatorics | Counting | 24 |
| 2022 AMC 12A | Find the ratio of largest to smallest segment length tangent to a circle. | Number Theory | Factors, Multiples & Divisibility | 25 |
| 2022 AMC 12B | Evaluate an expression involving a custom-defined absolute difference operation. | Algebra | Functions | 1 |
| 2022 AMC 12B | Find the area of a rhombus given a perpendicular segment and side lengths. | Geometry | Triangles & Polygons | 2 |
| 2022 AMC 12B | Determine how many of the first ten terms of a sequence are prime. | Number Theory | Factors, Multiples & Divisibility | 3 |
| 2022 AMC 12B | Count values of k for which the quadratic has two distinct integer roots. | Algebra | Polynomials | 4 |
| 2022 AMC 12B | Find coordinates after rotating a point about another point. | Geometry | Coordinate Geometry | 5 |
| 2022 AMC 12B | Count how many sets of ten consecutive integers contain exactly two multiples of 7. | Number Theory | Factors, Multiples & Divisibility | 6 |
| 2022 AMC 12B | Find the least possible mode given relationships between mode, median, and mean. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2022 AMC 12B | Identify the graph of an equation in the coordinate plane. | Geometry | Conic Sections | 8 |
| 2022 AMC 12B | Find the minimum possible value of a term in an arithmetic sequence. | Algebra | Sequences & Series | 9 |
| 2022 AMC 12B | Find the perimeter of a quadrilateral in a regular hexagon. | Geometry | Triangles & Polygons | 10 |
| 2022 AMC 12B | Evaluate a sum of powers of complex numbers. | Algebra | Complex Numbers | 11 |
| 2022 AMC 12B | Find probability of dice rolls meeting two conditions. | Combinatorics | Probability | 12 |
| 2022 AMC 12B | Find area of region inside both a square and a rectangle. | Geometry | Triangles & Polygons | 13 |
| 2022 AMC 12B | Find tangent of angle formed by parabola intercepts. | Geometry | Coordinate Geometry | 14 |
| 2022 AMC 12B | Identify which number is not divisible by any prime less than 10. | Number Theory | Modular Arithmetic | 15 |
| 2022 AMC 12B | Find greatest possible value of log base 2 of y given equations. | Algebra | Logarithms & Exponents | 16 |
| 2022 AMC 12B | Count 4x4 binary arrays with given row and column sums. | Combinatorics | Counting | 17 |
| 2022 AMC 12B | Count initial configurations leading to a single filled center square after one transformation. | Combinatorics | Counting | 18 |
| 2022 AMC 12B | Find cosine of angle C in triangle with equilateral median intersection. | Geometry | Triangles & Polygons | 19 |
| 2022 AMC 12B | Find the sum of squares of coefficients of a polynomial given two remainder conditions. | Algebra | Polynomials | 20 |
| 2022 AMC 12B | Find the sum of areas of all circles tangent to three given circles. | Geometry | Circular Geometry | 21 |
| 2022 AMC 12B | Find probability Amelia's position exceeds 1 given random step durations and increments. | Combinatorics | Probability | 22 |
| 2022 AMC 12B | Find the value of a binary-weighted sum given a modular condition on partial sums. | Number Theory | Modular Arithmetic | 23 |
| 2022 AMC 12B | Sum of 4th powers of all chords in a regular heptagon. | Geometry | Trigonometry | 24 |
| 2022 AMC 12B | Find area of 12-sided polygon formed by hexagons around a square. | Geometry | Triangles & Polygons | 25 |
| 2021 Fall AMC 12A | Evaluate (2112-2021)^2 / 169. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2021 Spring AMC 12A | Evaluate 2^(1+2+3) - (2^1+2^2+2^3). | Algebra | Systems & Algebraic Manipulation | 1 |
| 2021 Fall AMC 12A | Find area after shortening the other side of a 4x6 card by 1 inch. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2021 Spring AMC 12A | Find conditions for sqrt(a^2+b^2)=a+b to hold. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2021 Fall AMC 12A | Compare travel times on two routes to find time saved. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2021 Spring AMC 12A | Find difference of two numbers given sum and digit condition. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2021 Fall AMC 12A | Find digit A so that 20210A is prime. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2021 Spring AMC 12A | Determine which conclusion follows from statements about snakes. | Algebra | Logic & Truth Values | 4 |
| 2021 Fall AMC 12A | Find difference in leap length between emu and ostrich strides. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2021 Spring AMC 12A | Find two-digit number ab from repeating decimal multiplication error. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2021 Fall AMC 12A | Find angle AFE in a square with given angle and isosceles triangle. | Geometry | Triangles & Polygons | 6 |
| 2021 Spring AMC 12A | Find original number of cards given probability changes. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2021 Fall AMC 12A | Compute difference between teacher-average and student-average class size. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2021 Spring AMC 12A | Find least possible value of (xy-1)^2+(x+y)^2. | Algebra | Inequalities | 7 |
| 2021 Fall AMC 12A | Find N/M where M is LCM of 10-30 and N of M,32-40. | Number Theory | Factors, Multiples & Divisibility | 8 |
| 2021 Spring AMC 12A | Find parity of D_2021, D_2022, D_2023 given recurrence. | Algebra | Sequences & Series | 8 |
| 2021 Fall AMC 12A | Find x given surface area equals volume for log edge lengths. | Algebra | Logarithms & Exponents | 9 |
| 2021 Spring AMC 12A | Simplify product (2+3)(2^2+3^2)...(2^64+3^64). | Algebra | Polynomials | 9 |
| 2021 Fall AMC 12A | Find remainder when base-9 number N is divided by 5. | Number Theory | Modular Arithmetic | 10 |
| 2021 Spring AMC 12A | Find ratio of liquid level rises in two cones after dropping marble. | Geometry | 3D Geometry & Solids | 10 |
| 2021 Fall AMC 12A | Find chord length in larger circle with half inside smaller circle. | Geometry | Circular Geometry | 11 |
| 2021 Spring AMC 12A | Find total distance of laser beam reflecting off axes. | Geometry | Coordinate Geometry | 11 |
| 2021 Fall AMC 12A | Count terms with rational coefficients in binomial expansion. | Algebra | Polynomials | 12 |
| 2021 Spring AMC 12A | Find B in polynomial with positive integer roots. | Algebra | Polynomials | 12 |
| 2021 Fall AMC 12A | Find slope k of angle bisector between y=x and y=3x. | Geometry | Coordinate Geometry | 13 |
| 2021 Spring AMC 12A | Find which complex number has z^5 with greatest real part. | Algebra | Complex Numbers | 13 |
| 2021 Fall AMC 12A | Find perimeter of equilateral hexagon with 30° angles and area 6√3. | Geometry | Triangles & Polygons | 14 |
| 2021 Spring AMC 12A | Evaluate product of two sums of logarithms. | Algebra | Logarithms & Exponents | 14 |
| 2021 Fall AMC 12A | Find B+D for polynomial with roots f(z_i) given P(z). | Algebra | Complex Numbers | 15 |
| 2021 Spring AMC 12A | Count groups of tenors and basses with difference multiple of 4. | Combinatorics | Counting | 15 |
| 2021 Fall AMC 12A | Max cables connecting 20 brand A and 10 brand B computers. | Combinatorics | Counting | 16 |
| 2021 Spring AMC 12A | Find median of list where integer n appears n times. | Algebra | Sequences & Series | 16 |
| 2021 Fall AMC 12A | Count ordered pairs (b,c) where neither quadratic has two distinct real roots. | Algebra | Polynomials | 17 |
| 2021 Spring AMC 12A | Find AD length in trapezoid with given conditions. | Geometry | Triangles & Polygons | 17 |
| 2021 Fall AMC 12A | Find ratio p/q of probabilities for ball distribution into bins. | Combinatorics | Probability | 18 |
| 2021 Spring AMC 12A | Find which x gives f(x)<0 for multiplicative function f. | Algebra | Functions | 18 |
| 2021 Fall AMC 12A | Find smallest x>1 with sin(x)=sin(x^2) in degrees, rounded up. | Geometry | Trigonometry | 19 |
| 2021 Spring AMC 12A | Count solutions to sin(pi/2 cos x)=cos(pi/2 sin x) in [0,pi]. | Geometry | Trigonometry | 19 |
| 2021 Fall AMC 12A | Count n≤50 where f_50(n)=12 for divisor-based function f. | Number Theory | Factors, Multiples & Divisibility | 20 |
| 2021 Spring AMC 12A | Find sum of possible distances from focus to vertex of parabola. | Geometry | Conic Sections | 20 |
| 2021 Fall AMC 12A | Find area of isosceles trapezoid with given diagonal segments. | Geometry | Triangles & Polygons | 21 |
| 2021 Spring AMC 12A | Find eccentricity of ellipse through five complex roots. | Geometry | Conic Sections | 21 |
| 2021 Fall AMC 12A | Count final board configurations where Carl wins with 3 O's in a row. | Combinatorics | Counting | 22 |
| 2021 Spring AMC 12A | Find abc for cubic with roots cos(2pi/7), cos(4pi/7), cos(6pi/7). | Algebra | Polynomials | 22 |
| 2021 Fall AMC 12A | Find p(1) for unique disrespectful quadratic maximizing sum of roots. | Algebra | Polynomials | 23 |
| 2021 Spring AMC 12A | Probability frog reaches corner on 3x3 toroidal grid in ≤4 hops. | Combinatorics | Probability | 23 |
| 2021 Fall AMC 12A | Sum all possible side lengths a in quadrilateral with arithmetic progression sides. | Geometry | Triangles & Polygons | 24 |
| 2021 Spring AMC 12A | Find area of triangle formed by intersecting circles. | Geometry | Circular Geometry | 24 |
| 2021 Fall AMC 12A | Find c1 in polynomial q(m)=D(m) for quadruples summing to multiple of m. | Number Theory | Modular Arithmetic | 25 |
| 2021 Spring AMC 12A | Find N maximizing divisor count over cube root of N. | Number Theory | Factors, Multiples & Divisibility | 25 |
| 2021 Fall AMC 12B | Sum of four numbers formed by cycling digits 1,2,3,4. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2021 Spring AMC 12B | Count integer values of x satisfying |x| < 3π. | Algebra | Inequalities | 1 |
| 2021 Fall AMC 12B | Area of a shaded polygon on a 6x5 grid. | Geometry | Coordinate Geometry | 2 |
| 2021 Spring AMC 12B | Find number of pairs with both wearing yellow shirts. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2021 Fall AMC 12B | Find product of possible temperature differences N. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2021 Spring AMC 12B | Solve a continued fraction equation for x. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2021 Fall AMC 12B | Simplify n/4 where n = 8^2022. | Algebra | Logarithms & Exponents | 4 |
| 2021 Spring AMC 12B | Find the mean of combined class scores given ratio. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2021 Fall AMC 12B | Count distinct sums of two special fractions summing to 15. | Combinatorics | Counting | 5 |
| 2021 Spring AMC 12B | Find b-a after rotation and reflection of a point. | Geometry | Coordinate Geometry | 5 |
| 2021 Fall AMC 12B | Sum of digits of largest prime divisor of 16383. | Number Theory | Factors, Multiples & Divisibility | 6 |
| 2021 Spring AMC 12B | Find water height in cylinder after pouring from cone. | Geometry | 3D Geometry & Solids | 6 |
| 2021 Fall AMC 12B | Find condition guaranteeing x,y,z satisfy given equation. | Algebra | Systems & Algebraic Manipulation | 7 |
| 2021 Spring AMC 12B | Find ratio of sum of odd to even divisors of N. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2021 Fall AMC 12B | Vertex angle of obtuse isosceles triangle with given product condition. | Geometry | Trigonometry | 8 |
| 2021 Spring AMC 12B | Find distance between parallel lines intersecting a circle. | Geometry | Circular Geometry | 8 |
| 2021 Fall AMC 12B | Area of circle through A, O, C in equilateral triangle. | Geometry | Triangles & Polygons | 9 |
| 2021 Spring AMC 12B | Evaluate a difference of logarithmic expressions. | Algebra | Logarithms & Exponents | 9 |
| 2021 Fall AMC 12B | Sum of t values making triangle with given points isosceles. | Geometry | Trigonometry | 10 |
| 2021 Spring AMC 12B | Find difference of two numbers given sum and product condition. | Number Theory | Factors, Multiples & Divisibility | 10 |
| 2021 Fall AMC 12B | Probability product of 6 dice rolls divisible by 4. | Combinatorics | Probability | 11 |
| 2021 Spring AMC 12B | Find distance DE in trapezoid configuration of triangle. | Geometry | Triangles & Polygons | 11 |
| 2021 Fall AMC 12B | Difference f(768)-f(384) where f(n) is divisor sum over n. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2021 Spring AMC 12B | Find average of set given conditions on removing extremes. | Algebra | Rates, Mixtures, & Averages | 12 |
| 2021 Fall AMC 12B | Evaluate product of sines with argument multiples of 2π/11. | Geometry | Trigonometry | 13 |
| 2021 Spring AMC 12B | Count solutions to trig equation in given interval. | Geometry | Trigonometry | 13 |
| 2021 Fall AMC 12B | Minimum distinct complex solutions to P(z)Q(z)=R(z). | Algebra | Polynomials | 14 |
| 2021 Spring AMC 12B | Find volume of pyramid with rectangle base and given lengths. | Geometry | 3D Geometry & Solids | 14 |
| 2021 Fall AMC 12B | Area of 24-sided polygon from three rotated squares. | Geometry | Triangles & Polygons | 15 |
| 2021 Spring AMC 12B | Find area of pentagon formed by 11 congruent segments. | Geometry | Triangles & Polygons | 15 |
| 2021 Fall AMC 12B | Sum of a^2+b^2+c^2 given sum and gcd conditions. | Number Theory | Factors, Multiples & Divisibility | 16 |
| 2021 Spring AMC 12B | Find g(1) for polynomial with reciprocal roots of f(x). | Algebra | Polynomials | 16 |
| 2021 Fall AMC 12B | Probability bug stays within 1 unit after 5 moves on triangular grid. | Combinatorics | Probability | 17 |
| 2021 Spring AMC 12B | Find ratio of bases in trapezoid given triangle areas. | Geometry | Triangles & Polygons | 17 |
| 2021 Fall AMC 12B | Least k such that u_k is within 1/2^1000 of limit. | Algebra | Sequences & Series | 18 |
| 2021 Spring AMC 12B | Find value of z + 6/z for complex number satisfying equation. | Algebra | Complex Numbers | 18 |
| 2021 Fall AMC 12B | Number of interior intersections of sides of 5,6,7,8-gons. | Combinatorics | Counting | 19 |
| 2021 Spring AMC 12B | Find least possible total faces on two dice given probabilities. | Combinatorics | Probability | 19 |
| 2021 Fall AMC 12B | Number of distinct 2x2x2 cubes from 4 white and 4 blue unit cubes. | Combinatorics | Counting | 20 |
| 2021 Spring AMC 12B | Find remainder when z^2021+1 is divided by z^2+z+1. | Algebra | Polynomials | 20 |
| 2021 Fall AMC 12B | Number of x in [0,2π) satisfying P(x)=0 with complex exponentials. | Algebra | Complex Numbers | 21 |
| 2021 Spring AMC 12B | Determine range for sum of solutions to exponential equation. | Algebra | Logarithms & Exponents | 21 |
| 2021 Fall AMC 12B | Distance between centers of two circles tangent to triangle sides. | Geometry | Circular Geometry | 22 |
| 2021 Spring AMC 12B | Find starting configuration where Beth has winning strategy. | Combinatorics | Counting | 22 |
| 2021 Fall AMC 12B | Average number of consecutive integer pairs in a 5-element subset of 1..30. | Combinatorics | Probability | 23 |
| 2021 Spring AMC 12B | Find probability balls land in evenly spaced distinct bins. | Combinatorics | Probability | 23 |
| 2021 Fall AMC 12B | Length CF where F is intersection of circumcircle and line AB. | Geometry | Triangles & Polygons | 24 |
| 2021 Spring AMC 12B | Find d^2 for longer diagonal of parallelogram given projections. | Geometry | Triangles & Polygons | 24 |
| 2021 Fall AMC 12B | Two-digit n where sum of remainders equals that of n+1. | Number Theory | Modular Arithmetic | 25 |
| 2021 Spring AMC 12B | Find length of interval of slopes with exactly 300 lattice points below. | Geometry | Coordinate Geometry | 25 |
| 2020 AMC 12A | Carlos takes 70% of a pie, Maria takes 1/3 of the remainder. What portion is left? | Algebra | Rates, Mixtures, & Averages | 1 |
| 2020 AMC 12A | Sum of lengths of line segments forming the acronym AMC on a grid. | Geometry | Coordinate Geometry | 2 |
| 2020 AMC 12A | Driver travels 2 hours at 60 mph, car gets 30 mpg, paid $0.50 per mile, gas $2 per gallon. Find net hourly pay. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2020 AMC 12A | How many 4-digit positive integers with only even digits are divisible by 5? | Combinatorics | Counting | 4 |
| 2020 AMC 12A | 25 integers from -10 to 14 arranged in a 5x5 magic square. Find the common sum. | Algebra | Sequences & Series | 5 |
| 2020 AMC 12A | Least additional shaded squares so figure has two lines of symmetry. | Geometry | Triangles & Polygons | 6 |
| 2020 AMC 12A | Seven cubes stacked vertically, volumes 1 to 343. Find total surface area of the tower. | Geometry | 3D Geometry & Solids | 7 |
| 2020 AMC 12A | Median of the list of numbers 1 to 2020 and their squares. | Algebra | Sequences & Series | 8 |
| 2020 AMC 12A | Number of solutions to tan(2x)=cos(x/2) on [0,2π]. | Geometry | Trigonometry | 9 |
| 2020 AMC 12A | Find sum of digits of n satisfying log_2(log_16 n)=log_4(log_4 n). | Algebra | Logarithms & Exponents | 10 |
| 2020 AMC 12A | Frog jumps randomly on a 4x4 grid, ends when hitting a side. Probability it hits a vertical side. | Combinatorics | Probability | 11 |
| 2020 AMC 12A | x-intercept of line rotated 45° counterclockwise about (20,20). | Geometry | Coordinate Geometry | 12 |
| 2020 AMC 12A | Find b given sqrt[a]{N sqrt[b]{N sqrt[c]{N}}} = sqrt[36]{N^25} for all N>1. | Algebra | Logarithms & Exponents | 13 |
| 2020 AMC 12A | Ratio of area of quadrilateral ACEG to area of regular octagon ABCDEFGH. | Geometry | Triangles & Polygons | 14 |
| 2020 AMC 12A | Greatest distance between a solution of z^3-8=0 and z^3-8z^2-8z+64=0. | Algebra | Complex Numbers | 15 |
| 2020 AMC 12A | Point chosen randomly in a 2020x2020 square. Probability within d units of a lattice point is 1/2. Find d. | Geometry | Coordinate Geometry | 16 |
| 2020 AMC 12A | x-coordinate of leftmost vertex of quadrilateral on y=ln x with consecutive integer x-coords. | Algebra | Logarithms & Exponents | 17 |
| 2020 AMC 12A | Quadrilateral ABCD with right angles at B and C, AC=20, CD=30, AE=5. Find area of ABCD. | Geometry | Triangles & Polygons | 18 |
| 2020 AMC 12A | Find k such that (2^289+1)/(2^17+1) equals sum of k distinct powers of 2. | Algebra | Polynomials | 19 |
| 2020 AMC 12A | How many sequences of three isometries (rotations/reflections) return triangle T to original position? | Combinatorics | Counting | 20 |
| 2020 AMC 12A | Number of positive multiples of 5 where lcm(5!,n)=5*gcd(10!,n). | Number Theory | Factors, Multiples & Divisibility | 21 |
| 2020 AMC 12A | Sum from n=0 to infinity of a_n b_n / 7^n where (2+i)^n = a_n + b_n i. | Algebra | Complex Numbers | 22 |
| 2020 AMC 12A | Jason rolls three dice, may reroll a subset to maximize chance of sum 7. Probability he rerolls exactly two dice. | Combinatorics | Probability | 23 |
| 2020 AMC 12A | Side length s of equilateral triangle with interior point P such that AP=1, BP=√3, CP=2. | Geometry | Triangles & Polygons | 24 |
| 2020 AMC 12A | Find p+q where a=p/q and sum of x satisfying floor(x)*{x}=a x^2 is 420. | Algebra | Functions | 25 |
| 2020 AMC 12B | Sum of square roots of sums of consecutive odd numbers. | Algebra | Sequences & Series | 1 |
| 2020 AMC 12B | Simplify a product of rational expressions using difference of squares. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2020 AMC 12B | Find the ratio w:y given three ratios involving w, x, y, z. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2020 AMC 12B | Find the least possible prime acute angle in a right triangle. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2020 AMC 12B | Find number of games team A played given win ratios and differences. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2020 AMC 12B | Simplify factorial expression and determine what it always is. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2020 AMC 12B | Find max product of slopes of two lines forming a 45° angle. | Geometry | Trigonometry | 7 |
| 2020 AMC 12B | Count integer pairs (x,y) satisfying x^{2020}+y^2=2y. | Algebra | Polynomials | 8 |
| 2020 AMC 12B | Find the volume of a cone formed from a three-quarter circle sector. | Geometry | 3D Geometry & Solids | 9 |
| 2020 AMC 12B | Find length AP in unit square with inscribed circle. | Geometry | Circular Geometry | 10 |
| 2020 AMC 12B | Find the shaded area inside a hexagon but outside six semicircles. | Geometry | Circular Geometry | 11 |
| 2020 AMC 12B | Find sum of squares of chord segments in a circle. | Geometry | Circular Geometry | 12 |
| 2020 AMC 12B | Simplify expression involving sum of logarithms. | Algebra | Logarithms & Exponents | 13 |
| 2020 AMC 12B | Determine which player wins a number-picking game on [0,n]. | Combinatorics | Counting | 14 |
| 2020 AMC 12B | Count ways to pair 10 people around a circle who know each other. | Combinatorics | Counting | 15 |
| 2020 AMC 12B | Probability of 3 red and 3 blue balls after four draws with replacement. | Combinatorics | Probability | 16 |
| 2020 AMC 12B | Count polynomials with root closure under multiplication by cube root of unity. | Algebra | Polynomials | 17 |
| 2020 AMC 12B | Find FI^2 in a square with congruent-area regions. | Geometry | Triangles & Polygons | 18 |
| 2020 AMC 12B | Count sequences of 20 transformations returning a square to original. | Combinatorics | Counting | 19 |
| 2020 AMC 12B | Probability two randomly painted cubes can be rotated to match. | Combinatorics | Probability | 20 |
| 2020 AMC 12B | Count positive integers n satisfying (n+1000)/70 = floor(sqrt(n)). | Algebra | Inequalities | 21 |
| 2020 AMC 12B | Find maximum value of rational expression in t. | Algebra | Inequalities | 22 |
| 2020 AMC 12B | Count n such that unit complex numbers summing to zero are equally spaced. | Algebra | Complex Numbers | 23 |
| 2020 AMC 12B | Count ordered factorizations of 96 into integers greater than 1. | Combinatorics | Counting | 24 |
| 2020 AMC 12B | Maximize probability that sum of squared sines exceeds 1. | Combinatorics | Probability | 25 |
| 2019 AMC 12A | Find percent increase in area when pizza radius increases from 3 to 4. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2019 AMC 12A | If a is 150% of b, what percent of a is 3b? | Algebra | Rates, Mixtures, & Averages | 2 |
| 2019 AMC 12A | Minimum balls to draw to guarantee 15 of one color from six colors. | Combinatorics | Counting | 3 |
| 2019 AMC 12A | Greatest number of consecutive integers whose sum is 45. | Algebra | Sequences & Series | 4 |
| 2019 AMC 12A | Area of triangle formed by two lines and line x+y=10. | Geometry | Coordinate Geometry | 5 |
| 2019 AMC 12A | Number of rigid motions mapping a figure of squares to itself. | Geometry | Triangles & Polygons | 6 |
| 2019 AMC 12A | Compare mean, median, and median of modes of dates in 2019. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2019 AMC 12A | Sum of all possible numbers of intersection points of four lines. | Combinatorics | Counting | 8 |
| 2019 AMC 12A | Find a_2019 for a recursively defined sequence of fractions. | Algebra | Sequences & Series | 9 |
| 2019 AMC 12A | Area inside large circle but outside 13 unit circles arranged hexagonally. | Geometry | Circular Geometry | 10 |
| 2019 AMC 12A | Find base k such that 7/51 equals 0.overline{23}_k. | Algebra | Sequences & Series | 11 |
| 2019 AMC 12A | Find (log_2(x/y))^2 given log_2 x = log_y 16 and xy = 64. | Algebra | Logarithms & Exponents | 12 |
| 2019 AMC 12A | Find the number of ways to paint integers 2 through 9 with three colors such that each number has a different color from its proper divisors. | Combinatorics | Counting | 13 |
| 2019 AMC 12A | Find |c| such that polynomial (x^2-2x+2)(x^2-cx+4)(x^2-4x+8) has exactly 4 distinct roots. | Algebra | Polynomials | 14 |
| 2019 AMC 12A | Find ab given sqrt(log a) + sqrt(log b) + log sqrt(a) + log sqrt(b) = 100 with all terms positive integers. | Algebra | Logarithms & Exponents | 15 |
| 2019 AMC 12A | Probability that each row and column sum is odd in 3x3 grid. | Combinatorics | Probability | 16 |
| 2019 AMC 12A | Find a+b+c given recurrence s_{k+1}=a s_k+b s_{k-1}+c s_{k-2} for sums of powers of roots of x^3-5x^2+8x-13. | Algebra | Polynomials | 17 |
| 2019 AMC 12A | Distance from sphere center to plane of triangle tangent to sphere. | Geometry | 3D Geometry & Solids | 18 |
| 2019 AMC 12A | Find the least possible perimeter of triangle ABC with integer sides and given cosines. | Geometry | Trigonometry | 19 |
| 2019 AMC 12A | Probability that |x-y| > 1/2 with a two-stage random process. | Combinatorics | Probability | 20 |
| 2019 AMC 12A | Evaluate product of sums of powers of z=(1+i)/sqrt(2) from 1^2 to 12^2. | Algebra | Complex Numbers | 21 |
| 2019 AMC 12A | Find side length AB of equilateral triangle with vertex on outer circle and base tangent to inner circle. | Geometry | Triangles & Polygons | 22 |
| 2019 AMC 12A | Find log_7(a_2019) for recursively defined sequence with custom binary operations. | Algebra | Logarithms & Exponents | 23 |
| 2019 AMC 12A | Number of n from 1 to 50 for which (n^2-1)!/(n!)^n is integer. | Number Theory | Factors, Multiples & Divisibility | 24 |
| 2019 AMC 12A | Find smallest n such that triangle formed by feet of altitudes is obtuse. | Geometry | Triangles & Polygons | 25 |
| 2019 AMC 12B | Ratio of container volumes after pouring water between them. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2019 AMC 12B | Find a composite n such that n-2 is also composite. | Number Theory | Factors, Multiples & Divisibility | 2 |
| 2019 AMC 12B | Identify which rigid transformation maps segment AB to A'B' with given coordinates. | Geometry | Coordinate Geometry | 3 |
| 2019 AMC 12B | Solve factorial equation for n and sum its digits. | Algebra | Polynomials | 4 |
| 2019 AMC 12B | Find smallest n such that 20n is divisible by 12, 14, 15. | Number Theory | Factors, Multiples & Divisibility | 5 |
| 2019 AMC 12B | Count points C forming triangle with given perimeter and area. | Geometry | Triangles & Polygons | 6 |
| 2019 AMC 12B | Find sum of x where median equals mean of five numbers. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2019 AMC 12B | Evaluate an alternating sum of a function f(x)=x^2(1-x)^2 at fractions. | Algebra | Functions | 8 |
| 2019 AMC 12B | Find how many integer x values allow a triangle with side lengths log2 x, log4 x, 3. | Algebra | Logarithms & Exponents | 9 |
| 2019 AMC 12B | Count routes from A to L using exactly 13 of 17 roads without repeating any road. | Combinatorics | Counting | 10 |
| 2019 AMC 12B | Count unordered pairs of edges of a cube that determine a plane. | Combinatorics | Counting | 11 |
| 2019 AMC 12B | Find sin(2∠BAD) in a configuration of two right triangles with equal perimeters. | Geometry | Trigonometry | 12 |
| 2019 AMC 12B | Find probability red ball lands in a higher-numbered bin than green ball. | Combinatorics | Probability | 13 |
| 2019 AMC 12B | Count numbers that are product of two distinct divisors of 100,000. | Number Theory | Factors, Multiples & Divisibility | 14 |
| 2019 AMC 12B | Area of region inside circle but outside three semicircles. | Geometry | Circular Geometry | 15 |
| 2019 AMC 12B | Find probability Fiona reaches pad 10 without landing on predators at pads 3 and 6. | Combinatorics | Probability | 16 |
| 2019 AMC 12B | Count nonzero complex z such that 0, z, z^3 form an equilateral triangle. | Algebra | Complex Numbers | 17 |
| 2019 AMC 12B | Find area of triangle PQR in a square pyramid with given dimensions. | Geometry | 3D Geometry & Solids | 18 |
| 2019 AMC 12B | Probability all three players have $1 after 2019 money exchanges. | Combinatorics | Probability | 19 |
| 2019 AMC 12B | Area of circle given two points and tangent intersection on x-axis. | Geometry | Circular Geometry | 20 |
| 2019 AMC 12B | Count quadratic polynomials where the set of roots equals the set of coefficients. | Algebra | Polynomials | 21 |
| 2019 AMC 12B | Find interval containing least n with recursive sequence below threshold. | Algebra | Sequences & Series | 22 |
| 2019 AMC 12B | Count binary strings length 19 with no consecutive 0s or three 1s. | Combinatorics | Counting | 23 |
| 2019 AMC 12B | Find the area of the set of points a + bω + cω² with a,b,c in [0,1]. | Algebra | Complex Numbers | 24 |
| 2019 AMC 12B | Maximize area of quadrilateral ABCD given BC=2, CD=6, and centroids form equilateral triangle. | Geometry | Triangles & Polygons | 25 |
| 2018 AMC 12A | Find how many blue balls to remove so red percentage doubles. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2018 AMC 12A | Maximize value of rocks Carl can carry given weight limit. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2018 AMC 12A | Schedule 3 distinct math classes in 6 periods with no consecutive math classes. | Combinatorics | Counting | 3 |
| 2018 AMC 12A | Find the interval of possible distances given three false statements. | Algebra | Logic & Truth Values | 4 |
| 2018 AMC 12A | Find sum of k for which two quadratics share a root. | Algebra | Polynomials | 5 |
| 2018 AMC 12A | Find m+n given mean and median of set equal n. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2018 AMC 12A | Count integer n such that 4000*(2/5)^n is an integer. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2018 AMC 12A | Find area of trapezoid in similar isosceles triangles with area 1 small triangles. | Geometry | Triangles & Polygons | 8 |
| 2018 AMC 12A | Find largest y interval where sine inequality holds for all x. | Geometry | Trigonometry | 9 |
| 2018 AMC 12A | Count ordered pairs (x,y) satisfying x+3y=3 and ||x|-|y||=1. | Algebra | Systems & Algebraic Manipulation | 10 |
| 2018 AMC 12A | Find length of crease when folding a 3-4-5 triangle so A meets B. | Geometry | Triangles & Polygons | 11 |
| 2018 AMC 12A | Find least possible element in a 6-element subset of 1..12 with no multiples. | Combinatorics | Counting | 12 |
| 2018 AMC 12A | Count nonnegative integers representable as sum of powers of 3 with coefficients -1,0,1. | Combinatorics | Counting | 13 |
| 2018 AMC 12A | Solve logarithmic equation for x and find p+q. | Algebra | Logarithms & Exponents | 14 |
| 2018 AMC 12A | Count symmetric 7x7 black/white grids with at least one of each color. | Combinatorics | Counting | 15 |
| 2018 AMC 12A | Find a such that circle x^2+y^2=a^2 and parabola y=x^2-a intersect at 3 points. | Geometry | Coordinate Geometry | 16 |
| 2018 AMC 12A | Fraction of right triangle planted after removing a square at the right angle corner. | Geometry | Triangles & Polygons | 17 |
| 2018 AMC 12A | Area of quadrilateral formed by midpoints and angle bisector in triangle with area 120. | Geometry | Triangles & Polygons | 18 |
| 2018 AMC 12A | Find sum of numerator and denominator of infinite sum of reciprocals of numbers with only prime factors 2,3,5. | Algebra | Sequences & Series | 19 |
| 2018 AMC 12A | Find CI in isosceles right triangle with cyclic quadrilateral AIME of area 2. | Geometry | Triangles & Polygons | 20 |
| 2018 AMC 12A | Determine which polynomial has the greatest real root. | Algebra | Polynomials | 21 |
| 2018 AMC 12A | Find area of parallelogram formed by solutions to two complex equations. | Algebra | Complex Numbers | 22 |
| 2018 AMC 12A | Find acute angle between MN and PA in triangle with given points. | Geometry | Triangles & Polygons | 23 |
| 2018 AMC 12A | Find number Carol should choose to maximize chance of winning. | Combinatorics | Probability | 24 |
| 2018 AMC 12A | Max a+b+c such that C_n - B_n = A_n^2 for at least two n, with repdigit numbers. | Number Theory | Modular Arithmetic | 25 |
| 2018 AMC 12B | Find number of 2x2 pieces in a 20x18 pan of cornbread. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2018 AMC 12B | Find average speed in last 30 minutes given total distance and two speeds. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2018 AMC 12B | Find the distance between the x-intercepts of two lines with given slopes. | Geometry | Coordinate Geometry | 3 |
| 2018 AMC 12B | Find the area of a circle given a chord length and its distance from the center. | Geometry | Circular Geometry | 4 |
| 2018 AMC 12B | Count subsets of {2,...,9} that contain at least one prime number. | Combinatorics | Counting | 5 |
| 2018 AMC 12B | Express number of soda cans for D dollars given S cans cost Q quarters. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2018 AMC 12B | Evaluate the product of logarithms from log_3 7 to log_23 27. | Algebra | Logarithms & Exponents | 7 |
| 2018 AMC 12B | Find area traced by centroid of right triangle with fixed hypotenuse. | Geometry | Circular Geometry | 8 |
| 2018 AMC 12B | Evaluate the double sum of i+j from i=1 to 100 and j=1 to 100. | Algebra | Sequences & Series | 9 |
| 2018 AMC 12B | Least number of distinct values in a list with unique mode occurring 10 times. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2018 AMC 12B | Find area of square wrapping paper folded over a box with square base. | Geometry | Triangles & Polygons | 11 |
| 2018 AMC 12B | Find m+n where (m,n) is the open interval of possible AC lengths. | Geometry | Triangles & Polygons | 12 |
| 2018 AMC 12B | Find the area of the quadrilateral formed by centroids of four triangles. | Geometry | Triangles & Polygons | 13 |
| 2018 AMC 12B | Find sum of digits of Joey's age when it is next a multiple of Zoe's age. | Number Theory | Factors, Multiples & Divisibility | 14 |
| 2018 AMC 12B | Count odd 3-digit multiples of 3 that do not contain the digit 3. | Combinatorics | Counting | 15 |
| 2018 AMC 12B | Find the least possible area of a triangle formed by three vertices of a regular octagon. | Algebra | Complex Numbers | 16 |
| 2018 AMC 12B | Find q-p for the fraction p/q between 5/9 and 4/7 with smallest q. | Number Theory | Factors, Multiples & Divisibility | 17 |
| 2018 AMC 12B | Find f(2018) for a recursively defined function with f(1)=f(2)=1. | Algebra | Sequences & Series | 18 |
| 2018 AMC 12B | Find smallest possible next divisor after 323 in an even 4-digit number's divisor list. | Number Theory | Factors, Multiples & Divisibility | 19 |
| 2018 AMC 12B | Find area of intersection of triangles ACE and XYZ in a regular hexagon. | Geometry | Triangles & Polygons | 20 |
| 2018 AMC 12B | Find the area of triangle MOI formed by circumcenter, incenter, and center of a tangent circle. | Geometry | Triangles & Polygons | 21 |
| 2018 AMC 12B | Count degree ≤3 polynomials with coefficients 0-9 satisfying P(-1) = -9. | Combinatorics | Counting | 22 |
| 2018 AMC 12B | Find the degree measure of angle ACB between two points on Earth. | Geometry | 3D Geometry & Solids | 23 |
| 2018 AMC 12B | Number of real solutions to x^2 + 10000 floor(x) = 10000 x. | Algebra | Systems & Algebraic Manipulation | 24 |
| 2018 AMC 12B | Find a+b where the area of an equilateral triangle tangent to three circles is sqrt(a)+sqrt(b). | Geometry | Circular Geometry | 25 |
| 2017 AMC 12A | Maximize number of popsicles bought with $8 given three package options. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2017 AMC 12A | Find sum of reciprocals given sum equals 4 times product. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2017 AMC 12A | Identify which statement follows logically from a conditional promise. | Algebra | Logic & Truth Values | 3 |
| 2017 AMC 12A | Find percent shorter diagonal path is compared to two sides. | Geometry | Triangles & Polygons | 4 |
| 2017 AMC 12A | Count handshakes at a gathering with two groups of people. | Combinatorics | Counting | 5 |
| 2017 AMC 12A | Count possible fourth rod lengths to form a quadrilateral. | Geometry | Triangles & Polygons | 6 |
| 2017 AMC 12A | Evaluate a recursively defined function at a large odd input. | Algebra | Functions | 7 |
| 2017 AMC 12A | Find length of segment given volume of points within 3 units. | Geometry | 3D Geometry & Solids | 8 |
| 2017 AMC 12A | Describe set of points where two of three quantities are equal. | Geometry | Coordinate Geometry | 9 |
| 2017 AMC 12A | Find probability Laurent's number exceeds Chloe's given intervals. | Combinatorics | Probability | 10 |
| 2017 AMC 12A | Find missing interior angle of convex polygon given sum 2017. | Geometry | Triangles & Polygons | 11 |
| 2017 AMC 12A | Find least time when at least 5 horses are at starting point. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2017 AMC 12A | Find distance given travel time with speed reduction in storm. | Algebra | Rates, Mixtures, & Averages | 13 |
| 2017 AMC 12A | Count seating arrangements with adjacency restrictions for five people. | Combinatorics | Counting | 14 |
| 2017 AMC 12A | Find interval containing smallest positive x where trig sum is zero. | Geometry | Trigonometry | 15 |
| 2017 AMC 12A | Find radius of circle tangent to three semicircles in a larger semicircle. | Geometry | Circular Geometry | 16 |
| 2017 AMC 12A | Count 24th roots of unity whose 6th power is real. | Algebra | Complex Numbers | 17 |
| 2017 AMC 12A | Find possible digit sum of n+1 given digit sum of n is 1274. | Number Theory | Modular Arithmetic | 18 |
| 2017 AMC 12A | Find ratio of side lengths of squares inscribed in 3-4-5 triangles. | Geometry | Triangles & Polygons | 19 |
| 2017 AMC 12A | Count ordered pairs (b,a) satisfying a logarithmic equation. | Algebra | Logarithms & Exponents | 20 |
| 2017 AMC 12A | Find size of set S built by adding integer roots of polynomials with coefficients in S. | Algebra | Polynomials | 21 |
| 2017 AMC 12A | Find probability particle hits corner before side of square on lattice. | Combinatorics | Probability | 22 |
| 2017 AMC 12A | Find f(1) given cubic g(x) shares all roots with quartic f(x). | Algebra | Polynomials | 23 |
| 2017 AMC 12A | Find product XF * XG in cyclic quadrilateral with parallel lines. | Geometry | Circular Geometry | 24 |
| 2017 AMC 12A | Find probability product of 12 random complex numbers from set equals -1. | Algebra | Complex Numbers | 25 |
| 2017 AMC 12B | After how many months will LaShawn's collection have twice as many as Kymbrea's? | Algebra | Rates, Mixtures, & Averages | 1 |
| 2017 AMC 12B | Given ranges for x, y, z, determine which expression is always positive. | Algebra | Inequalities | 2 |
| 2017 AMC 12B | Given an equation relating x and y, find the value of a rational expression. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2017 AMC 12B | Given biking and walking speeds and total time, find the distance walked. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2017 AMC 12B | How many outliers does the data set have using the 1.5 IQR rule? | Algebra | Rates, Mixtures, & Averages | 5 |
| 2017 AMC 12B | Find the x-coordinate of the second x-intercept of a circle with diameter endpoints (0,0) and (8,6). | Geometry | Coordinate Geometry | 6 |
| 2017 AMC 12B | Find the least period of the function cos(sin(x)). | Geometry | Trigonometry | 7 |
| 2017 AMC 12B | Find the square of the ratio of short side to long side of a rectangle satisfying a given proportion. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2017 AMC 12B | Find c such that the line through the intersection points of two circles is x+y=c. | Geometry | Coordinate Geometry | 9 |
| 2017 AMC 12B | What fraction of students who say they dislike dancing actually like it? | Combinatorics | Probability | 10 |
| 2017 AMC 12B | Count positive integers whose digits are strictly increasing or decreasing. | Combinatorics | Counting | 11 |
| 2017 AMC 12B | Find the sum of the roots of z^12=64 that have positive real part. | Algebra | Complex Numbers | 12 |
| 2017 AMC 12B | How many distinct paintings of 6 disks with 3 blue, 2 red, 1 green are possible up to rotation and reflection? | Combinatorics | Counting | 13 |
| 2017 AMC 12B | Find the total volume of ice cream in a frustum topped with a cone. | Geometry | 3D Geometry & Solids | 14 |
| 2017 AMC 12B | Find the ratio of area of triangle A'B'C' to area of equilateral triangle ABC after extending sides by 3 times. | Geometry | Triangles & Polygons | 15 |
| 2017 AMC 12B | What is the probability that a randomly chosen divisor of 21! is odd? | Number Theory | Factors, Multiples & Divisibility | 16 |
| 2017 AMC 12B | Compare the probability of winning Game A (3 tosses all same) vs Game B (first two same, last two same). | Combinatorics | Probability | 17 |
| 2017 AMC 12B | Find the area of triangle ABC where AB is a diameter of a circle and E is a point outside. | Geometry | Circular Geometry | 18 |
| 2017 AMC 12B | Find the remainder when the concatenated numbers 1 to 44 are divided by 45. | Number Theory | Modular Arithmetic | 19 |
| 2017 AMC 12B | Find the probability that floor(log2 x) = floor(log2 y) for random x,y in (0,1). | Combinatorics | Probability | 20 |
| 2017 AMC 12B | Find Isabella's sixth test score given seven distinct scores 91-100 and integer averages after each test. | Number Theory | Modular Arithmetic | 21 |
| 2017 AMC 12B | Find probability that after 4 rounds of coin exchange each player ends with 4 coins. | Combinatorics | Probability | 22 |
| 2017 AMC 12B | Find f(0) for a cubic f through (2,4),(3,9),(4,16) where lines AB,AC,BC intersect f again at D,E,F with x-sum 24. | Algebra | Polynomials | 23 |
| 2017 AMC 12B | Find AB/BC in quadrilateral ABCD with right angles at B,C and similar triangles, given area ratio 17. | Geometry | Triangles & Polygons | 24 |
| 2017 AMC 12B | Find how many n between 9 and 2017 satisfy a condition about average number of teams in subsets. | Combinatorics | Counting | 25 |
| 2016 AMC 12A | Evaluate (11! - 10!) / 9!. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2016 AMC 12A | Solve 10^x * 100^(2x) = 1000^5 for x. | Algebra | Logarithms & Exponents | 2 |
| 2016 AMC 12A | Evaluate rem(3/8, -2/5) using floor function definition. | Algebra | Functions | 3 |
| 2016 AMC 12A | Find x such that mean, median, mode of 7 numbers equal x. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2016 AMC 12A | Identify what would constitute a counterexample to Goldbach's conjecture. | Algebra | Logic & Truth Values | 5 |
| 2016 AMC 12A | Find sum of digits of N for triangular number 2016. | Algebra | Sequences & Series | 6 |
| 2016 AMC 12A | Describe the graph of the equation x^2(x+y+1)=y^2(x+y+1). | Geometry | Coordinate Geometry | 7 |
| 2016 AMC 12A | Find area of shaded region in rectangle with cut corners. | Geometry | Triangles & Polygons | 8 |
| 2016 AMC 12A | Find the sum of a and b given the side length of small squares in a unit square. | Geometry | Triangles & Polygons | 9 |
| 2016 AMC 12A | Find Ada's original seat after friends move in a row. | Combinatorics | Counting | 10 |
| 2016 AMC 12A | Find the number of students with exactly two talents given totals for each talent. | Combinatorics | Counting | 11 |
| 2016 AMC 12A | Find the ratio AF:FD where F is the intersection of angle bisectors in triangle ABC. | Geometry | Triangles & Polygons | 12 |
| 2016 AMC 12A | Find least N multiple of 5 with probability condition on green balls. | Combinatorics | Probability | 13 |
| 2016 AMC 12A | Count cube vertex labelings with equal face sums, up to rotation. | Combinatorics | Counting | 14 |
| 2016 AMC 12A | Find the area of triangle formed by centers of three circles tangent to a line. | Geometry | Circular Geometry | 15 |
| 2016 AMC 12A | Find the number of points with positive x-coordinate lying on two or more logarithmic graphs. | Algebra | Logarithms & Exponents | 16 |
| 2016 AMC 12A | Find the ratio of the area of square EFGH to square ABCD formed by centers of equilateral triangles. | Geometry | Triangles & Polygons | 17 |
| 2016 AMC 12A | Find divisor count of 81n^4 given 110n^3 has 110 divisors. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2016 AMC 12A | Find the probability that a random walk of 8 coin flips reaches position 4 at some time. | Combinatorics | Probability | 19 |
| 2016 AMC 12A | Solve 2016 ◇ (6 ◇ x) = 100 for binary operation ◇. | Algebra | Functions | 20 |
| 2016 AMC 12A | Find fourth side of cyclic quadrilateral with three sides 200. | Geometry | Circular Geometry | 21 |
| 2016 AMC 12A | Count triples (x,y,z) with given LCMs 72, 600, 900. | Number Theory | Factors, Multiples & Divisibility | 22 |
| 2016 AMC 12A | Find the probability that three random numbers in [0,1] form a triangle. | Combinatorics | Probability | 23 |
| 2016 AMC 12A | Find the value of b such that x^3-ax^2+bx-a has all real roots for minimal a. | Algebra | Polynomials | 24 |
| 2016 AMC 12A | Find the sum of digits of f(2)+f(4)+...+f(2016) from a number-writing game. | Number Theory | Modular Arithmetic | 25 |
| 2016 AMC 12B | Evaluate an algebraic expression with negative exponents for a given value. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2016 AMC 12B | Compute the harmonic mean of two numbers and find the closest integer. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2016 AMC 12B | Evaluate an expression involving absolute values for a given negative number. | Algebra | Functions | 3 |
| 2016 AMC 12B | Find the sum of two acute angles given ratio and complement relationship. | Algebra | Systems & Algebraic Manipulation | 4 |
| 2016 AMC 12B | Determine the day of the week 919 days after a Thursday. | Number Theory | Modular Arithmetic | 5 |
| 2016 AMC 12B | Find the length of the base of a triangle on a parabola with given area. | Geometry | Coordinate Geometry | 6 |
| 2016 AMC 12B | Find the last remaining number after repeatedly crossing out numbers in a pattern. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2016 AMC 12B | Find the weight of a larger equilateral triangle given the weight of a smaller one. | Geometry | Triangles & Polygons | 8 |
| 2016 AMC 12B | Find the area of a rectangular garden given fence post spacing and counts. | Algebra | Systems & Algebraic Manipulation | 9 |
| 2016 AMC 12B | Find the sum of coordinates given quadrilateral area and integer constraints. | Geometry | Coordinate Geometry | 10 |
| 2016 AMC 12B | Count axis-aligned squares with integer vertices inside a triangular region. | Geometry | Coordinate Geometry | 11 |
| 2016 AMC 12B | Find the center number in a 3x3 grid with consecutive numbers sharing edges. | Combinatorics | Counting | 12 |
| 2016 AMC 12B | Find the altitude of an airplane given angles of elevation from two observers. | Geometry | Trigonometry | 13 |
| 2016 AMC 12B | Minimize the sum of an infinite geometric series with second term 1. | Algebra | Sequences & Series | 14 |
| 2016 AMC 12B | Maximize the sum of products of three faces meeting at each cube vertex. | Combinatorics | Counting | 15 |
| 2016 AMC 12B | Count ways to write 345 as sum of increasing consecutive positive integers. | Number Theory | Factors, Multiples & Divisibility | 16 |
| 2016 AMC 12B | Find the distance between intersection points of angle bisectors with altitude. | Geometry | Triangles & Polygons | 17 |
| 2016 AMC 12B | Find the area enclosed by the graph of x^2+y^2=|x|+|y|. | Geometry | Coordinate Geometry | 18 |
| 2016 AMC 12B | Find probability all three players flip the same number of times until first head. | Combinatorics | Probability | 19 |
| 2016 AMC 12B | Count sets of three teams in a round-robin tournament with cyclic wins. | Combinatorics | Counting | 20 |
| 2016 AMC 12B | Find the infinite sum of areas of triangles formed by recursive construction. | Geometry | Triangles & Polygons | 21 |
| 2016 AMC 12B | Find the interval containing n given repeating decimal periods of 1/n and 1/(n+6). | Number Theory | Modular Arithmetic | 22 |
| 2016 AMC 12B | Find the volume of the intersection of two octahedra defined by absolute value inequalities. | Geometry | 3D Geometry & Solids | 23 |
| 2016 AMC 12B | Find smallest n such that exactly 77000 ordered quadruplets have gcd 77 and lcm n. | Number Theory | Factors, Multiples & Divisibility | 24 |
| 2016 AMC 12B | Find smallest k so product of recursively defined sequence terms is an integer. | Algebra | Sequences & Series | 25 |
| 2015 AMC 12A | Evaluate an arithmetic expression involving exponents and a reciprocal. | Algebra | Logarithms & Exponents | 1 |
| 2015 AMC 12A | Find which perimeter is not possible for a triangle with sides 20 and 15. | Geometry | Triangles & Polygons | 2 |
| 2015 AMC 12A | Find Payton's test score given the class average before and after. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2015 AMC 12A | Find the ratio of two positive numbers given sum is 5 times difference. | Algebra | Systems & Algebraic Manipulation | 4 |
| 2015 AMC 12A | Determine which rounding strategy overestimates a given expression. | Algebra | Inequalities | 5 |
| 2015 AMC 12A | Find when Pete will be twice as old as Claire given past age ratios. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2015 AMC 12A | Compare heights of two cylinders with equal volume and radius difference. | Algebra | Systems & Algebraic Manipulation | 7 |
| 2015 AMC 12A | Find constant k such that area of rectangle equals k times diagonal squared. | Geometry | Triangles & Polygons | 8 |
| 2015 AMC 12A | Find probability Cheryl gets two marbles of same color from six marbles. | Combinatorics | Probability | 9 |
| 2015 AMC 12A | Find integer x given x+y+xy=80 with x>y>0. | Number Theory | Factors, Multiples & Divisibility | 10 |
| 2015 AMC 12A | Find number of possible values for number of common tangents to two circles. | Geometry | Circular Geometry | 11 |
| 2015 AMC 12A | Find a+b given parabolas intersect axes in kite of area 12. | Geometry | Coordinate Geometry | 12 |
| 2015 AMC 12A | Identify false statement about scores in a round-robin tournament with draws. | Combinatorics | Counting | 13 |
| 2015 AMC 12A | Solve equation involving sum of reciprocals of logs for a. | Algebra | Logarithms & Exponents | 14 |
| 2015 AMC 12A | Find minimum decimal digits needed for fraction with denominator powers of 2 and 5. | Number Theory | Factors, Multiples & Divisibility | 15 |
| 2015 AMC 12A | Find volume of tetrahedron given all six edge lengths. | Geometry | 3D Geometry & Solids | 16 |
| 2015 AMC 12A | Probability no two adjacent people stand when 8 flip coins in a circle. | Combinatorics | Probability | 17 |
| 2015 AMC 12A | Find sum of possible a such that quadratic has integer roots. | Algebra | Polynomials | 18 |
| 2015 AMC 12A | Count perimeters less than 2015 for quadrilateral with right angles and equal sides. | Geometry | Triangles & Polygons | 19 |
| 2015 AMC 12A | Find b closest to integer for isosceles triangle with same area and perimeter as given triangle. | Geometry | Triangles & Polygons | 20 |
| 2015 AMC 12A | Find a+b for interval of radii of circle through foci and four points on ellipse. | Geometry | Conic Sections | 21 |
| 2015 AMC 12A | Find remainder when number of sequences with no more than three consecutive same letters is divided by 12. | Combinatorics | Counting | 22 |
| 2015 AMC 12A | Find probability distance between two random points on square sides is at least 1/2. | Combinatorics | Probability | 23 |
| 2015 AMC 12A | Find probability that (cos(aπ)+i sin(bπ))^4 is real for rational a,b in [0,2). | Algebra | Complex Numbers | 24 |
| 2015 AMC 12A | Find sum of reciprocals of square roots of radii in layered circle construction. | Geometry | Circular Geometry | 25 |
| 2015 AMC 12B | Evaluate the expression 2 minus negative 2 to the negative second power. | Algebra | Logarithms & Exponents | 1 |
| 2015 AMC 12B | Find when Marie finishes the third task given start and end times. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2015 AMC 12B | Find the other integer given two numbers written multiple times summing to 100. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2015 AMC 12B | Determine who finished 8th in a race given relative finishing positions. | Algebra | Logic & Truth Values | 4 |
| 2015 AMC 12B | Find minimum N so Sharks win at least 95% of all games played. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2015 AMC 12B | Find fraction of odd products in a 0 to 12 multiplication table. | Combinatorics | Counting | 6 |
| 2015 AMC 12B | Find L+R for a regular 15-gon's lines of symmetry and rotational symmetry angle. | Geometry | Triangles & Polygons | 7 |
| 2015 AMC 12B | Evaluate the expression (625^{log_5 2015})^{1/4}. | Algebra | Logarithms & Exponents | 8 |
| 2015 AMC 12B | Find probability Larry wins a turn-based game with 1/2 success chance per turn. | Combinatorics | Probability | 9 |
| 2015 AMC 12B | Count noncongruent integer-sided triangles with perimeter less than 15, not isosceles or right. | Geometry | Triangles & Polygons | 10 |
| 2015 AMC 12B | Find sum of altitudes of triangle formed by line 12x+5y=60 and axes. | Geometry | Coordinate Geometry | 11 |
| 2015 AMC 12B | Maximize sum of roots of (x-a)(x-b)+(x-b)(x-c)=0 with distinct one-digit a,b,c. | Algebra | Polynomials | 12 |
| 2015 AMC 12B | Find AC in cyclic quadrilateral ABCD with given angles and side lengths. | Geometry | Circular Geometry | 13 |
| 2015 AMC 12B | Find difference between area inside circle but outside triangle and vice versa. | Geometry | Circular Geometry | 14 |
| 2015 AMC 12B | Find probability Rachelle gets GPA at least 3.5 given grade probabilities. | Combinatorics | Probability | 15 |
| 2015 AMC 12B | Find volume of pyramid formed by folding isosceles triangles onto a regular hexagon. | Geometry | 3D Geometry & Solids | 16 |
| 2015 AMC 12B | Find n such that probability of exactly 2 heads equals probability of exactly 3 heads. | Combinatorics | Probability | 17 |
| 2015 AMC 12B | Find the range of r(n) where r(n) sums prime factors of composite n. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2015 AMC 12B | Find perimeter of right triangle ABC with squares constructed externally on sides. | Geometry | Triangles & Polygons | 19 |
| 2015 AMC 12B | Evaluate f(2015,2) for a recursively defined function modulo 5. | Algebra | Functions | 20 |
| 2015 AMC 12B | Find sum of digits of sum of all possible staircase steps given jump counts. | Algebra | Functions | 21 |
| 2015 AMC 12B | Count ways 6 people at a circular table move to non-same, non-adjacent seats. | Combinatorics | Counting | 22 |
| 2015 AMC 12B | Count ordered triples (a,b,c) with a≤b≤c where volume equals surface area of box. | Algebra | Systems & Algebraic Manipulation | 23 |
| 2015 AMC 12B | Find sum of distances from midpoints of PQ to centers of four intersecting circles. | Geometry | Circular Geometry | 24 |
| 2015 AMC 12B | Find distance bee travels after 2015 moves turning 30° each time. | Algebra | Complex Numbers | 25 |
| 2014 AMC 12A | Evaluate an expression involving fractions and a reciprocal. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2014 AMC 12A | Find the cost of 8 adult and 6 child tickets given 5 adult and 4 child cost $24.50. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2014 AMC 12A | Count orderings of four colored houses with given constraints. | Combinatorics | Counting | 3 |
| 2014 AMC 12A | Find gallons of milk given cows and days using rates. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2014 AMC 12A | Find the difference between mean and median of given score percentages. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2014 AMC 12A | Find the sum of a two-digit number and its reverse given a relationship. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2014 AMC 12A | Find the fourth term of a geometric progression with given terms. | Algebra | Sequences & Series | 7 |
| 2014 AMC 12A | Determine which listed price makes coupon 1 give the largest discount. | Algebra | Inequalities | 8 |
| 2014 AMC 12A | Find the average of consecutive integers starting from b in terms of a. | Algebra | Sequences & Series | 9 |
| 2014 AMC 12A | Find the length of the congruent sides of isosceles triangles on an equilateral triangle. | Geometry | Triangles & Polygons | 10 |
| 2014 AMC 12A | Find total distance given speed changes and arrival time difference. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2014 AMC 12A | Find the ratio of areas of two intersecting circles given minor arc measures. | Geometry | Circular Geometry | 12 |
| 2014 AMC 12A | Find the number of ways to assign 5 friends to 5 rooms with at most 2 per room. | Combinatorics | Counting | 13 |
| 2014 AMC 12A | Find the smallest possible value of c given arithmetic and geometric progression conditions. | Algebra | Sequences & Series | 14 |
| 2014 AMC 12A | Find the sum of the digits of the sum of all five-digit palindromes. | Number Theory | Factors, Multiples & Divisibility | 15 |
| 2014 AMC 12A | Find k such that the digit sum of 8 times a k-digit number of 8s is 1000. | Number Theory | Modular Arithmetic | 16 |
| 2014 AMC 12A | Find the height of a box containing a large sphere and eight smaller spheres. | Geometry | 3D Geometry & Solids | 17 |
| 2014 AMC 12A | Find the sum of numerator and denominator of the length of the domain of a nested log function. | Algebra | Logarithms & Exponents | 18 |
| 2014 AMC 12A | Find the number of rational k such that a quadratic has an integer root. | Algebra | Polynomials | 19 |
| 2014 AMC 12A | Find the minimum possible value of BE+DE+CD in a triangle with given sides and angle. | Geometry | Triangles & Polygons | 20 |
| 2014 AMC 12A | Find the sum of lengths of intervals where a floor function inequality holds. | Algebra | Functions | 21 |
| 2014 AMC 12A | Count intervals between powers of 5 that contain three powers of 2. | Algebra | Logarithms & Exponents | 22 |
| 2014 AMC 12A | Find the sum of digits in the repeating decimal expansion of 1/99^2. | Number Theory | Modular Arithmetic | 23 |
| 2014 AMC 12A | Find the number of x such that f_100(x)=0 for a recursively defined function. | Algebra | Functions | 24 |
| 2014 AMC 12A | Find the number of integer points on a parabola with a given focus and points. | Geometry | Conic Sections | 25 |
| 2014 AMC 12B | Leah has 13 coins, pennies and nickels; find total value in cents. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2014 AMC 12B | Orvin buys balloons with a buy-one-get-one-third-off sale; find max balloons. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2014 AMC 12B | Randy drives a trip with gravel, pavement, and dirt road segments; find total length. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2014 AMC 12B | Susie and Calvin buy muffins and bananas; find muffin-to-banana price ratio. | Algebra | Systems & Algebraic Manipulation | 4 |
| 2014 AMC 12B | Square window with 8 panes of given ratio and borders; find side length. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2014 AMC 12B | Ed and Ann drink lemonade; find total ounces they drank together. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2014 AMC 12B | Find number of positive integers n such that n/(30-n) is a positive integer. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2014 AMC 12B | Cryptarithm with distinct digits A,B,C,D; find number of possible values for D. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2014 AMC 12B | Convex quadrilateral ABCD with given sides and right angle; find area. | Geometry | Triangles & Polygons | 9 |
| 2014 AMC 12B | Odometer shows abc then cba after trip at 55 mph; find a^2+b^2+c^2. | Number Theory | Factors, Multiples & Divisibility | 10 |
| 2014 AMC 12B | List of 11 positive integers with mean 10, median 9, unique mode 8; find max possible value. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2014 AMC 12B | Set of triangles with integer sides <5, no two congruent or similar; find max size. | Geometry | Triangles & Polygons | 12 |
| 2014 AMC 12B | Find least b>1 such that no triangle exists with sides 1,a,b nor with 1/b,1/a,1. | Geometry | Triangles & Polygons | 13 |
| 2014 AMC 12B | Rectangular box with surface area 94 and edge sum 48; find sum of interior diagonals. | Geometry | 3D Geometry & Solids | 14 |
| 2014 AMC 12B | p = sum k ln k from 1 to 6; find largest power of 2 dividing e^p. | Algebra | Logarithms & Exponents | 15 |
| 2014 AMC 12B | Cubic polynomial P with P(0)=k, P(1)=2k, P(-1)=3k; find P(2)+P(-2). | Algebra | Polynomials | 16 |
| 2014 AMC 12B | Parabola y=x^2 and point Q(20,14); find r+s where line slope m avoids parabola. | Geometry | Coordinate Geometry | 17 |
| 2014 AMC 12B | Numbers 1-5 arranged in a circle; count bad arrangements missing consecutive sums 1-15. | Combinatorics | Counting | 18 |
| 2014 AMC 12B | Sphere inscribed in truncated cone; volume ratio 2:1; find ratio of base radii. | Geometry | 3D Geometry & Solids | 19 |
| 2014 AMC 12B | Find number of positive integers x satisfying log10(x-40)+log10(60-x) < 2. | Algebra | Logarithms & Exponents | 20 |
| 2014 AMC 12B | Square of side 1 with two congruent rectangles; find length BE. | Geometry | Triangles & Polygons | 21 |
| 2014 AMC 12B | Frog on lily pads 0-10 jumps with probability N/10 left; find escape probability from pad 1. | Combinatorics | Probability | 22 |
| 2014 AMC 12B | Sum of binomial coefficients from 0 to 62 of 2014 choose k; find remainder mod 2017. | Number Theory | Modular Arithmetic | 23 |
| 2014 AMC 12B | Pentagon ABCDE inscribed in circle with given side lengths; find sum of all diagonals. | Geometry | Circular Geometry | 24 |
| 2014 AMC 12B | Solve 2cos2x(cos2x - cos(2014π^2/x)) = cos4x - 1; find sum of positive solutions. | Geometry | Trigonometry | 25 |
| 2013 AMC 12A | Find BE in a square with a triangle of area 40. | Geometry | Triangles & Polygons | 1 |
| 2013 AMC 12A | Find total opponent runs given game scores and win/loss conditions. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2013 AMC 12A | Find percent of flowers that are carnations given fractions. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2013 AMC 12A | Evaluate a fraction with powers of 2. | Algebra | Logarithms & Exponents | 4 |
| 2013 AMC 12A | Find t-d given amounts paid and equal sharing. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2013 AMC 12A | Find total points scored given shot percentages and attempts. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2013 AMC 12A | Find S4 in a Fibonacci-like sequence given S7 and S9. | Algebra | Sequences & Series | 7 |
| 2013 AMC 12A | Find xy given x + 2/x = y + 2/y with distinct x,y. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2013 AMC 12A | Find perimeter of parallelogram ADEF in an isosceles triangle. | Geometry | Triangles & Polygons | 9 |
| 2013 AMC 12A | Sum of n such that 1/n has repeating decimal 0.abab... with distinct digits. | Number Theory | Factors, Multiples & Divisibility | 10 |
| 2013 AMC 12A | Find DE+FG in equilateral triangle with equal-perimeter regions. | Geometry | Triangles & Polygons | 11 |
| 2013 AMC 12A | Sum possible x values for triangle with sides 4,5,x and angles in AP. | Geometry | Trigonometry | 12 |
| 2013 AMC 12A | Find intersection point of line through A dividing quadrilateral into equal areas. | Geometry | Coordinate Geometry | 13 |
| 2013 AMC 12A | Find x in arithmetic progression of logs with given first and last terms. | Algebra | Logarithms & Exponents | 14 |
| 2013 AMC 12A | Number of ways to distribute 5 rabbits to 4 stores with parent-child restriction. | Combinatorics | Counting | 15 |
| 2013 AMC 12A | Greatest possible integer mean weight of piles B and C given means. | Algebra | Rates, Mixtures, & Averages | 16 |
| 2013 AMC 12A | Number of coins the 12th pirate receives given fractional sharing rule. | Number Theory | Factors, Multiples & Divisibility | 17 |
| 2013 AMC 12A | Radius of eighth sphere tangent to six spheres and larger sphere. | Geometry | 3D Geometry & Solids | 18 |
| 2013 AMC 12A | Find BC given AB=86, AC=97, circle center A radius AB intersects BC. | Geometry | Circular Geometry | 19 |
| 2013 AMC 12A | Number of ordered triples (x,y,z) from {1..19} satisfying cyclic inequality. | Combinatorics | Counting | 20 |
| 2013 AMC 12A | Determine interval containing iterated log expression A. | Algebra | Logarithms & Exponents | 21 |
| 2013 AMC 12A | Probability that a random 6-digit palindrome divided by 11 is also a palindrome. | Combinatorics | Probability | 22 |
| 2013 AMC 12A | Area of region swept by square rotated 90° about point P on diagonal. | Geometry | Circular Geometry | 23 |
| 2013 AMC 12A | Probability three random chords of a regular 12-gon form a triangle. | Combinatorics | Probability | 24 |
| 2013 AMC 12A | Number of complex z with Im(z)>0 such that f(z)=z^2+iz+1 has integer real and imag parts ≤10. | Algebra | Complex Numbers | 25 |
| 2013 AMC 12B | Find the low temperature given high is 16 degrees higher and average is 3. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2013 AMC 12B | Find pounds of potatoes expected from a rectangular garden given step lengths and yield per square foot. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2013 AMC 12B | Find the position of 53 when counting backwards from 201 to 3. | Algebra | Sequences & Series | 3 |
| 2013 AMC 12B | Find combined miles per gallon when two cars drive the same distance with different fuel efficiencies. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2013 AMC 12B | Find the average age of 33 fifth-graders and 55 parents given their separate averages. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2013 AMC 12B | Find x+y given x^2+y^2=10x-6y-34. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2013 AMC 12B | Find the 53rd number said when Jo and Blair take turns counting increasing sequences. | Algebra | Sequences & Series | 7 |
| 2013 AMC 12B | Find the slope of line l3 given triangle area and intersection points of three lines. | Geometry | Coordinate Geometry | 8 |
| 2013 AMC 12B | Find sum of exponents of prime factors of the square root of the largest perfect square dividing 12!. | Number Theory | Factors, Multiples & Divisibility | 9 |
| 2013 AMC 12B | Find number of silver tokens after exchanging red and blue tokens at two booths until no more exchanges possible. | Algebra | Systems & Algebraic Manipulation | 10 |
| 2013 AMC 12B | Determine directions of two bees when they are exactly 10 feet apart after repeating patterns of movement. | Geometry | 3D Geometry & Solids | 11 |
| 2013 AMC 12B | Count routes from A to B using each road exactly once in a given graph. | Combinatorics | Counting | 12 |
| 2013 AMC 12B | Find largest possible sum of two largest angles of quadrilateral with angles in arithmetic progression and similar triangles. | Geometry | Triangles & Polygons | 13 |
| 2013 AMC 12B | Find smallest possible N given two non-decreasing sequences with different first terms and seventh term N. | Algebra | Sequences & Series | 14 |
| 2013 AMC 12B | Find |a1-b1| for representation of 2013 as product of factorials with minimal a1+b1. | Number Theory | Factors, Multiples & Divisibility | 15 |
| 2013 AMC 12B | Find difference between max and min perimeter of star formed by extending sides of equiangular pentagon of perimeter 1. | Geometry | Triangles & Polygons | 16 |
| 2013 AMC 12B | Find difference between max and min possible values of c given a+b+c=2 and a^2+b^2+c^2=12. | Algebra | Inequalities | 17 |
| 2013 AMC 12B | Determine winner for coin removal game with 2013 and 2014 coins given optimal play. | Combinatorics | Counting | 18 |
| 2013 AMC 12B | Find length DF in triangle ABC with given side lengths and perpendiculars. | Geometry | Triangles & Polygons | 19 |
| 2013 AMC 12B | Find sin(2x) given points P,Q,R,S form a trapezoid for x between 135 and 180 degrees. | Geometry | Trigonometry | 20 |
| 2013 AMC 12B | Count points in plane on two of 30 parabolas with focus (0,0) and integer directrix lines. | Geometry | Conic Sections | 21 |
| 2013 AMC 12B | Find m+n given product of solutions to log equation is smallest possible integer. | Algebra | Logarithms & Exponents | 22 |
| 2013 AMC 12B | Count three-digit N where last two digits of S equal those of 2N. | Number Theory | Modular Arithmetic | 23 |
| 2013 AMC 12B | Find BN^2 in triangle ABC with median BM, angle bisector CN, and equilateral triangle BXN. | Geometry | Triangles & Polygons | 24 |
| 2013 AMC 12B | Count polynomials with integer coefficients, constant term 50, and distinct integer-complex roots. | Algebra | Polynomials | 25 |
| 2012 AMC 12A | Bug crawls from -2 to -6 to 5; find total distance. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2012 AMC 12A | Cagney and Lacey frost cupcakes; find total in 5 minutes. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2012 AMC 12A | A box of given dimensions holds 40 grams; find grams for scaled box. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2012 AMC 12A | Fraction of red marbles after doubling red count. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2012 AMC 12A | Fruit salad with 280 pieces; find number of cherries given ratios. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2012 AMC 12A | Three numbers have pairwise sums 12, 17, 19; find middle. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2012 AMC 12A | 12 integer central angles in arithmetic sequence sum to 360; find smallest. | Algebra | Sequences & Series | 7 |
| 2012 AMC 12A | Iterative average of 1-5; find difference between max and min. | Algebra | Rates, Mixtures, & Averages | 8 |
| 2012 AMC 12A | 200th anniversary of Dickens on Tuesday; find birth day of week. | Number Theory | Modular Arithmetic | 9 |
| 2012 AMC 12A | Triangle with area 30, side 10, median 9; find sine of angle between them. | Geometry | Triangles & Polygons | 10 |
| 2012 AMC 12A | Probability Alex wins 3, Mel 2, Chelsea 1 in 6 independent rounds. | Combinatorics | Probability | 11 |
| 2012 AMC 12A | Square tangent to unit circle at (0,1); vertices on circle radius 2; find side. | Geometry | Coordinate Geometry | 12 |
| 2012 AMC 12A | Three painters with lunch break; find break length in minutes. | Algebra | Rates, Mixtures, & Averages | 13 |
| 2012 AMC 12A | Closed curve of 9 circular arcs; find enclosed area. | Geometry | Circular Geometry | 14 |
| 2012 AMC 12A | 3x3 grid rotated 90°; probability grid becomes all black. | Combinatorics | Probability | 15 |
| 2012 AMC 12A | Two intersecting circles; find radius of one given distances between points. | Geometry | Circular Geometry | 16 |
| 2012 AMC 12A | Largest subset of {1,...,30} with no two elements summing to a multiple of 5. | Number Theory | Modular Arithmetic | 17 |
| 2012 AMC 12A | Triangle with sides 27,26,25; find distance from incenter to vertex B. | Geometry | Triangles & Polygons | 18 |
| 2012 AMC 12A | 6 people each have same number of friends; count possible friend graphs. | Combinatorics | Counting | 19 |
| 2012 AMC 12A | Find exponent a such that coefficient of x^2012 in product is 2^a. | Algebra | Polynomials | 20 |
| 2012 AMC 12A | Positive integers a≥b≥c satisfy two equations; find a. | Algebra | Systems & Algebraic Manipulation | 21 |
| 2012 AMC 12A | Planes intersect cube; find difference between max and min number of planes. | Geometry | 3D Geometry & Solids | 22 |
| 2012 AMC 12A | Probability translated square contains exactly two integer lattice points. | Geometry | Coordinate Geometry | 23 |
| 2012 AMC 12A | Sequence defined by powers; find k where a_k equals its rank in decreasing order. | Algebra | Sequences & Series | 24 |
| 2012 AMC 12A | Smallest n so n f(x f(x)) = x has at least 2012 real solutions. | Algebra | Functions | 25 |
| 2012 AMC 12B | Find how many more students than rabbits in 4 classrooms. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2012 AMC 12B | Find area of rectangle given inscribed circle radius and ratio. | Geometry | Circular Geometry | 2 |
| 2012 AMC 12B | Find number of acorns hidden by chipmunk given squirrel needs fewer holes. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2012 AMC 12B | Find percent by which Etienne's money exceeds Diana's money. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2012 AMC 12B | Find minimum number of even integers among six integers with given sums. | Number Theory | Modular Arithmetic | 5 |
| 2012 AMC 12B | Determine effect of rounding x up and y down on x-y estimate. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2012 AMC 12B | Find distance between 3rd and 21st red light in repeating pattern. | Algebra | Sequences & Series | 7 |
| 2012 AMC 12B | Count dessert menus for a week with no repeats and cake on Friday. | Combinatorics | Counting | 8 |
| 2012 AMC 12B | Find time to ride escalator down without walking given walking times. | Algebra | Rates, Mixtures, & Averages | 9 |
| 2012 AMC 12B | Find area of polygon formed by intersection of circle and ellipse. | Geometry | Coordinate Geometry | 10 |
| 2012 AMC 12B | Find A+B given base equation with consecutive positive integers A and B. | Algebra | Systems & Algebraic Manipulation | 11 |
| 2012 AMC 12B | Count sequences of length 20 with all zeros or all ones consecutive. | Combinatorics | Counting | 12 |
| 2012 AMC 12B | Find probability two parabolas with random integer coefficients intersect. | Combinatorics | Probability | 13 |
| 2012 AMC 12B | Find smallest initial number for Bernardo to win the doubling game. | Algebra | Sequences & Series | 14 |
| 2012 AMC 12B | Find ratio of volumes of two cones made from sectors of a circle. | Geometry | 3D Geometry & Solids | 15 |
| 2012 AMC 12B | Count ways three girls like four songs with given pairwise conditions. | Combinatorics | Counting | 16 |
| 2012 AMC 12B | Find sum of coordinates of center of square given points on its sides. | Geometry | Coordinate Geometry | 17 |
| 2012 AMC 12B | Count lists of 1-10 where each number has a neighbor appearing earlier. | Combinatorics | Counting | 18 |
| 2012 AMC 12B | Find side length of regular octahedron inscribed in a unit cube. | Geometry | 3D Geometry & Solids | 19 |
| 2012 AMC 12B | Find sum of possible areas of trapezoid with sides 3,5,7,11. | Geometry | Triangles & Polygons | 20 |
| 2012 AMC 12B | Find side length of square inscribed in equiangular hexagon. | Geometry | Trigonometry | 21 |
| 2012 AMC 12B | Find sum of all possible values of P(1) for polynomials with root on unit circle. | Combinatorics | Counting | 22 |
| 2012 AMC 12B | Find sum of all possible values of P(1) for polynomials with root on unit circle. | Algebra | Polynomials | 23 |
| 2012 AMC 12B | Count N up to 400 for which iterated function sequence is unbounded. | Number Theory | Factors, Multiples & Divisibility | 24 |
| 2012 AMC 12B | Count paths from A to B in a hexagonal lattice with directed segments, no segment reused. | Geometry | Coordinate Geometry | 25 |
| 2011 AMC 12A | Calculate monthly cell phone bill with texts and overtime minutes. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2011 AMC 12A | Determine the stacking order of five overlapping coins. | Geometry | Circular Geometry | 2 |
| 2011 AMC 12A | Find minimum number of small bottles to fill a large bottle. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2011 AMC 12A | Find average run time given ratios of students per grade. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2011 AMC 12A | Find percent of non-swan birds that are geese. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2011 AMC 12A | Find number of free throws made given total points and relationships. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2011 AMC 12A | Find pencil cost in cents given total cost and constraints. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2011 AMC 12A | Find A+H in a sequence where sum of three consecutive terms is 30. | Algebra | Sequences & Series | 8 |
| 2011 AMC 12A | Count handshakes among twins and triplets at a convention. | Combinatorics | Counting | 9 |
| 2011 AMC 12A | Find probability that circle area is less than circumference. | Combinatorics | Probability | 10 |
| 2011 AMC 12A | Find area inside circle C but outside circles A and B. | Geometry | Circular Geometry | 11 |
| 2011 AMC 12A | Find time for power boat to go from A to B given meeting time. | Algebra | Rates, Mixtures, & Averages | 12 |
| 2011 AMC 12A | Find perimeter of triangle formed by line through incenter parallel to base. | Geometry | Triangles & Polygons | 13 |
| 2011 AMC 12A | Find probability that point (a,b) lies above parabola y=ax^2-bx. | Combinatorics | Probability | 14 |
| 2011 AMC 12A | Find edge length of square pyramid base with inscribed hemisphere. | Geometry | 3D Geometry & Solids | 15 |
| 2011 AMC 12A | Count colorings of pentagon vertices with diagonal color restriction. | Combinatorics | Counting | 16 |
| 2011 AMC 12A | Find area of triangle formed by tangency points of three circles. | Geometry | Circular Geometry | 17 |
| 2011 AMC 12A | Maximize x^2-6x+y^2 given |x+y|+|x-y|=2. | Algebra | Inequalities | 18 |
| 2011 AMC 12A | Find sum of two smallest N given elite status formula equals 19. | Algebra | Functions | 19 |
| 2011 AMC 12A | Find integer k such that f(100) is between 5000k and 5000(k+1). | Algebra | Polynomials | 20 |
| 2011 AMC 12A | Find N+c where N is largest n with nonempty domain of f_n. | Algebra | Functions | 21 |
| 2011 AMC 12A | Count 100-ray partitional points not 60-ray partitional in a square. | Combinatorics | Counting | 22 |
| 2011 AMC 12A | Find difference between max and min |b| given functional equation. | Algebra | Complex Numbers | 23 |
| 2011 AMC 12A | Find radius of largest circle inside quadrilateral with given sides. | Geometry | Triangles & Polygons | 24 |
| 2011 AMC 12A | Find angle CBA maximizing area of pentagon BCOIH in triangle. | Geometry | Triangles & Polygons | 25 |
| 2011 AMC 12B | Compute the difference of two fractions with arithmetic series. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2011 AMC 12B | Find minimum test score to raise average by 3 points. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2011 AMC 12B | Determine how much LeRoy must give Bernardo to share costs equally. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2011 AMC 12B | Find correct product after reversing digits of a two-digit number. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2011 AMC 12B | Find sum of digits of second smallest integer divisible by 1 through 6. | Number Theory | Factors, Multiples & Divisibility | 5 |
| 2011 AMC 12B | Find angle between two tangents given arc length ratio. | Geometry | Circular Geometry | 6 |
| 2011 AMC 12B | Maximize ratio of two two-digit numbers with mean 60. | Algebra | Inequalities | 7 |
| 2011 AMC 12B | Find speed given time difference between inside and outside track edges. | Geometry | Circular Geometry | 8 |
| 2011 AMC 12B | Find probability product of two random numbers from [-20,10] is positive. | Combinatorics | Probability | 9 |
| 2011 AMC 12B | Find angle AMD in rectangle with point M on side AB. | Geometry | Triangles & Polygons | 10 |
| 2011 AMC 12B | Find minimum jumps of length 5 from (0,0) to (1,0) on lattice. | Number Theory | Modular Arithmetic | 11 |
| 2011 AMC 12B | Find probability dart lands in center square of regular octagon. | Geometry | Triangles & Polygons | 12 |
| 2011 AMC 12B | Find sum of possible largest of four integers given pairwise differences. | Algebra | Systems & Algebraic Manipulation | 13 |
| 2011 AMC 12B | Find cosine of angle AVB for parabola with segment through focus. | Geometry | Conic Sections | 14 |
| 2011 AMC 12B | Count two-digit factors of 2^24 - 1. | Number Theory | Factors, Multiples & Divisibility | 15 |
| 2011 AMC 12B | Find area of points inside rhombus closer to vertex B than others. | Geometry | Triangles & Polygons | 16 |
| 2011 AMC 12B | Find sum of digits of h_{2011}(1) for iterated function composition. | Algebra | Functions | 17 |
| 2011 AMC 12B | Find volume of cube inside pyramid with square base and equilateral faces. | Geometry | 3D Geometry & Solids | 18 |
| 2011 AMC 12B | Find maximum a such that y=mx+2 has no lattice points for 1/2 < m < a. | Number Theory | Factors, Multiples & Divisibility | 19 |
| 2011 AMC 12B | Find sum of distances from X to vertices of triangle ABC. | Geometry | Circular Geometry | 20 |
| 2011 AMC 12B | Find |x-y| given arithmetic and geometric means are digit reversals. | Algebra | Systems & Algebraic Manipulation | 21 |
| 2011 AMC 12B | Find perimeter of last triangle in sequence from incircle tangency points. | Geometry | Triangles & Polygons | 22 |
| 2011 AMC 12B | Count integer points on paths of length ≤20 from A to B. | Combinatorics | Counting | 23 |
| 2011 AMC 12B | Find minimum perimeter of octagon with vertices as zeros of polynomial. | Algebra | Complex Numbers | 24 |
| 2011 AMC 12B | Find minimum probability that nearest integer equation holds for random n. | Algebra | Functions | 25 |
| 2010 AMC 12A | Evaluate the expression (20-(2010-201))+(2010-(201-20)). | Algebra | Systems & Algebraic Manipulation | 1 |
| 2010 AMC 12A | Find total tourists on 6 ferry trips starting at 100 and decreasing by 1 each trip. | Algebra | Sequences & Series | 2 |
| 2010 AMC 12A | Find AB/AD given rectangle shares 50% area with square, square shares 20% with rectangle. | Geometry | Triangles & Polygons | 3 |
| 2010 AMC 12A | For x<0, determine which expression must be positive. | Algebra | Functions | 4 |
| 2010 AMC 12A | Find minimum n such that n consecutive bullseyes guarantee victory in archery tournament. | Algebra | Inequalities | 5 |
| 2010 AMC 12A | Find sum of digits of x where x and x+32 are three- and four-digit palindromes. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2010 AMC 12A | Find height of scale model water tower given volume ratio and actual height. | Geometry | 3D Geometry & Solids | 7 |
| 2010 AMC 12A | Find angle ACB in triangle with AB=2AC and equilateral triangle CFE. | Geometry | Triangles & Polygons | 8 |
| 2010 AMC 12A | Find volume of cube with 2x2 square holes through each face. | Geometry | 3D Geometry & Solids | 9 |
| 2010 AMC 12A | Find 2010th term of arithmetic sequence with terms p, 9, 3p-q, 3p+q. | Algebra | Sequences & Series | 10 |
| 2010 AMC 12A | Find base b such that solution of 7^(x+7)=8^x is x=log_b(7^7). | Algebra | Logarithms & Exponents | 11 |
| 2010 AMC 12A | Determine number of frogs among four amphibians given truth-telling statements. | Algebra | Logic & Truth Values | 12 |
| 2010 AMC 12A | Count integer k for which circle x^2+y^2=k^2 and hyperbola xy=k do not intersect. | Algebra | Systems & Algebraic Manipulation | 13 |
| 2010 AMC 12A | Find smallest possible perimeter of triangle with angle bisector AD=3, DC=8. | Geometry | Triangles & Polygons | 14 |
| 2010 AMC 12A | Find probability of heads given 4 flips have 1/6 chance of equal heads and tails. | Combinatorics | Probability | 15 |
| 2010 AMC 12A | Probability Bernardo's 3-digit number > Silvia's when picking distinct numbers from 1-9 and 1-8. | Combinatorics | Probability | 16 |
| 2010 AMC 12A | Find sum of possible r in equiangular hexagon where triangle ACE area is 70% of hexagon. | Geometry | Triangles & Polygons | 17 |
| 2010 AMC 12A | Count 16-step paths from (-4,-4) to (4,4) staying outside or on boundary of square [-2,2]. | Combinatorics | Counting | 18 |
| 2010 AMC 12A | Find smallest n such that probability of stopping after n draws is less than 1/2010. | Combinatorics | Probability | 19 |
| 2010 AMC 12A | Find largest n such that arithmetic sequences a_n and b_n have integer terms and product 2010. | Number Theory | Factors, Multiples & Divisibility | 20 |
| 2010 AMC 12A | Find largest x where graph of y=x^6-10x^5+... lies above line y=bx+c except at three points. | Algebra | Polynomials | 21 |
| 2010 AMC 12A | Find minimum value of sum |x-1|+|2x-1|+...+|119x-1|. | Algebra | Functions | 22 |
| 2010 AMC 12A | Find last two nonzero digits of 90!. | Number Theory | Modular Arithmetic | 23 |
| 2010 AMC 12A | Find number of disjoint open intervals in domain of f(x)=log(product sin(kπx)) on [0,1]. | Algebra | Functions | 24 |
| 2010 AMC 12A | Count convex cyclic quadrilaterals with integer sides and perimeter 32, up to rotation/translation. | Combinatorics | Counting | 25 |
| 2010 AMC 12B | Find percent of 9-hour workday spent in two meetings totaling 135 minutes. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2010 AMC 12B | Find area of an L-shaped figure composed of two rectangles. | Geometry | Triangles & Polygons | 2 |
| 2010 AMC 12B | Find number of possible whole-number ticket prices given two total costs. | Number Theory | Factors, Multiples & Divisibility | 3 |
| 2010 AMC 12B | Find how many days of the week could start a 31-day month with equal Mondays and Wednesdays. | Number Theory | Modular Arithmetic | 4 |
| 2010 AMC 12B | Find the number substituted for e so that ignoring parentheses gives the correct result. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2010 AMC 12B | Find difference between max and min possible percent of students who changed their answer. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2010 AMC 12B | Find minutes driven in rain given total distance and time with two speeds. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2010 AMC 12B | Find number of schools given median score and two teammates' ranks. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2010 AMC 12B | Find number of digits of smallest n divisible by 20 with n^2 a cube and n^3 a square. | Number Theory | Factors, Multiples & Divisibility | 9 |
| 2010 AMC 12B | Find x such that average of 1 through 99 and x equals 100x. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2010 AMC 12B | Find probability a random 4-digit palindrome is divisible by 7. | Combinatorics | Probability | 11 |
| 2010 AMC 12B | Solve logarithmic equation with multiple bases for x. | Algebra | Logarithms & Exponents | 12 |
| 2010 AMC 12B | Find BC in triangle ABC given cos(2A-B)+sin(A+B)=2 and AB=4. | Geometry | Trigonometry | 13 |
| 2010 AMC 12B | Minimize the maximum of adjacent sums of five positive integers totaling 2010. | Algebra | Inequalities | 14 |
| 2010 AMC 12B | Count ordered triples (x,y,z) under 20 with exactly two distinct values in set of complex powers. | Algebra | Complex Numbers | 15 |
| 2010 AMC 12B | Find probability that abc+ab+a is divisible by 3 for random a,b,c from 1 to 2010. | Combinatorics | Probability | 16 |
| 2010 AMC 12B | Count 3x3 arrays with digits 1-9 in increasing order in each row and column. | Combinatorics | Counting | 17 |
| 2010 AMC 12B | Find probability frog ends within 1 meter of start after three random 1-meter jumps. | Combinatorics | Probability | 18 |
| 2010 AMC 12B | Find total first-half points given geometric and arithmetic quarterly scores with 1-point win. | Algebra | Sequences & Series | 19 |
| 2010 AMC 12B | Find n such that a_n = 1+cos x in geometric sequence with sin x, cos x, tan x. | Algebra | Sequences & Series | 20 |
| 2010 AMC 12B | Find smallest a such that polynomial P with integer coefficients has given alternating values. | Algebra | Polynomials | 21 |
| 2010 AMC 12B | Find largest possible BD in cyclic quadrilateral with distinct integer sides under 15 and BC*CD=AB*DA. | Geometry | Circular Geometry | 22 |
| 2010 AMC 12B | Find sum of minimum values of monic quadratics P and Q given zeros of compositions. | Algebra | Polynomials | 23 |
| 2010 AMC 12B | Find sum of lengths of intervals where sum of three reciprocals is at least 1. | Algebra | Inequalities | 24 |
| 2010 AMC 12B | Find largest m such that 2010^m divides product of pow(n) for n=2 to 5300. | Number Theory | Factors, Multiples & Divisibility | 25 |
| 2009 AMC 12A | Kim's flight from Newark to Miami takes h hours and m minutes; find h+m. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2009 AMC 12A | Evaluate the continued fraction 1 + 1/(1 + 1/(1+1)). | Algebra | Systems & Algebraic Manipulation | 2 |
| 2009 AMC 12A | Find the number one third of the way from 1/4 to 3/4. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2009 AMC 12A | Four coins from pennies, nickels, dimes, quarters; which total is impossible? | Combinatorics | Counting | 4 |
| 2009 AMC 12A | Cube dimensions changed by ±1; volume decreases by 5. Find original volume. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2009 AMC 12A | Given P=2^m and Q=3^n, express 12^{mn} in terms of P and Q. | Algebra | Logarithms & Exponents | 6 |
| 2009 AMC 12A | First three terms of arithmetic sequence given; find n for nth term 2009. | Algebra | Sequences & Series | 7 |
| 2009 AMC 12A | Four congruent rectangles in a square; outer area 4× inner. Find rectangle side ratio. | Geometry | Triangles & Polygons | 8 |
| 2009 AMC 12A | Given f(x+3)=3x^2+7x+4 and f(x)=ax^2+bx+c, find a+b+c. | Algebra | Functions | 9 |
| 2009 AMC 12A | Quadrilateral ABCD with sides 5,17,5,9; BD integer. Find BD. | Geometry | Triangles & Polygons | 10 |
| 2009 AMC 12A | Sequence of diamond figures; find number of diamonds in F_20. | Algebra | Sequences & Series | 11 |
| 2009 AMC 12A | Positive integers less than 1000 that are 6 times the sum of their digits. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2009 AMC 12A | Ship sails 10 then 20 miles with turn 45-60°; find interval for AC². | Geometry | Trigonometry | 13 |
| 2009 AMC 12A | Line y=mx divides triangle with vertices (0,0),(1,1),(6m,0) into equal areas. | Geometry | Coordinate Geometry | 14 |
| 2009 AMC 12A | Find n such that i+2i²+3i³+...+ni^n = 48+49i. | Algebra | Complex Numbers | 15 |
| 2009 AMC 12A | Circle tangent to axes and externally tangent to circle at (3,0) radius 1. | Geometry | Coordinate Geometry | 16 |
| 2009 AMC 12A | Two geometric series with same first term; sums equal common ratios. Find r1+r2. | Algebra | Sequences & Series | 17 |
| 2009 AMC 12A | I_k = 10...064 with k zeros; find max exponent of 2 in prime factorization. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2009 AMC 12A | Compare area between incircle and circumcircle of pentagon vs heptagon side 2. | Geometry | Circular Geometry | 19 |
| 2009 AMC 12A | Quadrilateral ABCD with AB=9, CD=12, AC=14; triangles AED and BEC equal area. Find AE. | Geometry | Triangles & Polygons | 20 |
| 2009 AMC 12A | Cubic p(x) with given zeros; find number of nonreal zeros of p(x^4). | Algebra | Polynomials | 21 |
| 2009 AMC 12A | Plane parallel to opposite faces cuts regular octahedron side 1; find intersection area. | Geometry | 3D Geometry & Solids | 22 |
| 2009 AMC 12A | Quadratic f and g with g(x)=-f(100-x); x-intercepts differ by 150. Find x4-x1. | Algebra | Functions | 23 |
| 2009 AMC 12A | Tower function T(n); find largest k such that log_2...log_2(B) is defined. | Algebra | Logarithms & Exponents | 24 |
| 2009 AMC 12A | Sequence a1=1, a2=1/√3, a_{n+2}=(a_n+a_{n+1})/(1-a_n a_{n+1}); find |a_2009|. | Algebra | Sequences & Series | 25 |
| 2009 AMC 12B | Jane buys muffins and bagels for a week; total cost is a whole number of dollars. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2009 AMC 12B | Paint for 30 rooms lost 3 cans; now only enough for 25 rooms. Find cans used. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2009 AMC 12B | Twenty percent less than 60 is one-third more than what number? | Algebra | Systems & Algebraic Manipulation | 3 |
| 2009 AMC 12B | Rectangular yard with two congruent isosceles right triangle flower beds; find fraction occupied. | Geometry | Triangles & Polygons | 4 |
| 2009 AMC 12B | Product of three ages (two twin brothers and Kiana) is 128; find sum. | Number Theory | Factors, Multiples & Divisibility | 5 |
| 2009 AMC 12B | Insert parentheses in 2×3+4×5 to get different values; count distinct results. | Combinatorics | Counting | 6 |
| 2009 AMC 12B | Gasoline price changes by given percentages; find the final percent decrease to return to original. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2009 AMC 12B | Bucket weights at two-thirds and one-half full; find weight when full in terms of a and b. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2009 AMC 12B | Find the area of a triangle with a vertex on a given line. | Geometry | Coordinate Geometry | 9 |
| 2009 AMC 12B | Find the fraction of the day a faulty clock shows the correct time. | Combinatorics | Counting | 10 |
| 2009 AMC 12B | Millie adds seeds daily; birds eat millet and other seeds; find when millet exceeds half. | Algebra | Sequences & Series | 11 |
| 2009 AMC 12B | Find the first term of a geometric sequence given two later terms. | Algebra | Sequences & Series | 12 |
| 2009 AMC 12B | Find the sum of the two possible lengths of the third side of a triangle. | Geometry | Triangles & Polygons | 13 |
| 2009 AMC 12B | Find the x-intercept of a line dividing a figure into equal areas. | Geometry | Coordinate Geometry | 14 |
| 2009 AMC 12B | Determine which exponential equation has the largest solution for x. | Algebra | Logarithms & Exponents | 15 |
| 2009 AMC 12B | Find the length of a side of a trapezoid given angles and a ratio. | Geometry | Triangles & Polygons | 16 |
| 2009 AMC 12B | Each face of a cube gets a random stripe; find probability of a continuous stripe encircling the cube. | Combinatorics | Probability | 17 |
| 2009 AMC 12B | Two runners on a circular track; find probability both are in a photo taken during a random minute. | Combinatorics | Probability | 18 |
| 2009 AMC 12B | Find the sum of all prime values of a quartic polynomial for positive integers. | Algebra | Polynomials | 19 |
| 2009 AMC 12B | Find the number of edges of a polyhedron after truncating its vertices. | Geometry | 3D Geometry & Solids | 20 |
| 2009 AMC 12B | Find the number of ways ten women can reseat themselves with restrictions. | Combinatorics | Counting | 21 |
| 2009 AMC 12B | Count parallelograms with given area and vertices on specific lines. | Geometry | Coordinate Geometry | 22 |
| 2009 AMC 12B | Find the probability that a scaled and rotated point stays in a square. | Algebra | Complex Numbers | 23 |
| 2009 AMC 12B | Find the number of solutions to an equation with inverse trig functions. | Geometry | Trigonometry | 24 |
| 2009 AMC 12B | Count squares with side at least 6 whose vertices are in a given set of lattice points. | Combinatorics | Counting | 25 |
| 2008 AMC 12A | A bakery machine completes one third of a job by 11:10 AM after starting at 8:30 AM. Find completion time. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2008 AMC 12A | Find the reciprocal of the sum 1/2 + 2/3. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2008 AMC 12A | Given 2/3 of 10 bananas equals 8 oranges, find how many oranges equal 1/2 of 5 bananas. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2008 AMC 12A | Compute the product of fractions from 8/4 to 2008/2004. | Algebra | Sequences & Series | 4 |
| 2008 AMC 12A | Determine which statement must be true about x if (2x/3 - x/6) is an integer. | Number Theory | Factors, Multiples & Divisibility | 5 |
| 2008 AMC 12A | Find the sticker price of a computer given discounts and rebates at two stores. | Algebra | Systems & Algebraic Manipulation | 6 |
| 2008 AMC 12A | Find the slowest bailing rate to prevent a boat from sinking while rowing to shore. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2008 AMC 12A | Find the volume of a cube whose surface area is twice that of a unit cube. | Geometry | 3D Geometry & Solids | 8 |
| 2008 AMC 12A | Find the height of darkened strips on a TV screen when letterboxing a movie. | Geometry | Triangles & Polygons | 9 |
| 2008 AMC 12A | Find the equation for total time including lunch when two people paint a room together. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2008 AMC 12A | Maximize the sum of visible numbers on three stacked cubes made from a given net. | Combinatorics | Counting | 11 |
| 2008 AMC 12A | Find the domain and range of g(x)=1-f(x+1) given f has domain [0,2] and range [0,1]. | Algebra | Functions | 12 |
| 2008 AMC 12A | Find the ratio of areas of two internally tangent circles with a 60-degree central angle. | Geometry | Circular Geometry | 13 |
| 2008 AMC 12A | Find the area of the region defined by |3x-18|+|2y+7| ≤ 3. | Geometry | Coordinate Geometry | 14 |
| 2008 AMC 12A | Find the units digit of k^2 + 2^k where k = 2008^2 + 2^2008. | Number Theory | Modular Arithmetic | 15 |
| 2008 AMC 12A | Find n such that the 12th term of an arithmetic sequence of logs is log(b^n). | Algebra | Logarithms & Exponents | 16 |
| 2008 AMC 12A | Count positive integers a1 ≤ 2008 where a1 is less than a2, a3, and a4 in a Collatz-like sequence. | Number Theory | Modular Arithmetic | 17 |
| 2008 AMC 12A | Find the volume of tetrahedron OABC with vertices on positive axes and side lengths 5, 6, 7. | Geometry | 3D Geometry & Solids | 18 |
| 2008 AMC 12A | Find the coefficient of x^28 in the expansion of (1+x+...+x^27)(1+x+...+x^14)^2. | Combinatorics | Counting | 19 |
| 2008 AMC 12A | Find the ratio of inradii of two triangles formed by the angle bisector of the right angle in a 3-4-5 triangle. | Geometry | Triangles & Polygons | 20 |
| 2008 AMC 12A | Count permutations of (1,2,3,4,5) where a1+a2 < a4+a5. | Combinatorics | Counting | 21 |
| 2008 AMC 12A | Find the length x of rectangular placemats arranged around a round table of radius 4. | Geometry | Circular Geometry | 22 |
| 2008 AMC 12A | Find the area of the convex polygon whose vertices are the roots of z^4+4z^3i-6z^2-4zi-i=0. | Algebra | Complex Numbers | 23 |
| 2008 AMC 12A | Find the maximum possible value of tan(∠BAD) in triangle ABC with ∠C=60° and BC=4, D the midpoint of BC. | Geometry | Trigonometry | 24 |
| 2008 AMC 12A | Find a1+b1 given a recurrence for points in the plane and (a100,b100)=(2,4). | Algebra | Complex Numbers | 25 |
| 2008 AMC 12B | Basketball player makes 5 baskets worth 2 or 3 points each; find number of possible total points. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2008 AMC 12B | Reverse rows of a 4x4 calendar block and find positive difference between diagonal sums. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2008 AMC 12B | Find maximum possible salary for one player given minimum salary and total team salary cap. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2008 AMC 12B | Find ratio of sector area to circle area given two angles on a diameter. | Geometry | Circular Geometry | 4 |
| 2008 AMC 12B | Find number of bouquets possible spending exactly $50 on $3 roses and $2 carnations. | Algebra | Systems & Algebraic Manipulation | 5 |
| 2008 AMC 12B | Calculate miles walked given pedometer flips and final reading. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2008 AMC 12B | Evaluate custom operation a$b = (a-b)^2 for (x-y)^2$(y-x)^2. | Algebra | Functions | 7 |
| 2008 AMC 12B | Find fraction BC/AD given AB=4*BD and AC=9*CD on segment AD. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2008 AMC 12B | Find length AC where C is midpoint of minor arc AB on circle radius 5 with chord AB=6. | Geometry | Triangles & Polygons | 9 |
| 2008 AMC 12B | Find number of bricks in chimney given individual and combined work rates with distraction. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2008 AMC 12B | Find ocean depth at base of cone-shaped mountain given top 1/8 volume above water. | Geometry | 3D Geometry & Solids | 11 |
| 2008 AMC 12B | Find 2008th term of sequence where mean of first n terms is n. | Algebra | Sequences & Series | 12 |
| 2008 AMC 12B | Find area of region inside square and outside triangle with distance constraints from side. | Geometry | Triangles & Polygons | 13 |
| 2008 AMC 12B | Find log_a(b) given circle radius log(a^2) and circumference log(b^4). | Algebra | Logarithms & Exponents | 14 |
| 2008 AMC 12B | Find area of region S minus region R formed by equilateral triangles on a square. | Geometry | Triangles & Polygons | 15 |
| 2008 AMC 12B | Find number of ordered pairs (a,b) for floor dimensions with 1-foot border occupying half area. | Number Theory | Factors, Multiples & Divisibility | 16 |
| 2008 AMC 12B | Find sum of digits of y-coordinate of C on y=x^2 forming right triangle with area 2008. | Geometry | Coordinate Geometry | 17 |
| 2008 AMC 12B | Find volume of pyramid with square base area 196 and given lateral face areas. | Geometry | 3D Geometry & Solids | 18 |
| 2008 AMC 12B | Minimize |alpha|+|gamma| for complex quadratic with f(1) and f(i) real. | Algebra | Complex Numbers | 19 |
| 2008 AMC 12B | Count meetings between Michael walking 5 ft/s and truck moving 10 ft/s stopping 30s at each pail. | Algebra | Rates, Mixtures, & Averages | 20 |
| 2008 AMC 12B | Probability two unit circles with centers on parallel segments intersect. | Combinatorics | Probability | 21 |
| 2008 AMC 12B | Probability SUV requiring 2 adjacent spaces can park after 12 cars park randomly in 16 spaces. | Combinatorics | Probability | 22 |
| 2008 AMC 12B | Find n such that sum of base-10 logs of divisors of 10^n equals 792. | Number Theory | Factors, Multiples & Divisibility | 23 |
| 2008 AMC 12B | Find least n so that A_0A_n >= 100 for equilateral triangles on y=sqrt(x). | Algebra | Sequences & Series | 24 |
| 2008 AMC 12B | Find area of hexagon formed by angle bisectors in trapezoid with sides 11,5,19,7. | Geometry | Triangles & Polygons | 25 |
| 2007 AMC 12A | Susan buys 4 tickets at 25% off, Pam buys 5 at 30% off. How much more does Pam pay? | Algebra | Rates, Mixtures, & Averages | 1 |
| 2007 AMC 12A | A brick is placed in an aquarium; find how much the water rises. | Geometry | 3D Geometry & Solids | 2 |
| 2007 AMC 12A | The larger of two consecutive odd integers is three times the smaller. Find their sum. | Algebra | Systems & Algebraic Manipulation | 3 |
| 2007 AMC 12A | Kate rode 30 min at 16 mph then walked 90 min at 4 mph. Find overall average speed. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2007 AMC 12A | Mr. Public paid 20% federal then 10% state tax on remainder, total $10500. Find inheritance. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2007 AMC 12A | In isosceles triangles ABC and ADC, find angle BAD given angles ABC=40 and ADC=140. | Geometry | Triangles & Polygons | 6 |
| 2007 AMC 12A | Five consecutive terms in an arithmetic sequence sum to 30. Which term can be found? | Algebra | Sequences & Series | 7 |
| 2007 AMC 12A | A star polygon is drawn on a clock face by connecting each number to the fifth clockwise. Find vertex angle. | Geometry | Circular Geometry | 8 |
| 2007 AMC 12A | Yan walks to stadium or walks home then bikes to stadium in same time. Find ratio of distances. | Algebra | Rates, Mixtures, & Averages | 9 |
| 2007 AMC 12A | A 3-4-5 triangle is inscribed in a circle of radius 3. Find its area. | Geometry | Triangles & Polygons | 10 |
| 2007 AMC 12A | A sequence of three-digit integers where each term's tens/units become next term's hundreds/tens. Find largest prime factor always dividing sum. | Number Theory | Factors, Multiples & Divisibility | 11 |
| 2007 AMC 12A | Integers a,b,c,d chosen from 0 to 2007. Find probability that ad-bc is even. | Combinatorics | Probability | 12 |
| 2007 AMC 12A | Mouse runs along line y=-5x+18; cheese at (12,10). Find a+b where mouse starts getting farther. | Geometry | Coordinate Geometry | 13 |
| 2007 AMC 12A | Distinct integers a,b,c,d,e satisfy (6-a)(6-b)(6-c)(6-d)(6-e)=45. Find a+b+c+d+e. | Number Theory | Factors, Multiples & Divisibility | 14 |
| 2007 AMC 12A | Set {3,6,9,10} augmented by n; median equals mean. Find sum of all possible n. | Algebra | Rates, Mixtures, & Averages | 15 |
| 2007 AMC 12A | How many three-digit numbers with distinct digits have one digit equal to the average of the other two? | Combinatorics | Counting | 16 |
| 2007 AMC 12A | Given sin a + sin b = sqrt(5/3) and cos a + cos b = 1, find cos(a-b). | Geometry | Trigonometry | 17 |
| 2007 AMC 12A | Polynomial f(x)=x^4+ax^3+bx^2+cx+d has real coefficients, f(2i)=f(2+i)=0. Find a+b+c+d. | Algebra | Polynomials | 18 |
| 2007 AMC 12A | Triangles ABC and ADE have areas 2007 and 7002. Find sum of all possible x-coordinates of A. | Geometry | Coordinate Geometry | 19 |
| 2007 AMC 12A | Corners sliced off a unit cube so faces become regular octagons. Find total volume of removed tetrahedra. | Geometry | 3D Geometry & Solids | 20 |
| 2007 AMC 12A | Sum of zeros, product of zeros, and sum of coefficients of f(x)=ax^2+bx+c are equal. Find common value. | Algebra | Polynomials | 21 |
| 2007 AMC 12A | For how many positive integers n does n + S(n) + S(S(n)) = 2007, where S(n) is sum of digits? | Number Theory | Modular Arithmetic | 22 |
| 2007 AMC 12A | Square ABCD of area 36 has AB parallel to x-axis; vertices on y=log_a x, y=2log_a x, y=3log_a x. Find a. | Algebra | Logarithms & Exponents | 23 |
| 2007 AMC 12A | For n>1, F(n) is number of solutions to sin x = sin(nx) on [0,pi]. Find sum from n=2 to 2007. | Geometry | Trigonometry | 24 |
| 2007 AMC 12A | A set of integers is spacy if it contains no more than one out of any three consecutive integers. How many subsets of {1,...,12} are spacy? | Combinatorics | Counting | 25 |
| 2007 AMC 12B | Calculate total wall area to paint in three bedrooms, excluding doors and windows. | Geometry | 3D Geometry & Solids | 1 |
| 2007 AMC 12B | Find average gas mileage for a round trip with different fuel efficiencies. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2007 AMC 12B | Find angle ABC in a triangle given central angles of its circumcircle. | Geometry | Circular Geometry | 3 |
| 2007 AMC 12B | Determine how many oranges cost as much as 18 bananas given fruit price ratios. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2007 AMC 12B | Find minimum correct answers needed to score at least 100 points on a test. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2007 AMC 12B | Find distance BD where two bugs meet on triangle sides traveling opposite directions. | Geometry | Triangles & Polygons | 6 |
| 2007 AMC 12B | Find angle E in a pentagon with equal sides and two right angles. | Geometry | Triangles & Polygons | 7 |
| 2007 AMC 12B | Tom's age equals sum of his three children's ages; find ratio of his age to years ago. | Algebra | Systems & Algebraic Manipulation | 8 |
| 2007 AMC 12B | Evaluate f(5) given f(3x-1) = x^2 + x + 1 for all real x. | Algebra | Functions | 9 |
| 2007 AMC 12B | Find initial number of girls given percentage changes after two leave and two boys arrive. | Algebra | Rates, Mixtures, & Averages | 10 |
| 2007 AMC 12B | Quadrilateral angles satisfy proportional relationship; find measure of angle A rounded. | Algebra | Systems & Algebraic Manipulation | 11 |
| 2007 AMC 12B | Find the common score of juniors given class average and seniors' average. | Algebra | Rates, Mixtures, & Averages | 12 |
| 2007 AMC 12B | Find probability that traffic light changes color during a random 3-second interval. | Combinatorics | Probability | 13 |
| 2007 AMC 12B | Find side length of equilateral triangle given distances from interior point to sides. | Geometry | Triangles & Polygons | 14 |
| 2007 AMC 12B | Find a+r for a geometric series with given sums of all terms and odd-power terms. | Algebra | Sequences & Series | 15 |
| 2007 AMC 12B | Count distinguishable colorings of a regular tetrahedron's faces with three colors. | Combinatorics | Counting | 16 |
| 2007 AMC 12B | Find median of set {0,1,a,b,1/b} given equation ab^2 = log_10(b). | Algebra | Logarithms & Exponents | 17 |
| 2007 AMC 12B | Find sum of digits of three-digit integer lying one-third between consecutive squares. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2007 AMC 12B | Find sin(angle ABC) when rhombus is rolled into a cylinder of given volume. | Geometry | 3D Geometry & Solids | 19 |
| 2007 AMC 12B | Minimize sum of positive integers a,b,c,d given areas of two parallelograms. | Geometry | Coordinate Geometry | 20 |
| 2007 AMC 12B | Count base-3 palindromes among the first 2007 positive integers. | Number Theory | Modular Arithmetic | 21 |
| 2007 AMC 12B | Find ratio of area enclosed by midpoint of two particles moving on triangle edges. | Geometry | Triangles & Polygons | 22 |
| 2007 AMC 12B | Count non-congruent right triangles with integer legs where area equals 3 times perimeter. | Number Theory | Factors, Multiples & Divisibility | 23 |
| 2007 AMC 12B | Count coprime positive integer pairs (a,b) such that a/b + 14b/(9a) is integer. | Number Theory | Factors, Multiples & Divisibility | 24 |
| 2007 AMC 12B | Find area of triangle BDE in 3D space given segment lengths and right angles. | Geometry | 3D Geometry & Solids | 25 |
| 2006 AMC 12A | Cost of 5 sandwiches at $3 and 8 sodas at $2. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2006 AMC 12A | Evaluate h⊗(h⊗h) given x⊗y = x³−y. | Algebra | Functions | 2 |
| 2006 AMC 12A | Find Mary's age given ratio 3:5 and Alice is 30. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2006 AMC 12A | Largest possible sum of digits on a digital clock. | Algebra | Systems & Algebraic Manipulation | 4 |
| 2006 AMC 12A | How much more Dave pays than Doug for pizza. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2006 AMC 12A | Find y so rectangle cut into hexagons forms a square. | Geometry | Triangles & Polygons | 6 |
| 2006 AMC 12A | Mary's age on next birthday given percentages and sum. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2006 AMC 12A | Number of sets of consecutive positive integers summing to 15. | Algebra | Sequences & Series | 8 |
| 2006 AMC 12A | Cost of one pencil and one eraser given 13 pencils and 3 erasers cost $1. | Number Theory | Modular Arithmetic | 9 |
| 2006 AMC 12A | Number of real x such that sqrt(120−sqrt(x)) is an integer. | Algebra | Systems & Algebraic Manipulation | 10 |
| 2006 AMC 12A | Describe the graph of (x+y)² = x²+y². | Geometry | Coordinate Geometry | 11 |
| 2006 AMC 12A | Distance from top of top ring to bottom of bottom ring. | Algebra | Sequences & Series | 12 |
| 2006 AMC 12A | Sum of areas of three externally tangent circles at triangle vertices. | Geometry | Circular Geometry | 13 |
| 2006 AMC 12A | Smallest positive debt resolvable with pigs and goats. | Number Theory | Factors, Multiples & Divisibility | 14 |
| 2006 AMC 12A | Smallest positive z given cos x = 0 and cos(x+z) = 1/2. | Geometry | Trigonometry | 15 |
| 2006 AMC 12A | Length CD of common internal tangent of two circles. | Geometry | Circular Geometry | 16 |
| 2006 AMC 12A | Ratio r/s for circle tangent to square with given AF length. | Geometry | Circular Geometry | 17 |
| 2006 AMC 12A | Largest domain of f satisfying f(x)+f(1/x)=x. | Algebra | Functions | 18 |
| 2006 AMC 12A | Find b for common external tangent y=mx+b to two circles. | Geometry | Coordinate Geometry | 19 |
| 2006 AMC 12A | Probability bug visits every cube vertex exactly once in 7 moves. | Combinatorics | Probability | 20 |
| 2006 AMC 12A | Ratio of areas of S₂ to S₁ defined by log inequalities. | Algebra | Logarithms & Exponents | 21 |
| 2006 AMC 12A | Radius r such that probability of seeing 3 hexagon sides is 1/2. | Geometry | Circular Geometry | 22 |
| 2006 AMC 12A | Find x given A^100(S) = 1/2^50 for S = (1,x,...,x^100). | Algebra | Sequences & Series | 23 |
| 2006 AMC 12A | Number of terms in simplified (x+y+z)^2006 + (x−y−z)^2006. | Combinatorics | Counting | 24 |
| 2006 AMC 12A | Number of non-empty subsets of {1,...,15} with no consecutive numbers and element ≥ size. | Combinatorics | Counting | 25 |
| 2006 AMC 12B | Sum of alternating powers of -1 from 1 to 2006. | Algebra | Sequences & Series | 1 |
| 2006 AMC 12B | Evaluate a custom-defined operation with nested parentheses. | Algebra | Functions | 2 |
| 2006 AMC 12B | Find the losing team's score given total and margin. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2006 AMC 12B | Estimate the percentage change from a $20 bill for five items. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2006 AMC 12B | Time for Bob to catch John walking east at different speeds. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2006 AMC 12B | Calories in 200g of lemonade given recipe and calorie counts. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2006 AMC 12B | Seating arrangements for a family of four with driver restriction. | Combinatorics | Counting | 7 |
| 2006 AMC 12B | Find a+b given two lines intersect at (1,2). | Algebra | Systems & Algebraic Manipulation | 8 |
| 2006 AMC 12B | Count even three-digit numbers with strictly increasing digits. | Combinatorics | Counting | 9 |
| 2006 AMC 12B | Max perimeter of triangle with sides x, 3x, and 15. | Geometry | Triangles & Polygons | 10 |
| 2006 AMC 12B | Ratio of cream in Joe's vs JoAnn's coffee after different steps. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2006 AMC 12B | Find b for parabola with vertex (p,p) and y-intercept (0,-p). | Algebra | Polynomials | 12 |
| 2006 AMC 12B | Area of smaller rhombus similar to larger rhombus with area 24. | Geometry | Triangles & Polygons | 13 |
| 2006 AMC 12B | Cost of jam given sandwich ingredients and total cost $2.53. | Number Theory | Factors, Multiples & Divisibility | 14 |
| 2006 AMC 12B | Area of hexagon formed by two externally tangent circles and tangents. | Geometry | Circular Geometry | 15 |
| 2006 AMC 12B | Area of regular hexagon given coordinates of two vertices. | Geometry | Coordinate Geometry | 16 |
| 2006 AMC 12B | Probability of rolling sum 7 with weighted dice in ratio 1:2:3:4:5:6. | Combinatorics | Probability | 17 |
| 2006 AMC 12B | Number of distinct points reachable in 10 steps on a lattice. | Combinatorics | Counting | 18 |
| 2006 AMC 12B | Find which age is not among eight children given license plate clues. | Number Theory | Factors, Multiples & Divisibility | 19 |
| 2006 AMC 12B | Probability that floor(log10(4x)) equals floor(log10(x)) for x in (0,1). | Algebra | Functions | 20 |
| 2006 AMC 12B | Perimeter of rectangle with given area and ellipse through vertices. | Geometry | Conic Sections | 21 |
| 2006 AMC 12B | Minimize trailing zeros in a!b!c! with a+b+c=2006. | Number Theory | Factors, Multiples & Divisibility | 22 |
| 2006 AMC 12B | Find a+b for side length s = sqrt(a + b sqrt(2)) in right isosceles triangle. | Geometry | Triangles & Polygons | 23 |
| 2006 AMC 12B | Area of region in [0,pi/2]^2 satisfying sin^2 x - sin x sin y + sin^2 y <= 3/4. | Geometry | Trigonometry | 24 |
| 2006 AMC 12B | Number of a_2 values such that a_{2006}=1 in absolute difference sequence. | Number Theory | Modular Arithmetic | 25 |
| 2005 AMC 12A | Two is 10% of x and 20% of y; find x minus y. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2005 AMC 12A | Two equations have the same solution; find the value of b. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2005 AMC 12A | Rectangle diagonal is x, length twice width; find area. | Geometry | Triangles & Polygons | 3 |
| 2005 AMC 12A | Buy 4 windows get 1 free; find savings buying together vs separately. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2005 AMC 12A | Average of 20 numbers is 30, of 30 numbers is 20; find overall average. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2005 AMC 12A | Josh and Mike bike toward each other; find how far Mike rode. | Algebra | Rates, Mixtures, & Averages | 6 |
| 2005 AMC 12A | Square inside square with given side lengths; find inner square area. | Geometry | Triangles & Polygons | 7 |
| 2005 AMC 12A | Three-digit number times digit sum equals 2005; find the hundreds digit. | Number Theory | Factors, Multiples & Divisibility | 8 |
| 2005 AMC 12A | Quadratic has only one solution for two values of a; find their sum. | Algebra | Polynomials | 9 |
| 2005 AMC 12A | Painted cube cut into unit cubes; find n given fraction of red faces. | Algebra | Systems & Algebraic Manipulation | 10 |
| 2005 AMC 12A | Three-digit numbers where middle digit is average of first and last. | Combinatorics | Counting | 11 |
| 2005 AMC 12A | Line through (1,1) and (100,1000); count integer points strictly between. | Geometry | Coordinate Geometry | 12 |
| 2005 AMC 12A | Five-pointed star with numbers; sums form arithmetic sequence; find middle term. | Algebra | Sequences & Series | 13 |
| 2005 AMC 12A | Dot removed from die, then rolled; probability top face has odd dots. | Combinatorics | Probability | 14 |
| 2005 AMC 12A | Diameter AB, point C on AB, D and E on circle; find ratio of triangle areas. | Geometry | Circular Geometry | 15 |
| 2005 AMC 12A | Three small circles tangent to axes and each other; find ratio r/s. | Geometry | Circular Geometry | 16 |
| 2005 AMC 12A | Unit cube cut into prisms then again; find volume of piece containing vertex W. | Geometry | 3D Geometry & Solids | 17 |
| 2005 AMC 12A | Prime-looking numbers composite not divisible by 2,3,5; count under 1000. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2005 AMC 12A | Odometer skips digit 4; reading 002005; find actual miles traveled. | Number Theory | Modular Arithmetic | 19 |
| 2005 AMC 12A | Piecewise function f iterated 2005 times equals 1/2; count solutions in [0,1]. | Algebra | Functions | 20 |
| 2005 AMC 12A | Ordered triples (a,b,c) with log_a b = c^2005 and a+b+c=2005; count them. | Algebra | Logarithms & Exponents | 21 |
| 2005 AMC 12A | Rectangular box inscribed in sphere; surface area 384, edge sum 112; find radius. | Geometry | 3D Geometry & Solids | 22 |
| 2005 AMC 12A | Two distinct numbers from powers of 2; probability log base a of b is integer. | Combinatorics | Probability | 23 |
| 2005 AMC 12A | P(x)=(x-1)(x-2)(x-3); count quadratics Q such that P(Q(x)) = P(x)R(x). | Algebra | Polynomials | 24 |
| 2005 AMC 12A | Points with coordinates from {0,1,2}; count equilateral triangles with vertices in set. | Geometry | 3D Geometry & Solids | 25 |
| 2005 AMC 12B | Profit from buying 1000 candy bars at five for $2 and selling at two for $1. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2005 AMC 12B | Find x such that x% of x equals 4. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2005 AMC 12B | Fraction of money left after buying all CDs given one fifth buys one third. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2005 AMC 12B | Maximum number of remaining quizzes Lisa can score below an A. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2005 AMC 12B | Shaded area of tiled bathroom floor with quarter-circle patterns. | Geometry | Circular Geometry | 5 |
| 2005 AMC 12B | Find BD in triangle ABC with AC=BC=7, AB=2, and CD=8. | Geometry | Triangles & Polygons | 6 |
| 2005 AMC 12B | Area enclosed by the graph of |3x|+|4y|=12. | Geometry | Coordinate Geometry | 7 |
| 2005 AMC 12B | Number of a such that y=x+a passes through vertex of y=x^2+a^2. | Algebra | Functions | 8 |
| 2005 AMC 12B | Difference between mean and median score on an exam with given percentages. | Algebra | Rates, Mixtures, & Averages | 9 |
| 2005 AMC 12B | 2005th term of sequence where each term is sum of cubes of digits of previous. | Algebra | Sequences & Series | 10 |
| 2005 AMC 12B | Probability sum of two random bills from envelope is $20 or more. | Combinatorics | Probability | 11 |
| 2005 AMC 12B | Find n/p given quadratic x^2+mx+n has roots twice those of x^2+px+m. | Algebra | Polynomials | 12 |
| 2005 AMC 12B | Product x1*x2*...*x124 given 4^x1=5, 5^x2=6, ..., 127^x124=128. | Algebra | Logarithms & Exponents | 13 |
| 2005 AMC 12B | Radius of circle centered at (0,k) tangent to y=x, y=-x, and y=6. | Geometry | Circular Geometry | 14 |
| 2005 AMC 12B | Digit not used among eight digits of four two-digit numbers summing to 221. | Number Theory | Modular Arithmetic | 15 |
| 2005 AMC 12B | Radius of smallest sphere centered at origin containing eight unit spheres. | Geometry | 3D Geometry & Solids | 16 |
| 2005 AMC 12B | Number of rational quadruples (a,b,c,d) satisfying log equation equal to 2005. | Algebra | Logarithms & Exponents | 17 |
| 2005 AMC 12B | Area of region R of points C making triangle ABC acute with A(2,2), B(7,7). | Geometry | Coordinate Geometry | 18 |
| 2005 AMC 12B | Find x+y+m given x and y are two-digit reversals and x^2-y^2=m^2. | Number Theory | Factors, Multiples & Divisibility | 19 |
| 2005 AMC 12B | Minimum possible value of (a+b+c+d)^2+(e+f+g+h)^2 from given set. | Algebra | Inequalities | 20 |
| 2005 AMC 12B | Greatest k such that 7^k divides n, where n has 60 divisors and 7n has 80. | Number Theory | Factors, Multiples & Divisibility | 21 |
| 2005 AMC 12B | Number of possible z0 given z_{n+1}=i z_n / conjugate(z_n) and z_{2005}=1. | Algebra | Complex Numbers | 22 |
| 2005 AMC 12B | Find a+b given x^3+y^3 = a*10^{3z}+b*10^{2z} with log constraints. | Algebra | Logarithms & Exponents | 23 |
| 2005 AMC 12B | Sum of x-coordinates of equilateral triangle vertices on y=x^2 with side slope 2. | Geometry | Coordinate Geometry | 24 |
| 2005 AMC 12B | Probability six ants on octahedron vertices move to adjacent vertices without collision. | Combinatorics | Probability | 25 |
| 2004 AMC 12A | Alicia earns $20 per hour; 1.45% is deducted for local taxes. Find cents per hour deducted. | Algebra | Rates, Mixtures, & Averages | 1 |
| 2004 AMC 12A | Charlyn leaves 8 of 25 problems unanswered; find how many correct to score at least 100. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2004 AMC 12A | Find number of ordered positive integer pairs (x,y) satisfying x + 2y = 100. | Combinatorics | Counting | 3 |
| 2004 AMC 12A | Bertha has 6 daughters; some have 6 daughters. Total 30 women. Find how many have no daughters. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2004 AMC 12A | Given graph of line y=mx+b, determine which inequality about mb is true. | Geometry | Coordinate Geometry | 5 |
| 2004 AMC 12A | Given expressions U through Z involving powers of 2004, find which difference is largest. | Algebra | Logarithms & Exponents | 6 |
| 2004 AMC 12A | Three players with tokens; each round the leader gives one token to each other and discards one. Find number of rounds. | Algebra | Sequences & Series | 7 |
| 2004 AMC 12A | Two overlapping right triangles share side AB; find difference in areas of triangles ADE and BDC. | Geometry | Triangles & Polygons | 8 |
| 2004 AMC 12A | Cylindrical jar diameter increased 25% without changing volume; find percent height decrease. | Geometry | 3D Geometry & Solids | 9 |
| 2004 AMC 12A | Sum of 49 consecutive integers is 7^5; find their median. | Algebra | Sequences & Series | 10 |
| 2004 AMC 12A | Average value of coins in purse is 20 cents; adding a quarter makes average 21. Find number of dimes. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2004 AMC 12A | Points A(0,9) and B(0,12); lines AA' and BB' intersect at C(2,8); A',B' on y=x. Find A'B' length. | Geometry | Coordinate Geometry | 12 |
| 2004 AMC 12A | Set S of points (a,b) with a,b in {-1,0,1}. Count distinct lines through at least two points of S. | Combinatorics | Counting | 13 |
| 2004 AMC 12A | Arithmetic progression with first term 9; adding 2 to second and 20 to third yields geometric progression. Find smallest possible third term of geometric progression. | Algebra | Sequences & Series | 14 |
| 2004 AMC 12A | Brenda and Sally run opposite directions on circular track from opposite points; find track length. | Algebra | Rates, Mixtures, & Averages | 15 |
| 2004 AMC 12A | Find smallest x such that the nested logarithm expression is defined. | Algebra | Logarithms & Exponents | 16 |
| 2004 AMC 12A | Function f defined by f(1)=1 and f(2n)=n*f(n); find f(2^100). | Algebra | Functions | 17 |
| 2004 AMC 12A | Square ABCD side 2; semicircle on AB inside square; tangent from C meets AD at E. Find CE length. | Geometry | Circular Geometry | 18 |
| 2004 AMC 12A | Three externally tangent circles A(radius 1), B, C; internally tangent to circle D. Find radius of B. | Geometry | Circular Geometry | 19 |
| 2004 AMC 12A | Select a,b in [0,1] randomly; let c=a+b. A,B,C are a,b,c rounded to nearest integer. Find P(A+B=C). | Combinatorics | Probability | 20 |
| 2004 AMC 12A | Infinite sum of cos^(2n)(theta) equals 5; find cos(2theta). | Algebra | Sequences & Series | 21 |
| 2004 AMC 12A | Three unit spheres on plane; sphere radius 2 rests on them. Find distance from plane to top of larger sphere. | Geometry | 3D Geometry & Solids | 22 |
| 2004 AMC 12A | Polynomial with real coefficients, 2004 distinct complex zeros; given sum of real parts equals sum of imaginary parts. Find which quantity can be nonzero. | Algebra | Polynomials | 23 |
| 2004 AMC 12A | Plane contains points A,B with AB=1; S is union of all unit disks covering AB. Find area of S. | Geometry | Circular Geometry | 24 |
| 2004 AMC 12A | For n>=4, a_n = 0.overline{133}_n (base n). Find product a_4*a_5*...*a_99 expressed as m/n! with minimal n; find m. | Algebra | Sequences & Series | 25 |
| 2004 AMC 12B | Jenny doubles free throws each practice; fifth practice she makes 48. Find first practice count. | Algebra | Sequences & Series | 1 |
| 2004 AMC 12B | Maximize c·a^b - d using digits 0,1,2,3 each once. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2004 AMC 12B | Find x+y given 2^x * 3^y = 1296 with positive integers x,y. | Number Theory | Factors, Multiples & Divisibility | 3 |
| 2004 AMC 12B | Probability a two-digit integer from 10-99 has at least one digit 7. | Combinatorics | Probability | 4 |
| 2004 AMC 12B | Isabella exchanges US to Canadian dollars; find sum of digits of initial amount. | Algebra | Rates, Mixtures, & Averages | 5 |
| 2004 AMC 12B | Find distance between two cities given distances and directions from airport. | Geometry | Triangles & Polygons | 6 |
| 2004 AMC 12B | Area of union of a square and a circle centered at a vertex. | Geometry | Circular Geometry | 7 |
| 2004 AMC 12B | Number of rows in a can display where each row has two more cans than above. | Algebra | Sequences & Series | 8 |
| 2004 AMC 12B | Coordinates after rotating point 90° clockwise then reflecting over y=x. | Geometry | Coordinate Geometry | 9 |
| 2004 AMC 12B | Find area of annulus in terms of tangent segment length a. | Geometry | Circular Geometry | 10 |
| 2004 AMC 12B | Smallest class size given five 100s, all ≥60, mean 76. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2004 AMC 12B | Find 2004th term of sequence defined by subtracting previous from sum of two before. | Algebra | Sequences & Series | 12 |
| 2004 AMC 12B | Find a+b given f(x)=ax+b and f^{-1}(x)=bx+a with a,b real. | Algebra | Functions | 13 |
| 2004 AMC 12B | Area of pentagon formed by perpendiculars from points on legs of right triangle. | Geometry | Triangles & Polygons | 14 |
| 2004 AMC 12B | Difference in ages when Jack's age digits reverse Bill's; in 5 years Jack twice Bill. | Algebra | Systems & Algebraic Manipulation | 15 |
| 2004 AMC 12B | Number of complex z with |z|=5 and f(z)=i*conjugate(z)=z. | Algebra | Complex Numbers | 16 |
| 2004 AMC 12B | Find a given cubic with three positive roots; sum of base-2 logs of roots is 5. | Algebra | Polynomials | 17 |
| 2004 AMC 12B | Length of segment AB on parabola y=4x^2+7x-1 with origin as midpoint. | Geometry | Coordinate Geometry | 18 |
| 2004 AMC 12B | Radius of sphere tangent to top, bottom, and lateral surface of truncated cone. | Geometry | 3D Geometry & Solids | 19 |
| 2004 AMC 12B | Probability cube can be placed so four vertical faces same color. | Combinatorics | Probability | 20 |
| 2004 AMC 12B | Sum of max and min of y/x over points on ellipse in first quadrant. | Geometry | Conic Sections | 21 |
| 2004 AMC 12B | Sum of possible values of g in multiplicative magic square with positive integers. | Number Theory | Factors, Multiples & Divisibility | 22 |
| 2004 AMC 12B | Number of possible n for cubic with integer coefficients and three distinct positive roots. | Algebra | Polynomials | 23 |
| 2004 AMC 12B | Area of isosceles triangle given tangents form geometric and arithmetic progressions. | Geometry | Trigonometry | 24 |
| 2004 AMC 12B | Number of powers of 2 from 2^0 to 2^2003 with first digit 4. | Number Theory | Logarithms & Exponents | 25 |
| 2003 AMC 12A | Difference between sum of first 2003 even and odd numbers | Algebra | Sequences & Series | 1 |
| 2003 AMC 12A | Number of soccer league members given total cost | Algebra | Rates, Mixtures, & Averages | 2 |
| 2003 AMC 12A | Percent of original volume removed from box corners | Geometry | 3D Geometry & Solids | 3 |
| 2003 AMC 12A | Average speed for round trip uphill and downhill | Algebra | Rates, Mixtures, & Averages | 4 |
| 2003 AMC 12A | Sum of digits A+M+C from sum of two 5-digit numbers | Algebra | Systems & Algebraic Manipulation | 5 |
| 2003 AMC 12A | Which statement about a custom absolute value operation is false | Algebra | Functions | 6 |
| 2003 AMC 12A | Number of non-congruent triangles with integer sides and perimeter 7 | Combinatorics | Counting | 7 |
| 2003 AMC 12A | Probability a random positive factor of 60 is less than 7 | Combinatorics | Probability | 8 |
| 2003 AMC 12A | Smallest number of points in a set symmetric about origin and axes | Geometry | Coordinate Geometry | 9 |
| 2003 AMC 12A | Fraction of candy unclaimed after three people take wrong shares | Algebra | Rates, Mixtures, & Averages | 10 |
| 2003 AMC 12A | Ratio of areas of circles circumscribed about square and triangle | Geometry | Circular Geometry | 11 |
| 2003 AMC 12A | Sum of numbers on middle three alternating color cards | Combinatorics | Counting | 12 |
| 2003 AMC 12A | Number of positions to attach a square to form a cube missing one face | Geometry | 3D Geometry & Solids | 13 |
| 2003 AMC 12A | Area of square formed by outer vertices of four equilateral triangles | Geometry | Triangles & Polygons | 14 |
| 2003 AMC 12A | Area of lune formed by two semicircles | Geometry | Circular Geometry | 15 |
| 2003 AMC 12A | Probability triangle ABP has greatest area among three subtriangles | Combinatorics | Probability | 16 |
| 2003 AMC 12A | Distance from intersection point of two circles to side of square | Geometry | Circular Geometry | 17 |
| 2003 AMC 12A | Number of 5-digit numbers where quotient plus remainder is divisible by 11 | Number Theory | Modular Arithmetic | 18 |
| 2003 AMC 12A | Graph of sum of reflected and translated parabolas | Algebra | Functions | 19 |
| 2003 AMC 12A | Number of 15-letter arrangements with restrictions on positions of letters | Combinatorics | Counting | 20 |
| 2003 AMC 12A | Which coefficient of a quintic with five distinct x-intercepts cannot be zero | Algebra | Polynomials | 21 |
| 2003 AMC 12A | Probability two objects moving randomly on grid meet | Combinatorics | Probability | 22 |
| 2003 AMC 12A | Number of perfect square divisors of product of factorials 1! through 9! | Number Theory | Factors, Multiples & Divisibility | 23 |
| 2003 AMC 12A | Largest possible value of sum of two log expressions | Algebra | Logarithms & Exponents | 24 |
| 2003 AMC 12A | Number of real a such that domain and range of sqrt(ax^2+bx) are equal | Algebra | Functions | 25 |
| 2003 AMC 12B | Simplify a fraction with alternating signs in numerator and denominator. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2003 AMC 12B | Find the cost of one green pill given total cost for two weeks. | Algebra | Rates, Mixtures, & Averages | 2 |
| 2003 AMC 12B | Minimize cost of planting flowers in rectangular regions of a flower bed. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2003 AMC 12B | Find time to mow a rectangular lawn with overlapping swath. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2003 AMC 12B | Find horizontal length of a TV screen given diagonal and aspect ratio. | Geometry | Triangles & Polygons | 5 |
| 2003 AMC 12B | Find a possible first term of a geometric sequence given two terms. | Algebra | Sequences & Series | 6 |
| 2003 AMC 12B | Find the largest integer dividing (n+1)(n+3)(n+5)(n+7)(n+9) for all even n. | Number Theory | Factors, Multiples & Divisibility | 7 |
| 2003 AMC 12B | Find the ratio of cone height to radius if melted ice cream fills the cone. | Number Theory | Factors, Multiples & Divisibility | 8 |
| 2003 AMC 12B | Linear function f satisfies f(6) - f(2) = 12; find f(12) - f(2). | Algebra | Functions | 9 |
| 2003 AMC 12B | Count non-congruent figures made by attaching two equilateral triangles to a regular pentagon in two of five positions. | Combinatorics | Counting | 10 |
| 2003 AMC 12B | Find a+b+c+d for the minimum x satisfying 7x^5 = 11y^13. | Algebra | Rates, Mixtures, & Averages | 11 |
| 2003 AMC 12B | Find probability second term is 2 in random permutation of 1-5 with first term not 1. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2003 AMC 12B | Find the ratio of cone height to radius given ice cream sphere melts to fill cone. | Geometry | 3D Geometry & Solids | 13 |
| 2003 AMC 12B | Find area of triangle formed by intersecting lines in a rectangle. | Geometry | Triangles & Polygons | 14 |
| 2003 AMC 12B | Find area of rectangle inside a regular octagon of unit area. | Geometry | Triangles & Polygons | 15 |
| 2003 AMC 12B | Find shaded area inside large semicircle but outside three smaller semicircles. | Geometry | Circular Geometry | 16 |
| 2003 AMC 12B | Find minimum c so system 2x+y=2003, y=|x-a|+|x-b|+|x-c| has exactly one solution. | Algebra | Logarithms & Exponents | 17 |
| 2003 AMC 12B | Find probability all three pairwise distances on a circle are less than the radius. | Number Theory | Factors, Multiples & Divisibility | 18 |
| 2003 AMC 12B | Probability that second term is 2 in random permutation of 1-5 with first term not 1. | Combinatorics | Probability | 19 |
| 2003 AMC 12B | Find coefficient b of cubic given graph with roots at -1, 0, 1. | Algebra | Polynomials | 20 |
| 2003 AMC 12B | Probability that distance AC is less than 7 given random turn angle. | Geometry | Trigonometry | 21 |
| 2003 AMC 12B | Minimum distance from point on rhombus side to intersection of perpendiculars to diagonals. | Geometry | Triangles & Polygons | 22 |
| 2003 AMC 12B | Number of x-intercepts of sin(1/x) in interval (0.0001, 0.001). | Algebra | Functions | 23 |
| 2003 AMC 12B | Minimum c such that system with absolute values has exactly one solution. | Algebra | Functions | 24 |
| 2003 AMC 12B | Probability all three pairwise distances on a circle are less than the radius. | Combinatorics | Probability | 25 |
| 2002 AMC 12A | Sum of all roots of (2x+3)(x-4)+(2x+3)(x-6)=0 | Algebra | Polynomials | 1 |
| 2002 AMC 12A | Find correct result after reversing subtraction and division steps | Algebra | Systems & Algebraic Manipulation | 2 |
| 2002 AMC 12A | Number of distinct values from different parenthesizations of 2^2^2^2 | Algebra | Logarithms & Exponents | 3 |
| 2002 AMC 12A | Find angle whose complement is 25% of its supplement | Algebra | Systems & Algebraic Manipulation | 4 |
| 2002 AMC 12A | Area of shaded region in concentric circles with tangent small circles | Geometry | Circular Geometry | 5 |
| 2002 AMC 12A | Number of positive integers m with n such that m*n ≤ m+n | Algebra | Inequalities | 6 |
| 2002 AMC 12A | Ratio of areas of two circles given equal arc lengths | Geometry | Circular Geometry | 7 |
| 2002 AMC 12A | Compare areas of blue triangles, white squares, and red square in flag | Geometry | Triangles & Polygons | 8 |
| 2002 AMC 12A | Minimum number of disks to store files of given sizes | Algebra | Rates, Mixtures, & Averages | 9 |
| 2002 AMC 12A | Fraction of cream in first cup after mixing coffee and cream | Algebra | Rates, Mixtures, & Averages | 10 |
| 2002 AMC 12A | Speed needed to arrive exactly on time given early/late data | Algebra | Rates, Mixtures, & Averages | 11 |
| 2002 AMC 12A | Number of possible k such that quadratic has both roots prime | Algebra | Polynomials | 12 |
| 2002 AMC 12A | Sum of two positive numbers each differing from reciprocal by 1 | Algebra | Systems & Algebraic Manipulation | 13 |
| 2002 AMC 12A | Evaluate N = f(11)+f(13)+f(14) with f(n)=log_{2002} n^2 | Algebra | Logarithms & Exponents | 14 |
| 2002 AMC 12A | Largest possible integer in set of eight with mean, median, mode, range 8 | Algebra | Rates, Mixtures, & Averages | 15 |
| 2002 AMC 12A | Probability Sergio's number exceeds sum of Tina's two distinct numbers | Combinatorics | Probability | 16 |
| 2002 AMC 12A | Smallest possible sum of primes using each nonzero digit once | Number Theory | Factors, Multiples & Divisibility | 17 |
| 2002 AMC 12A | Length of common external tangent segment between two circles | Geometry | Circular Geometry | 18 |
| 2002 AMC 12A | Number of solutions to f(f(x))=6 from piecewise linear graph | Algebra | Functions | 19 |
| 2002 AMC 12A | Number of possible denominators for 0.overline{ab} in lowest terms | Number Theory | Factors, Multiples & Divisibility | 20 |
| 2002 AMC 12A | Smallest n such that sum of Fibonacci-like digit sequence exceeds 10000 | Algebra | Sequences & Series | 21 |
| 2002 AMC 12A | Probability that BD > 5√2 for random point P in right triangle | Geometry | Triangles & Polygons | 22 |
| 2002 AMC 12A | Area of triangle ABD given AD=9, DC=7, with perpendicular bisector and angle bisector | Geometry | Triangles & Polygons | 23 |
| 2002 AMC 12A | Number of ordered pairs (a,b) such that (a+bi)^2002 = a-bi | Algebra | Complex Numbers | 24 |
| 2002 AMC 12A | Identify graph of polynomial P and Q where coefficients replaced by mean | Algebra | Polynomials | 25 |
| 2002 AMC 12B | Find the missing digit in the arithmetic mean of nine numbers consisting of repeated 9s. | Algebra | Sequences & Series | 1 |
| 2002 AMC 12B | Evaluate an algebraic expression at x=4 by simplifying or substituting. | Algebra | Systems & Algebraic Manipulation | 2 |
| 2002 AMC 12B | Count positive integers n for which n^2-3n+2 is prime. | Number Theory | Factors, Multiples & Divisibility | 3 |
| 2002 AMC 12B | Determine which statement about n is false given the sum is an integer. | Number Theory | Factors, Multiples & Divisibility | 4 |
| 2002 AMC 12B | Find the middle term of an arithmetic sequence of pentagon angles summing to 540. | Algebra | Sequences & Series | 5 |
| 2002 AMC 12B | Find the pair (a,b) given that a and b are roots of x^2+ax+b=0. | Algebra | Polynomials | 6 |
| 2002 AMC 12B | Find the sum of squares of three consecutive positive integers with given product-sum relation. | Algebra | Systems & Algebraic Manipulation | 7 |
| 2002 AMC 12B | Determine which weekday must appear five times in August given July has five Mondays. | Number Theory | Modular Arithmetic | 8 |
| 2002 AMC 12B | Find a/d given a,b,c,d form an increasing arithmetic and a,b,d a geometric sequence. | Algebra | Sequences & Series | 9 |
| 2002 AMC 12B | Count distinct sums of three distinct members from the set {1,4,7,...,19}. | Combinatorics | Counting | 10 |
| 2002 AMC 12B | Determine the nature of the sum of four primes A, B, A-B, A+B. | Number Theory | Factors, Multiples & Divisibility | 11 |
| 2002 AMC 12B | Count integers n for which n/(20-n) is a perfect square. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2002 AMC 12B | Find the smallest perfect square sum of 18 consecutive positive integers. | Algebra | Sequences & Series | 13 |
| 2002 AMC 12B | Find the maximum number of intersection points among four distinct circles. | Combinatorics | Counting | 14 |
| 2002 AMC 12B | Count four-digit numbers N where removing the leftmost digit gives N/9. | Algebra | Systems & Algebraic Manipulation | 15 |
| 2002 AMC 12B | Find probability that product of an octahedral and a six-sided die roll is a multiple of 3. | Combinatorics | Probability | 16 |
| 2002 AMC 12B | Determine who finishes mowing first given lawn areas and mower speeds. | Algebra | Rates, Mixtures, & Averages | 17 |
| 2002 AMC 12B | Find probability a point in a rectangle is closer to the origin than to (3,1). | Combinatorics | Probability | 18 |
| 2002 AMC 12B | Find abc given a(b+c)=152, b(c+a)=162, c(a+b)=170. | Algebra | Systems & Algebraic Manipulation | 19 |
| 2002 AMC 12B | Find XY in a right triangle given distances from vertices to midpoints of legs. | Geometry | Triangles & Polygons | 20 |
| 2002 AMC 12B | Sum a_n for n<2002 where a_n depends on divisibility by 11,13,14. | Number Theory | Factors, Multiples & Divisibility | 21 |
| 2002 AMC 12B | Compute b-c where b and c are sums of reciprocals of logs base n of 2002. | Algebra | Logarithms & Exponents | 22 |
| 2002 AMC 12B | Find BC in triangle ABC where median from A equals BC, AB=1, AC=2. | Geometry | Triangles & Polygons | 23 |
| 2002 AMC 12B | Find perimeter of convex quadrilateral with interior point P and given distances. | Geometry | Triangles & Polygons | 24 |
| 2002 AMC 12B | Find area of region defined by f(x)+f(y)≤0 and f(x)-f(y)≤0 where f(x)=x^2+6x+1. | Geometry | Coordinate Geometry | 25 |
| 2001 AMC 12 | Two numbers sum to S; add 3 to each, double each, find new sum. | Algebra | Systems & Algebraic Manipulation | 1 |
| 2001 AMC 12 | Two-digit number N equals product plus sum of its digits; find units digit. | Number Theory | Factors, Multiples & Divisibility | 2 |
| 2001 AMC 12 | Find annual income given a piecewise tax rate equals a flat percentage. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2001 AMC 12 | Mean is 10 more than least and 15 less than greatest; median is 5; find sum. | Algebra | Rates, Mixtures, & Averages | 4 |
| 2001 AMC 12 | Find expression for product of all positive odd integers less than 10000. | Algebra | Sequences & Series | 5 |
| 2001 AMC 12 | Phone number with decreasing digits in each part; find A given sum condition. | Combinatorics | Counting | 6 |
| 2001 AMC 12 | 140 tickets sold for $2001; full and half price; find full-price ticket revenue. | Algebra | Rates, Mixtures, & Averages | 7 |
| 2001 AMC 12 | Cone formed from a 252° sector of radius 10; find slant height and radius. | Geometry | 3D Geometry & Solids | 8 |
| 2001 AMC 12 | Function f(xy)=f(x)/y for positive reals; f(500)=3; find f(600). | Algebra | Functions | 9 |
| 2001 AMC 12 | Plane tiled with squares and pentagons; find percent enclosed by pentagons. | Geometry | Triangles & Polygons | 10 |
| 2001 AMC 12 | 5 chips (3 red, 2 white) drawn without replacement; probability last chip is white. | Combinatorics | Probability | 11 |
| 2001 AMC 12 | Count positive integers ≤2001 that are multiples of 3 or 4 but not 5. | Number Theory | Factors, Multiples & Divisibility | 12 |
| 2001 AMC 12 | Parabola reflected about horizontal line through vertex; find sum of coefficients. | Algebra | Functions | 13 |
| 2001 AMC 12 | Regular 9-gon; count distinct equilateral triangles with at least two vertices from set. | Combinatorics | Counting | 14 |
| 2001 AMC 12 | Shortest path on tetrahedron surface from midpoint of edge to opposite edge midpoint. | Geometry | 3D Geometry & Solids | 15 |
| 2001 AMC 12 | Spider puts on sock then shoe on each of 8 legs; count possible orders. | Combinatorics | Counting | 16 |
| 2001 AMC 12 | Random point in pentagon; probability angle APB is obtuse. | Geometry | Coordinate Geometry | 17 |
| 2001 AMC 12 | Two externally tangent circles of radii 1 and 4; find radius of circle tangent to both and common external tangent. | Geometry | Circular Geometry | 18 |
| 2001 AMC 12 | Cubic with average of zeros, product of zeros, sum of coefficients equal; y-intercept 2; find b. | Algebra | Polynomials | 19 |
| 2001 AMC 12 | Quadrilateral ABCD in first quadrant; midpoints form a square; find sum of coordinates of D. | Geometry | Coordinate Geometry | 20 |
| 2001 AMC 12 | Four positive integers with product 8! satisfy three equations; find a-d. | Number Theory | Factors, Multiples & Divisibility | 21 |
| 2001 AMC 12 | Rectangle area 70; points E,F,G on sides; find area of triangle EHJ. | Geometry | Triangles & Polygons | 22 |
| 2001 AMC 12 | Degree-4 polynomial with leading coefficient 1, integer coefficients, two integer zeros; which complex number can be a zero? | Algebra | Polynomials | 23 |
| 2001 AMC 12 | Triangle ABC with angle ABC=45°, D on BC with 2·BD=CD, angle DAB=15°; find angle ACB. | Geometry | Trigonometry | 24 |
| 2001 AMC 12 | Sequence: each term after first is 1 less than product of neighbors; find how many x make 2001 appear. | Algebra | Sequences & Series | 25 |
| 2000 AMC 12 | Find largest sum of three distinct positive integers whose product is 2001. | Number Theory | Factors, Multiples & Divisibility | 1 |
| 2000 AMC 12 | Simplify the expression 2000(2000^{2000}). | Algebra | Logarithms & Exponents | 2 |
| 2000 AMC 12 | Find original number of jellybeans given 20% eaten each day and 32 left after two days. | Algebra | Rates, Mixtures, & Averages | 3 |
| 2000 AMC 12 | Find which digit is last to appear in the units place of Fibonacci numbers. | Number Theory | Modular Arithmetic | 4 |
| 2000 AMC 12 | If |x-2|=p and x<2, find x-p in terms of p. | Algebra | Functions | 5 |
| 2000 AMC 12 | Find which number could be pq-(p+q) for two primes between 4 and 18. | Number Theory | Factors, Multiples & Divisibility | 6 |
| 2000 AMC 12 | Count positive integers b such that log_b(729) is a positive integer. | Algebra | Logarithms & Exponents | 7 |
| 2000 AMC 12 | Find number of unit squares in figure 100 of a pattern. | Algebra | Sequences & Series | 8 |
| 2000 AMC 12 | Find last score entered given each partial average was an integer. | Number Theory | Modular Arithmetic | 9 |
| 2000 AMC 12 | Find coordinates after reflecting, rotating, and translating a 3D point. | Geometry | Coordinate Geometry | 10 |
| 2000 AMC 12 | Find possible value of a/b + b/a - ab given ab = a - b. | Algebra | Systems & Algebraic Manipulation | 11 |
| 2000 AMC 12 | Maximize AMC+AM+MC+AC given A+M+C=12 with nonnegative integers. | Algebra | Inequalities | 12 |
| 2000 AMC 12 | Find number of family members given Angela drank 1/4 milk and 1/6 coffee. | Algebra | Rates, Mixtures, & Averages | 13 |
| 2000 AMC 12 | Find sum of all x such that mean, median, mode form an arithmetic progression. | Algebra | Rates, Mixtures, & Averages | 14 |
| 2000 AMC 12 | Find sum of z satisfying f(3z)=7 given f(x/3)=x^2+x+1. | Algebra | Functions | 15 |
| 2000 AMC 12 | Find sum of numbers that are the same in row-major and column-major numbering. | Algebra | Systems & Algebraic Manipulation | 16 |
| 2000 AMC 12 | Find OC in terms of theta given tangent and angle bisector in a circle. | Geometry | Trigonometry | 17 |
| 2000 AMC 12 | Find day of week for 100th day of year N-1 given conditions on Tuesdays. | Number Theory | Modular Arithmetic | 18 |
| 2000 AMC 12 | Find area of triangle ADE where D is midpoint and E is foot of angle bisector. | Geometry | Triangles & Polygons | 19 |
| 2000 AMC 12 | Find xyz given three equations relating x, y, z and their reciprocals. | Algebra | Systems & Algebraic Manipulation | 20 |
| 2000 AMC 12 | Find ratio of area of small triangle to square in a right triangle with parallel lines. | Geometry | Triangles & Polygons | 21 |
| 2000 AMC 12 | Find smallest among five expressions involving a quartic polynomial from its graph. | Algebra | Polynomials | 22 |
| 2000 AMC 12 | Find probability winning ticket has same property: sum of logs of six numbers is integer. | Number Theory | Factors, Multiples & Divisibility | 23 |
| 2000 AMC 12 | Find circumference of circle tangent to two circular arcs and a line segment. | Geometry | Circular Geometry | 24 |
| 2000 AMC 12 | Count distinguishable colorings of a regular octahedron with 8 colors. | Combinatorics | Counting | 25 |
Two cyclists leave from the same point at different times and speeds; find when they are equidistant from the start.
Two nut mixes with different percentages are combined; find the pounds of cashews in the final mix.
Ash joins student or teacher teams, changing their average ages; find Ash's age.
Four statements about truth/false counts are given; determine how many are false.
An infinite pattern of nested squares with alternating shading; find the side-length ratio k.
Six chairs around a round table; find probability that two students and two teachers sit in adjacent pairs.
Given log equations relating running speed to toes and eyes, find the sum of constants k, a, b.
Pentagon inscribed in a circle with given angles and side lengths; find the length BF.
Find the real number r such that r, w, and w^2 are collinear in the complex plane.
Two concentric arcs and segments of length 2π; find the distance from the center to point A.
Given coordinates of triangle vertices, find the sum of the coordinates of the orthocenter.
Find the harmonic mean of all real roots of a product of 2025 quadratics.
Find the probability that a maximal subset of {1,...,13} with no five consecutive integers is chosen.
Two ellipses with same eccentricity, one internally tangent to the other; find the eccentricity e.
Find the maximum size of a sum-free subset of {1, 2, ..., 20}.
Triangle with given side lengths; find the length from vertex B to intersection of angle bisector and altitude.
Find the area of the triangle formed by the three roots of a given cubic polynomial.
Count ordered triples of distinct integers from 1 to 8 satisfying xy > z, xz > y, yz > x.
Given roots a, b, c of x^3 + kx + 1, find the value of a symmetric sum expression.
Find the volume of a pentahedron with a rectangular base and given lateral faces.
Solve for nonnegative integers a, k, m in a geometric series ratio equation equal to 964.
Three random numbers in [0,1]; find probability the greatest exceeds twice each of the others.
Count positive integers with no repeated digits, no 0s, and no digit adjacent to two greater digits.
A central circle is surrounded by 12 unit circles; find the radius r of the central circle.
Count ordered pairs of monic cubic polynomials with roots in {1,...,5} such that f(x) ≤ 0 on [a,b]∪(c,d).
Find max number of 20-gram coffee mugs from a 350-gram bag
Sum of ones digits of first 2025 positive squares.
Value of i(i-1)(i-2)(i-3) where i = sqrt(-1).
Two-digit numbers in base 7 and base 9 are equal; find a+b.
Positive integers x,y satisfy 57x+22y=400; minimize x+y.
Total cost ABB.BA is divisible by 36; find A+B.
Sum of a telescoping series with logarithms from n=2 to 255.
Polynomial x^3-5x^2+ax+b has root 4+sqrt(5); find a+b.
Tens digit of 6^(6^6).
Ratio x/(x+y) on altitude of 30-60-90 triangle divided by median.
Probability that the three tallest athletes are group captains.
Area cleaned by a windshield wiper sweeping a 60-degree arc.
Number of colorings of 6 sectors with 2 each of red, green, blue, no adjacent same.
Greatest n for decreasing sequence with given average conditions.
Time to fill remainder of a truncated pyramid container.
Tangent of acute angle between hour and minute hand after 2025 minutes.
Number of 3x3 grid colorings with red-blue-yellow adjacency constraints.
Expected number of games until at least one win and one loss.
Number of squares with same number in horizontal and vertical fillings.
Probability frog reaches 4 on number line with given transition rules.
Sum of integer third sides of two non-congruent triangles with sides 8,9 and equal area.
Greatest area of triangle with vertices 2z, (1+i)z, (1-i)z given |4z-2|=1.
Sum of integers z>1 such that remainders of 2025x mod z increase with x.
Number of real solutions to sin(20πx) = log_20(x).
Side length squared of equilateral triangle with vertices on concentric circles radii 1,2,3.
Evaluate 9901*101 - 99*10101.
Find hiking time given linear model T=aL+bG with two data points.
Least number of two-digit numbers summing to 2024.
Least n such that n! is a multiple of 2024.
Find how many 6s were in a data set given means.
Least possible positive sum of three integers with product 60.
Find the length of the sum of vectors from a vertex to points on the hypotenuse.
Find the number of angles theta satisfying a logarithmic equation.
Units digit of greatest M such that M+1213 and M+3773 are perfect squares.
Express the smallest angle of a 7-24-25 triangle in terms of that of a 3-4-5 triangle.
Count bases b between 5 and 2024 where 2024_b is divisible by 16.
Sum of digits of least b in geometric sequence a, 720, b with a<720<b.
Find the reflection of a point over the axis of symmetry of a graph.
Find entry (1,2) in 5x5 grid with arithmetic progressions in rows and columns.
Evaluate an expression involving the roots of a cubic polynomial.
Find the probability that each player gets specific colored tokens.
Find ab+bc+ca given ab+c=100, bc+a=87, ca+b=60.
Find how many cards are needed until a vertex lands on a given point.
Find the length of the shorter diagonal of a cyclic quadrilateral.
Find the probability that triangle area is less than half the total area.
Find the greatest integer less than or equal to a sum of squares from a recurrence.
Number of ways to place toothpicks forming a closed loop on an 8x3 grid with numbered cells.
Find the value of a trigonometric expression involving tangent squares.
Find the least total surface area of a disphenoid with integer side lengths.
Count quadruples of integers making a rational function symmetric about y=x.
Find total people given 1013th from left and 1010th from right.
Evaluate 10! - 7! * 6!.
Count integer x satisfying |2x| ≤ 7π.
Find bin for ball 2024 in a triangular deposit pattern.
Minimize sign flips to make sum of odds negative.
Find number of base-5 digits of 5×10^13.
Find area of right triangle WMA in a rectangle.
Solve equation with log_2 x and log_3 x.
Probability dart lands in annular region of a square.
Count ordered triples (x,y,z) given range, mean, median constraints.
Find mean of sin^2(1°) through sin^2(90°).
Find imaginary part of z given |z|=2 and quadrilateral area 15.
Minimize h+k given two circle equations in x and y.
Number of remainders of n^100 mod 125.
Area of triangle with vertices at log points.
Find exponent of 3 in number of committee assignments.
Probability cubic has 3 distinct integer roots.
Sum of ratios of Fibonacci numbers F_{2n}/F_n.
Find tanθ given area of hexagon from rotated equilateral triangle.
Find p+q+r+s for median length function of triangle.
Perimeter of third primitive triple with angles summing to 90°.
Least perimeter of triangle with angle B = 2A and integer sides.
Square of height of pyramid with regular octagon base.
Count triples of altitudes giving integer inradius.
Probability color and pattern are independent for selected ball.
Alicia and Beth bike toward each other from cities 45 miles apart; find meeting distance from Alicia's city.
Find weight of a large pizza given equal weights of pizza fractions and orange slices.
Count positive perfect squares less than 2023 that are divisible by 5.
Find number of digits in base-ten representation of 8^5 * 5^10 * 15^5.
Probability that running total of 4 die rolls equals 3 at some point.
Points A and B on y=log2(x) have midpoint (6,2); find positive difference of x-coordinates.
Count 2023 dates where each digit appears an even number of times in 8-digit display.
Find current mean quiz score given effect of one or three additional 11s.
Find ratio of shorter to longer leg in right triangle formed by inscribed squares.
Positive reals x,y satisfy y^3=x^2 and (y-x)^2=4y^2; find x+y.
Find acute angle between lines with slopes 2 and 1/3.
Evaluate alternating sum of cubes from 1^3 to 18^3.
Find total games in round-robin tournament given left-handed win 40% more than right-handed.
Count complex numbers z satisfying z^5 = conjugate(z).
Find angle theta so zigzag path across 100x30 field has total length 120 meters.
Maximize imaginary part of z given |1+z+z^2|=4; express as sqrt(m)/n.
Probability frog starting at 0 eventually lands at 10 with jump distances geometric.
Find radius of circle internally tangent to two unit circles and externally tangent to another.
Find product of all solutions to logarithmic equation with variable bases.
Find units digit of sum of 2023 numbers in 2023rd row of triangular array.
Probability d(Q,R) > d(R,S) for three random vertices of regular icosahedron.
Find f(2023) for function on positive integers with sum over divisors condition.
Count ordered pairs of positive reals (a,b) satisfying (1+2a)(2+2b)(2a+b)=32ab.
Count sequences of nested subsets of {1,...,10} with length at most 10.
Find coefficient a_{2023} in tangent multiple-angle formula for tan(2023x).
Pour juice from full glasses into a partial glass to equalize amounts.
Find original price given discount, tax, and maximum budget.
Find ratio of areas of circles circumscribing 3-4-5 and 5-12-13 right triangles.
Convert millimeters and meters to find area in square centimeters.
Find minimum guesses to guarantee finding a hidden 2x1 rectangle on a 3x3 grid.
Count intervals where polynomial with repeated roots is positive.
Find integer n for which a log expression is real.
Count subsets where the number of elements equals the least element.
Find area of region defined by nested absolute value inequality.
Find slope of line through intersection points of two tangent circles.
Maximize area of isosceles trapezoid with legs 1 and bases in ratio 2:1.
Find modulus of complex number z given a custom binary operation.
Find space diagonal of rectangular box given edge sum, surface area, volume.
Count integer pairs (a,b) so cubic has three distinct integer roots.
Determine which statements about gcd are true given a linear Diophantine equation.
Find largest non-representable value using 6, 10, 15 cent coins.
Find area of triangle with sides in arithmetic progression and a 120° angle.
Determine which statement about yearly quiz averages cannot be true.
Find probability each of 3 bins gets an odd number of 2023 balls.
Find probability frog lands within 1 unit after two 2-unit jumps.
Find shortest path on frustum surface from bottom to farthest top point.
Find which value of f(1) is impossible given a functional equation.
Find n such that product of n dice rolls has 936 possible values.
Find gcd of four numbers given product and pairwise lcm relations.
Find area of smaller pentagon formed by folding vertices of a regular pentagon.
Evaluate the continued fraction 3 + 1/(3 + 1/(3 + 1/3)).
Find the absolute difference between the first and second numbers given sum and relationships.
Identify the middle rectangle in a square arrangement.
Find the sum of digits of n given LCM(n,18)=180 and GCD(n,45)=15.
Count lattice points with taxicab distance at most 20 from origin.
Find the sum of all positive X such that the mean of the data set equals a value in the set.
Count colorings of five regions in a rectangle so touching regions differ.
Evaluate an infinite product of nested cube roots of 10.
Determine how many pieces of candy truth-tellers received based on yes/no answers.
Count ways to pair numbers 1-14 so each pair's larger is at least double the smaller.
Find the product of all x satisfying a logarithmic distance equation.
Find the cosine of angle CMD in a regular tetrahedron.
Find the area of a region in the complex plane defined by a Minkowski sum.
Evaluate an expression involving base-10 logarithms.
Find the volume of a box formed by adding 2 to each edge of a box with given polynomial roots.
Find the sum of digits of the fourth triangular number that is a perfect square.
Find p+q+r for the set of a where a trig equation has more than one solution.
Find the least n so that applying T_1 through T_n returns (1,0) to itself.
Count orderings of cards 1-13 that are picked up in exactly two passes.
Find BC/AD in an isosceles trapezoid given distances from point P to vertices.
Identify which polynomial is a factor of x^2022 + x^1011 + 1.
Find c when the area of a quadrilateral formed by roots and their reciprocals is maximized.
Count n up to 22 where the denominator of the harmonic sum is less than LCM(1..n).
Count 5-digit strings from 0-4 where at least j digits are less than j for j=1..4.
Find the ratio of largest to smallest segment length tangent to a circle.
Evaluate an expression involving a custom-defined absolute difference operation.
Find the area of a rhombus given a perpendicular segment and side lengths.
Determine how many of the first ten terms of a sequence are prime.
Count values of k for which the quadratic has two distinct integer roots.
Find coordinates after rotating a point about another point.
Count how many sets of ten consecutive integers contain exactly two multiples of 7.
Find the least possible mode given relationships between mode, median, and mean.
Identify the graph of an equation in the coordinate plane.
Find the minimum possible value of a term in an arithmetic sequence.
Find the perimeter of a quadrilateral in a regular hexagon.
Evaluate a sum of powers of complex numbers.
Find probability of dice rolls meeting two conditions.
Find area of region inside both a square and a rectangle.
Find tangent of angle formed by parabola intercepts.
Identify which number is not divisible by any prime less than 10.
Find greatest possible value of log base 2 of y given equations.
Count 4x4 binary arrays with given row and column sums.
Count initial configurations leading to a single filled center square after one transformation.
Find cosine of angle C in triangle with equilateral median intersection.
Find the sum of squares of coefficients of a polynomial given two remainder conditions.
Find the sum of areas of all circles tangent to three given circles.
Find probability Amelia's position exceeds 1 given random step durations and increments.
Find the value of a binary-weighted sum given a modular condition on partial sums.
Sum of 4th powers of all chords in a regular heptagon.
Find area of 12-sided polygon formed by hexagons around a square.
Evaluate (2112-2021)^2 / 169.
Evaluate 2^(1+2+3) - (2^1+2^2+2^3).
Find area after shortening the other side of a 4x6 card by 1 inch.
Find conditions for sqrt(a^2+b^2)=a+b to hold.
Compare travel times on two routes to find time saved.
Find difference of two numbers given sum and digit condition.
Find digit A so that 20210A is prime.
Determine which conclusion follows from statements about snakes.
Find difference in leap length between emu and ostrich strides.
Find two-digit number ab from repeating decimal multiplication error.
Find angle AFE in a square with given angle and isosceles triangle.
Find original number of cards given probability changes.
Compute difference between teacher-average and student-average class size.
Find least possible value of (xy-1)^2+(x+y)^2.
Find N/M where M is LCM of 10-30 and N of M,32-40.
Find parity of D_2021, D_2022, D_2023 given recurrence.
Find x given surface area equals volume for log edge lengths.
Simplify product (2+3)(2^2+3^2)...(2^64+3^64).
Find remainder when base-9 number N is divided by 5.
Find ratio of liquid level rises in two cones after dropping marble.
Find chord length in larger circle with half inside smaller circle.
Find total distance of laser beam reflecting off axes.
Count terms with rational coefficients in binomial expansion.
Find B in polynomial with positive integer roots.
Find slope k of angle bisector between y=x and y=3x.
Find which complex number has z^5 with greatest real part.
Find perimeter of equilateral hexagon with 30° angles and area 6√3.
Evaluate product of two sums of logarithms.
Find B+D for polynomial with roots f(z_i) given P(z).
Count groups of tenors and basses with difference multiple of 4.
Max cables connecting 20 brand A and 10 brand B computers.
Find median of list where integer n appears n times.
Count ordered pairs (b,c) where neither quadratic has two distinct real roots.
Find AD length in trapezoid with given conditions.
Find ratio p/q of probabilities for ball distribution into bins.
Find which x gives f(x)<0 for multiplicative function f.
Find smallest x>1 with sin(x)=sin(x^2) in degrees, rounded up.
Count solutions to sin(pi/2 cos x)=cos(pi/2 sin x) in [0,pi].
Count n≤50 where f_50(n)=12 for divisor-based function f.
Find sum of possible distances from focus to vertex of parabola.
Find area of isosceles trapezoid with given diagonal segments.
Find eccentricity of ellipse through five complex roots.
Count final board configurations where Carl wins with 3 O's in a row.
Find abc for cubic with roots cos(2pi/7), cos(4pi/7), cos(6pi/7).
Find p(1) for unique disrespectful quadratic maximizing sum of roots.
Probability frog reaches corner on 3x3 toroidal grid in ≤4 hops.
Sum all possible side lengths a in quadrilateral with arithmetic progression sides.
Find area of triangle formed by intersecting circles.
Find c1 in polynomial q(m)=D(m) for quadruples summing to multiple of m.
Find N maximizing divisor count over cube root of N.
Sum of four numbers formed by cycling digits 1,2,3,4.
Count integer values of x satisfying |x| < 3π.
Area of a shaded polygon on a 6x5 grid.
Find number of pairs with both wearing yellow shirts.
Find product of possible temperature differences N.
Solve a continued fraction equation for x.
Simplify n/4 where n = 8^2022.
Find the mean of combined class scores given ratio.
Count distinct sums of two special fractions summing to 15.
Find b-a after rotation and reflection of a point.
Sum of digits of largest prime divisor of 16383.
Find water height in cylinder after pouring from cone.
Find condition guaranteeing x,y,z satisfy given equation.
Find ratio of sum of odd to even divisors of N.
Vertex angle of obtuse isosceles triangle with given product condition.
Find distance between parallel lines intersecting a circle.
Area of circle through A, O, C in equilateral triangle.
Evaluate a difference of logarithmic expressions.
Sum of t values making triangle with given points isosceles.
Find difference of two numbers given sum and product condition.
Probability product of 6 dice rolls divisible by 4.
Find distance DE in trapezoid configuration of triangle.
Difference f(768)-f(384) where f(n) is divisor sum over n.
Find average of set given conditions on removing extremes.
Evaluate product of sines with argument multiples of 2π/11.
Count solutions to trig equation in given interval.
Minimum distinct complex solutions to P(z)Q(z)=R(z).
Find volume of pyramid with rectangle base and given lengths.
Area of 24-sided polygon from three rotated squares.
Find area of pentagon formed by 11 congruent segments.
Sum of a^2+b^2+c^2 given sum and gcd conditions.
Find g(1) for polynomial with reciprocal roots of f(x).
Probability bug stays within 1 unit after 5 moves on triangular grid.
Find ratio of bases in trapezoid given triangle areas.
Least k such that u_k is within 1/2^1000 of limit.
Find value of z + 6/z for complex number satisfying equation.
Number of interior intersections of sides of 5,6,7,8-gons.
Find least possible total faces on two dice given probabilities.
Number of distinct 2x2x2 cubes from 4 white and 4 blue unit cubes.
Find remainder when z^2021+1 is divided by z^2+z+1.
Number of x in [0,2π) satisfying P(x)=0 with complex exponentials.
Determine range for sum of solutions to exponential equation.
Distance between centers of two circles tangent to triangle sides.
Find starting configuration where Beth has winning strategy.
Average number of consecutive integer pairs in a 5-element subset of 1..30.
Find probability balls land in evenly spaced distinct bins.
Length CF where F is intersection of circumcircle and line AB.
Find d^2 for longer diagonal of parallelogram given projections.
Two-digit n where sum of remainders equals that of n+1.
Find length of interval of slopes with exactly 300 lattice points below.
Carlos takes 70% of a pie, Maria takes 1/3 of the remainder. What portion is left?
Sum of lengths of line segments forming the acronym AMC on a grid.
Driver travels 2 hours at 60 mph, car gets 30 mpg, paid $0.50 per mile, gas $2 per gallon. Find net hourly pay.
How many 4-digit positive integers with only even digits are divisible by 5?
25 integers from -10 to 14 arranged in a 5x5 magic square. Find the common sum.
Least additional shaded squares so figure has two lines of symmetry.
Seven cubes stacked vertically, volumes 1 to 343. Find total surface area of the tower.
Median of the list of numbers 1 to 2020 and their squares.
Number of solutions to tan(2x)=cos(x/2) on [0,2π].
Find sum of digits of n satisfying log_2(log_16 n)=log_4(log_4 n).
Frog jumps randomly on a 4x4 grid, ends when hitting a side. Probability it hits a vertical side.
x-intercept of line rotated 45° counterclockwise about (20,20).
Find b given sqrt[a]{N sqrt[b]{N sqrt[c]{N}}} = sqrt[36]{N^25} for all N>1.
Ratio of area of quadrilateral ACEG to area of regular octagon ABCDEFGH.
Greatest distance between a solution of z^3-8=0 and z^3-8z^2-8z+64=0.
Point chosen randomly in a 2020x2020 square. Probability within d units of a lattice point is 1/2. Find d.
x-coordinate of leftmost vertex of quadrilateral on y=ln x with consecutive integer x-coords.
Quadrilateral ABCD with right angles at B and C, AC=20, CD=30, AE=5. Find area of ABCD.
Find k such that (2^289+1)/(2^17+1) equals sum of k distinct powers of 2.
How many sequences of three isometries (rotations/reflections) return triangle T to original position?
Number of positive multiples of 5 where lcm(5!,n)=5*gcd(10!,n).
Sum from n=0 to infinity of a_n b_n / 7^n where (2+i)^n = a_n + b_n i.
Jason rolls three dice, may reroll a subset to maximize chance of sum 7. Probability he rerolls exactly two dice.
Side length s of equilateral triangle with interior point P such that AP=1, BP=√3, CP=2.
Find p+q where a=p/q and sum of x satisfying floor(x)*{x}=a x^2 is 420.
Sum of square roots of sums of consecutive odd numbers.
Simplify a product of rational expressions using difference of squares.
Find the ratio w:y given three ratios involving w, x, y, z.
Find the least possible prime acute angle in a right triangle.
Find number of games team A played given win ratios and differences.
Simplify factorial expression and determine what it always is.
Find max product of slopes of two lines forming a 45° angle.
Count integer pairs (x,y) satisfying x^{2020}+y^2=2y.
Find the volume of a cone formed from a three-quarter circle sector.
Find length AP in unit square with inscribed circle.
Find the shaded area inside a hexagon but outside six semicircles.
Find sum of squares of chord segments in a circle.
Simplify expression involving sum of logarithms.
Determine which player wins a number-picking game on [0,n].
Count ways to pair 10 people around a circle who know each other.
Probability of 3 red and 3 blue balls after four draws with replacement.
Count polynomials with root closure under multiplication by cube root of unity.
Find FI^2 in a square with congruent-area regions.
Count sequences of 20 transformations returning a square to original.
Probability two randomly painted cubes can be rotated to match.
Count positive integers n satisfying (n+1000)/70 = floor(sqrt(n)).
Find maximum value of rational expression in t.
Count n such that unit complex numbers summing to zero are equally spaced.
Count ordered factorizations of 96 into integers greater than 1.
Maximize probability that sum of squared sines exceeds 1.
Find percent increase in area when pizza radius increases from 3 to 4.
If a is 150% of b, what percent of a is 3b?
Minimum balls to draw to guarantee 15 of one color from six colors.
Greatest number of consecutive integers whose sum is 45.
Area of triangle formed by two lines and line x+y=10.
Number of rigid motions mapping a figure of squares to itself.
Compare mean, median, and median of modes of dates in 2019.
Sum of all possible numbers of intersection points of four lines.
Find a_2019 for a recursively defined sequence of fractions.
Area inside large circle but outside 13 unit circles arranged hexagonally.
Find base k such that 7/51 equals 0.overline{23}_k.
Find (log_2(x/y))^2 given log_2 x = log_y 16 and xy = 64.
Find the number of ways to paint integers 2 through 9 with three colors such that each number has a different color from its proper divisors.
Find |c| such that polynomial (x^2-2x+2)(x^2-cx+4)(x^2-4x+8) has exactly 4 distinct roots.
Find ab given sqrt(log a) + sqrt(log b) + log sqrt(a) + log sqrt(b) = 100 with all terms positive integers.
Probability that each row and column sum is odd in 3x3 grid.
Find a+b+c given recurrence s_{k+1}=a s_k+b s_{k-1}+c s_{k-2} for sums of powers of roots of x^3-5x^2+8x-13.
Distance from sphere center to plane of triangle tangent to sphere.
Find the least possible perimeter of triangle ABC with integer sides and given cosines.
Probability that |x-y| > 1/2 with a two-stage random process.
Evaluate product of sums of powers of z=(1+i)/sqrt(2) from 1^2 to 12^2.
Find side length AB of equilateral triangle with vertex on outer circle and base tangent to inner circle.
Find log_7(a_2019) for recursively defined sequence with custom binary operations.
Number of n from 1 to 50 for which (n^2-1)!/(n!)^n is integer.
Find smallest n such that triangle formed by feet of altitudes is obtuse.
Ratio of container volumes after pouring water between them.
Find a composite n such that n-2 is also composite.
Identify which rigid transformation maps segment AB to A'B' with given coordinates.
Solve factorial equation for n and sum its digits.
Find smallest n such that 20n is divisible by 12, 14, 15.
Count points C forming triangle with given perimeter and area.
Find sum of x where median equals mean of five numbers.
Evaluate an alternating sum of a function f(x)=x^2(1-x)^2 at fractions.
Find how many integer x values allow a triangle with side lengths log2 x, log4 x, 3.
Count routes from A to L using exactly 13 of 17 roads without repeating any road.
Count unordered pairs of edges of a cube that determine a plane.
Find sin(2∠BAD) in a configuration of two right triangles with equal perimeters.
Find probability red ball lands in a higher-numbered bin than green ball.
Count numbers that are product of two distinct divisors of 100,000.
Area of region inside circle but outside three semicircles.
Find probability Fiona reaches pad 10 without landing on predators at pads 3 and 6.
Count nonzero complex z such that 0, z, z^3 form an equilateral triangle.
Find area of triangle PQR in a square pyramid with given dimensions.
Probability all three players have $1 after 2019 money exchanges.
Area of circle given two points and tangent intersection on x-axis.
Count quadratic polynomials where the set of roots equals the set of coefficients.
Find interval containing least n with recursive sequence below threshold.
Count binary strings length 19 with no consecutive 0s or three 1s.
Find the area of the set of points a + bω + cω² with a,b,c in [0,1].
Maximize area of quadrilateral ABCD given BC=2, CD=6, and centroids form equilateral triangle.
Find how many blue balls to remove so red percentage doubles.
Maximize value of rocks Carl can carry given weight limit.
Schedule 3 distinct math classes in 6 periods with no consecutive math classes.
Find the interval of possible distances given three false statements.
Find sum of k for which two quadratics share a root.
Find m+n given mean and median of set equal n.
Count integer n such that 4000*(2/5)^n is an integer.
Find area of trapezoid in similar isosceles triangles with area 1 small triangles.
Find largest y interval where sine inequality holds for all x.
Count ordered pairs (x,y) satisfying x+3y=3 and ||x|-|y||=1.
Find length of crease when folding a 3-4-5 triangle so A meets B.
Find least possible element in a 6-element subset of 1..12 with no multiples.
Count nonnegative integers representable as sum of powers of 3 with coefficients -1,0,1.
Solve logarithmic equation for x and find p+q.
Count symmetric 7x7 black/white grids with at least one of each color.
Find a such that circle x^2+y^2=a^2 and parabola y=x^2-a intersect at 3 points.
Fraction of right triangle planted after removing a square at the right angle corner.
Area of quadrilateral formed by midpoints and angle bisector in triangle with area 120.
Find sum of numerator and denominator of infinite sum of reciprocals of numbers with only prime factors 2,3,5.
Find CI in isosceles right triangle with cyclic quadrilateral AIME of area 2.
Determine which polynomial has the greatest real root.
Find area of parallelogram formed by solutions to two complex equations.
Find acute angle between MN and PA in triangle with given points.
Find number Carol should choose to maximize chance of winning.
Max a+b+c such that C_n - B_n = A_n^2 for at least two n, with repdigit numbers.
Find number of 2x2 pieces in a 20x18 pan of cornbread.
Find average speed in last 30 minutes given total distance and two speeds.
Find the distance between the x-intercepts of two lines with given slopes.
Find the area of a circle given a chord length and its distance from the center.
Count subsets of {2,...,9} that contain at least one prime number.
Express number of soda cans for D dollars given S cans cost Q quarters.
Evaluate the product of logarithms from log_3 7 to log_23 27.
Find area traced by centroid of right triangle with fixed hypotenuse.
Evaluate the double sum of i+j from i=1 to 100 and j=1 to 100.
Least number of distinct values in a list with unique mode occurring 10 times.
Find area of square wrapping paper folded over a box with square base.
Find m+n where (m,n) is the open interval of possible AC lengths.
Find the area of the quadrilateral formed by centroids of four triangles.
Find sum of digits of Joey's age when it is next a multiple of Zoe's age.
Count odd 3-digit multiples of 3 that do not contain the digit 3.
Find the least possible area of a triangle formed by three vertices of a regular octagon.
Find q-p for the fraction p/q between 5/9 and 4/7 with smallest q.
Find f(2018) for a recursively defined function with f(1)=f(2)=1.
Find smallest possible next divisor after 323 in an even 4-digit number's divisor list.
Find area of intersection of triangles ACE and XYZ in a regular hexagon.
Find the area of triangle MOI formed by circumcenter, incenter, and center of a tangent circle.
Count degree ≤3 polynomials with coefficients 0-9 satisfying P(-1) = -9.
Find the degree measure of angle ACB between two points on Earth.
Number of real solutions to x^2 + 10000 floor(x) = 10000 x.
Find a+b where the area of an equilateral triangle tangent to three circles is sqrt(a)+sqrt(b).
Maximize number of popsicles bought with $8 given three package options.
Find sum of reciprocals given sum equals 4 times product.
Identify which statement follows logically from a conditional promise.
Find percent shorter diagonal path is compared to two sides.
Count handshakes at a gathering with two groups of people.
Count possible fourth rod lengths to form a quadrilateral.
Evaluate a recursively defined function at a large odd input.
Find length of segment given volume of points within 3 units.
Describe set of points where two of three quantities are equal.
Find probability Laurent's number exceeds Chloe's given intervals.
Find missing interior angle of convex polygon given sum 2017.
Find least time when at least 5 horses are at starting point.
Find distance given travel time with speed reduction in storm.
Count seating arrangements with adjacency restrictions for five people.
Find interval containing smallest positive x where trig sum is zero.
Find radius of circle tangent to three semicircles in a larger semicircle.
Count 24th roots of unity whose 6th power is real.
Find possible digit sum of n+1 given digit sum of n is 1274.
Find ratio of side lengths of squares inscribed in 3-4-5 triangles.
Count ordered pairs (b,a) satisfying a logarithmic equation.
Find size of set S built by adding integer roots of polynomials with coefficients in S.
Find probability particle hits corner before side of square on lattice.
Find f(1) given cubic g(x) shares all roots with quartic f(x).
Find product XF * XG in cyclic quadrilateral with parallel lines.
Find probability product of 12 random complex numbers from set equals -1.
After how many months will LaShawn's collection have twice as many as Kymbrea's?
Given ranges for x, y, z, determine which expression is always positive.
Given an equation relating x and y, find the value of a rational expression.
Given biking and walking speeds and total time, find the distance walked.
How many outliers does the data set have using the 1.5 IQR rule?
Find the x-coordinate of the second x-intercept of a circle with diameter endpoints (0,0) and (8,6).
Find the least period of the function cos(sin(x)).
Find the square of the ratio of short side to long side of a rectangle satisfying a given proportion.
Find c such that the line through the intersection points of two circles is x+y=c.
What fraction of students who say they dislike dancing actually like it?
Count positive integers whose digits are strictly increasing or decreasing.
Find the sum of the roots of z^12=64 that have positive real part.
How many distinct paintings of 6 disks with 3 blue, 2 red, 1 green are possible up to rotation and reflection?
Find the total volume of ice cream in a frustum topped with a cone.
Find the ratio of area of triangle A'B'C' to area of equilateral triangle ABC after extending sides by 3 times.
What is the probability that a randomly chosen divisor of 21! is odd?
Compare the probability of winning Game A (3 tosses all same) vs Game B (first two same, last two same).
Find the area of triangle ABC where AB is a diameter of a circle and E is a point outside.
Find the remainder when the concatenated numbers 1 to 44 are divided by 45.
Find the probability that floor(log2 x) = floor(log2 y) for random x,y in (0,1).
Find Isabella's sixth test score given seven distinct scores 91-100 and integer averages after each test.
Find probability that after 4 rounds of coin exchange each player ends with 4 coins.
Find f(0) for a cubic f through (2,4),(3,9),(4,16) where lines AB,AC,BC intersect f again at D,E,F with x-sum 24.
Find AB/BC in quadrilateral ABCD with right angles at B,C and similar triangles, given area ratio 17.
Find how many n between 9 and 2017 satisfy a condition about average number of teams in subsets.
Evaluate (11! - 10!) / 9!.
Solve 10^x * 100^(2x) = 1000^5 for x.
Evaluate rem(3/8, -2/5) using floor function definition.
Find x such that mean, median, mode of 7 numbers equal x.
Identify what would constitute a counterexample to Goldbach's conjecture.
Find sum of digits of N for triangular number 2016.
Describe the graph of the equation x^2(x+y+1)=y^2(x+y+1).
Find area of shaded region in rectangle with cut corners.
Find the sum of a and b given the side length of small squares in a unit square.
Find Ada's original seat after friends move in a row.
Find the number of students with exactly two talents given totals for each talent.
Find the ratio AF:FD where F is the intersection of angle bisectors in triangle ABC.
Find least N multiple of 5 with probability condition on green balls.
Count cube vertex labelings with equal face sums, up to rotation.
Find the area of triangle formed by centers of three circles tangent to a line.
Find the number of points with positive x-coordinate lying on two or more logarithmic graphs.
Find the ratio of the area of square EFGH to square ABCD formed by centers of equilateral triangles.
Find divisor count of 81n^4 given 110n^3 has 110 divisors.
Find the probability that a random walk of 8 coin flips reaches position 4 at some time.
Solve 2016 ◇ (6 ◇ x) = 100 for binary operation ◇.
Find fourth side of cyclic quadrilateral with three sides 200.
Count triples (x,y,z) with given LCMs 72, 600, 900.
Find the probability that three random numbers in [0,1] form a triangle.
Find the value of b such that x^3-ax^2+bx-a has all real roots for minimal a.
Find the sum of digits of f(2)+f(4)+...+f(2016) from a number-writing game.
Evaluate an algebraic expression with negative exponents for a given value.
Compute the harmonic mean of two numbers and find the closest integer.
Evaluate an expression involving absolute values for a given negative number.
Find the sum of two acute angles given ratio and complement relationship.
Determine the day of the week 919 days after a Thursday.
Find the length of the base of a triangle on a parabola with given area.
Find the last remaining number after repeatedly crossing out numbers in a pattern.
Find the weight of a larger equilateral triangle given the weight of a smaller one.
Find the area of a rectangular garden given fence post spacing and counts.
Find the sum of coordinates given quadrilateral area and integer constraints.
Count axis-aligned squares with integer vertices inside a triangular region.
Find the center number in a 3x3 grid with consecutive numbers sharing edges.
Find the altitude of an airplane given angles of elevation from two observers.
Minimize the sum of an infinite geometric series with second term 1.
Maximize the sum of products of three faces meeting at each cube vertex.
Count ways to write 345 as sum of increasing consecutive positive integers.
Find the distance between intersection points of angle bisectors with altitude.
Find the area enclosed by the graph of x^2+y^2=|x|+|y|.
Find probability all three players flip the same number of times until first head.
Count sets of three teams in a round-robin tournament with cyclic wins.
Find the infinite sum of areas of triangles formed by recursive construction.
Find the interval containing n given repeating decimal periods of 1/n and 1/(n+6).
Find the volume of the intersection of two octahedra defined by absolute value inequalities.
Find smallest n such that exactly 77000 ordered quadruplets have gcd 77 and lcm n.
Find smallest k so product of recursively defined sequence terms is an integer.
Evaluate an arithmetic expression involving exponents and a reciprocal.
Find which perimeter is not possible for a triangle with sides 20 and 15.
Find Payton's test score given the class average before and after.
Find the ratio of two positive numbers given sum is 5 times difference.
Determine which rounding strategy overestimates a given expression.
Find when Pete will be twice as old as Claire given past age ratios.
Compare heights of two cylinders with equal volume and radius difference.
Find constant k such that area of rectangle equals k times diagonal squared.
Find probability Cheryl gets two marbles of same color from six marbles.
Find integer x given x+y+xy=80 with x>y>0.
Find number of possible values for number of common tangents to two circles.
Find a+b given parabolas intersect axes in kite of area 12.
Identify false statement about scores in a round-robin tournament with draws.
Solve equation involving sum of reciprocals of logs for a.
Find minimum decimal digits needed for fraction with denominator powers of 2 and 5.
Find volume of tetrahedron given all six edge lengths.
Probability no two adjacent people stand when 8 flip coins in a circle.
Find sum of possible a such that quadratic has integer roots.
Count perimeters less than 2015 for quadrilateral with right angles and equal sides.
Find b closest to integer for isosceles triangle with same area and perimeter as given triangle.
Find a+b for interval of radii of circle through foci and four points on ellipse.
Find remainder when number of sequences with no more than three consecutive same letters is divided by 12.
Find probability distance between two random points on square sides is at least 1/2.
Find probability that (cos(aπ)+i sin(bπ))^4 is real for rational a,b in [0,2).
Find sum of reciprocals of square roots of radii in layered circle construction.
Evaluate the expression 2 minus negative 2 to the negative second power.
Find when Marie finishes the third task given start and end times.
Find the other integer given two numbers written multiple times summing to 100.
Determine who finished 8th in a race given relative finishing positions.
Find minimum N so Sharks win at least 95% of all games played.
Find fraction of odd products in a 0 to 12 multiplication table.
Find L+R for a regular 15-gon's lines of symmetry and rotational symmetry angle.
Evaluate the expression (625^{log_5 2015})^{1/4}.
Find probability Larry wins a turn-based game with 1/2 success chance per turn.
Count noncongruent integer-sided triangles with perimeter less than 15, not isosceles or right.
Find sum of altitudes of triangle formed by line 12x+5y=60 and axes.
Maximize sum of roots of (x-a)(x-b)+(x-b)(x-c)=0 with distinct one-digit a,b,c.
Find AC in cyclic quadrilateral ABCD with given angles and side lengths.
Find difference between area inside circle but outside triangle and vice versa.
Find probability Rachelle gets GPA at least 3.5 given grade probabilities.
Find volume of pyramid formed by folding isosceles triangles onto a regular hexagon.
Find n such that probability of exactly 2 heads equals probability of exactly 3 heads.
Find the range of r(n) where r(n) sums prime factors of composite n.
Find perimeter of right triangle ABC with squares constructed externally on sides.
Evaluate f(2015,2) for a recursively defined function modulo 5.
Find sum of digits of sum of all possible staircase steps given jump counts.
Count ways 6 people at a circular table move to non-same, non-adjacent seats.
Count ordered triples (a,b,c) with a≤b≤c where volume equals surface area of box.
Find sum of distances from midpoints of PQ to centers of four intersecting circles.
Find distance bee travels after 2015 moves turning 30° each time.
Evaluate an expression involving fractions and a reciprocal.
Find the cost of 8 adult and 6 child tickets given 5 adult and 4 child cost $24.50.
Count orderings of four colored houses with given constraints.
Find gallons of milk given cows and days using rates.
Find the difference between mean and median of given score percentages.
Find the sum of a two-digit number and its reverse given a relationship.
Find the fourth term of a geometric progression with given terms.
Determine which listed price makes coupon 1 give the largest discount.
Find the average of consecutive integers starting from b in terms of a.
Find the length of the congruent sides of isosceles triangles on an equilateral triangle.
Find total distance given speed changes and arrival time difference.
Find the ratio of areas of two intersecting circles given minor arc measures.
Find the number of ways to assign 5 friends to 5 rooms with at most 2 per room.
Find the smallest possible value of c given arithmetic and geometric progression conditions.
Find the sum of the digits of the sum of all five-digit palindromes.
Find k such that the digit sum of 8 times a k-digit number of 8s is 1000.
Find the height of a box containing a large sphere and eight smaller spheres.
Find the sum of numerator and denominator of the length of the domain of a nested log function.
Find the number of rational k such that a quadratic has an integer root.
Find the minimum possible value of BE+DE+CD in a triangle with given sides and angle.
Find the sum of lengths of intervals where a floor function inequality holds.
Count intervals between powers of 5 that contain three powers of 2.
Find the sum of digits in the repeating decimal expansion of 1/99^2.
Find the number of x such that f_100(x)=0 for a recursively defined function.
Find the number of integer points on a parabola with a given focus and points.
Leah has 13 coins, pennies and nickels; find total value in cents.
Orvin buys balloons with a buy-one-get-one-third-off sale; find max balloons.
Randy drives a trip with gravel, pavement, and dirt road segments; find total length.
Susie and Calvin buy muffins and bananas; find muffin-to-banana price ratio.
Square window with 8 panes of given ratio and borders; find side length.
Ed and Ann drink lemonade; find total ounces they drank together.
Find number of positive integers n such that n/(30-n) is a positive integer.
Cryptarithm with distinct digits A,B,C,D; find number of possible values for D.
Convex quadrilateral ABCD with given sides and right angle; find area.
Odometer shows abc then cba after trip at 55 mph; find a^2+b^2+c^2.
List of 11 positive integers with mean 10, median 9, unique mode 8; find max possible value.
Set of triangles with integer sides <5, no two congruent or similar; find max size.
Find least b>1 such that no triangle exists with sides 1,a,b nor with 1/b,1/a,1.
Rectangular box with surface area 94 and edge sum 48; find sum of interior diagonals.
p = sum k ln k from 1 to 6; find largest power of 2 dividing e^p.
Cubic polynomial P with P(0)=k, P(1)=2k, P(-1)=3k; find P(2)+P(-2).
Parabola y=x^2 and point Q(20,14); find r+s where line slope m avoids parabola.
Numbers 1-5 arranged in a circle; count bad arrangements missing consecutive sums 1-15.
Sphere inscribed in truncated cone; volume ratio 2:1; find ratio of base radii.
Find number of positive integers x satisfying log10(x-40)+log10(60-x) < 2.
Square of side 1 with two congruent rectangles; find length BE.
Frog on lily pads 0-10 jumps with probability N/10 left; find escape probability from pad 1.
Sum of binomial coefficients from 0 to 62 of 2014 choose k; find remainder mod 2017.
Pentagon ABCDE inscribed in circle with given side lengths; find sum of all diagonals.
Solve 2cos2x(cos2x - cos(2014π^2/x)) = cos4x - 1; find sum of positive solutions.
Find BE in a square with a triangle of area 40.
Find total opponent runs given game scores and win/loss conditions.
Find percent of flowers that are carnations given fractions.
Evaluate a fraction with powers of 2.
Find t-d given amounts paid and equal sharing.
Find total points scored given shot percentages and attempts.
Find S4 in a Fibonacci-like sequence given S7 and S9.
Find xy given x + 2/x = y + 2/y with distinct x,y.
Find perimeter of parallelogram ADEF in an isosceles triangle.
Sum of n such that 1/n has repeating decimal 0.abab... with distinct digits.
Find DE+FG in equilateral triangle with equal-perimeter regions.
Sum possible x values for triangle with sides 4,5,x and angles in AP.
Find intersection point of line through A dividing quadrilateral into equal areas.
Find x in arithmetic progression of logs with given first and last terms.
Number of ways to distribute 5 rabbits to 4 stores with parent-child restriction.
Greatest possible integer mean weight of piles B and C given means.
Number of coins the 12th pirate receives given fractional sharing rule.
Radius of eighth sphere tangent to six spheres and larger sphere.
Find BC given AB=86, AC=97, circle center A radius AB intersects BC.
Number of ordered triples (x,y,z) from {1..19} satisfying cyclic inequality.
Determine interval containing iterated log expression A.
Probability that a random 6-digit palindrome divided by 11 is also a palindrome.
Area of region swept by square rotated 90° about point P on diagonal.
Probability three random chords of a regular 12-gon form a triangle.
Number of complex z with Im(z)>0 such that f(z)=z^2+iz+1 has integer real and imag parts ≤10.
Find the low temperature given high is 16 degrees higher and average is 3.
Find pounds of potatoes expected from a rectangular garden given step lengths and yield per square foot.
Find the position of 53 when counting backwards from 201 to 3.
Find combined miles per gallon when two cars drive the same distance with different fuel efficiencies.
Find the average age of 33 fifth-graders and 55 parents given their separate averages.
Find x+y given x^2+y^2=10x-6y-34.
Find the 53rd number said when Jo and Blair take turns counting increasing sequences.
Find the slope of line l3 given triangle area and intersection points of three lines.
Find sum of exponents of prime factors of the square root of the largest perfect square dividing 12!.
Find number of silver tokens after exchanging red and blue tokens at two booths until no more exchanges possible.
Determine directions of two bees when they are exactly 10 feet apart after repeating patterns of movement.
Count routes from A to B using each road exactly once in a given graph.
Find largest possible sum of two largest angles of quadrilateral with angles in arithmetic progression and similar triangles.
Find smallest possible N given two non-decreasing sequences with different first terms and seventh term N.
Find |a1-b1| for representation of 2013 as product of factorials with minimal a1+b1.
Find difference between max and min perimeter of star formed by extending sides of equiangular pentagon of perimeter 1.
Find difference between max and min possible values of c given a+b+c=2 and a^2+b^2+c^2=12.
Determine winner for coin removal game with 2013 and 2014 coins given optimal play.
Find length DF in triangle ABC with given side lengths and perpendiculars.
Find sin(2x) given points P,Q,R,S form a trapezoid for x between 135 and 180 degrees.
Count points in plane on two of 30 parabolas with focus (0,0) and integer directrix lines.
Find m+n given product of solutions to log equation is smallest possible integer.
Count three-digit N where last two digits of S equal those of 2N.
Find BN^2 in triangle ABC with median BM, angle bisector CN, and equilateral triangle BXN.
Count polynomials with integer coefficients, constant term 50, and distinct integer-complex roots.
Bug crawls from -2 to -6 to 5; find total distance.
Cagney and Lacey frost cupcakes; find total in 5 minutes.
A box of given dimensions holds 40 grams; find grams for scaled box.
Fraction of red marbles after doubling red count.
Fruit salad with 280 pieces; find number of cherries given ratios.
Three numbers have pairwise sums 12, 17, 19; find middle.
12 integer central angles in arithmetic sequence sum to 360; find smallest.
Iterative average of 1-5; find difference between max and min.
200th anniversary of Dickens on Tuesday; find birth day of week.
Triangle with area 30, side 10, median 9; find sine of angle between them.
Probability Alex wins 3, Mel 2, Chelsea 1 in 6 independent rounds.
Square tangent to unit circle at (0,1); vertices on circle radius 2; find side.
Three painters with lunch break; find break length in minutes.
Closed curve of 9 circular arcs; find enclosed area.
3x3 grid rotated 90°; probability grid becomes all black.
Two intersecting circles; find radius of one given distances between points.
Largest subset of {1,...,30} with no two elements summing to a multiple of 5.
Triangle with sides 27,26,25; find distance from incenter to vertex B.
6 people each have same number of friends; count possible friend graphs.
Find exponent a such that coefficient of x^2012 in product is 2^a.
Positive integers a≥b≥c satisfy two equations; find a.
Planes intersect cube; find difference between max and min number of planes.
Probability translated square contains exactly two integer lattice points.
Sequence defined by powers; find k where a_k equals its rank in decreasing order.
Smallest n so n f(x f(x)) = x has at least 2012 real solutions.
Find how many more students than rabbits in 4 classrooms.
Find area of rectangle given inscribed circle radius and ratio.
Find number of acorns hidden by chipmunk given squirrel needs fewer holes.
Find percent by which Etienne's money exceeds Diana's money.
Find minimum number of even integers among six integers with given sums.
Determine effect of rounding x up and y down on x-y estimate.
Find distance between 3rd and 21st red light in repeating pattern.
Count dessert menus for a week with no repeats and cake on Friday.
Find time to ride escalator down without walking given walking times.
Find area of polygon formed by intersection of circle and ellipse.
Find A+B given base equation with consecutive positive integers A and B.
Count sequences of length 20 with all zeros or all ones consecutive.
Find probability two parabolas with random integer coefficients intersect.
Find smallest initial number for Bernardo to win the doubling game.
Find ratio of volumes of two cones made from sectors of a circle.
Count ways three girls like four songs with given pairwise conditions.
Find sum of coordinates of center of square given points on its sides.
Count lists of 1-10 where each number has a neighbor appearing earlier.
Find side length of regular octahedron inscribed in a unit cube.
Find sum of possible areas of trapezoid with sides 3,5,7,11.
Find side length of square inscribed in equiangular hexagon.
Find sum of all possible values of P(1) for polynomials with root on unit circle.
Find sum of all possible values of P(1) for polynomials with root on unit circle.
Count N up to 400 for which iterated function sequence is unbounded.
Count paths from A to B in a hexagonal lattice with directed segments, no segment reused.
Calculate monthly cell phone bill with texts and overtime minutes.
Determine the stacking order of five overlapping coins.
Find minimum number of small bottles to fill a large bottle.
Find average run time given ratios of students per grade.
Find percent of non-swan birds that are geese.
Find number of free throws made given total points and relationships.
Find pencil cost in cents given total cost and constraints.
Find A+H in a sequence where sum of three consecutive terms is 30.
Count handshakes among twins and triplets at a convention.
Find probability that circle area is less than circumference.
Find area inside circle C but outside circles A and B.
Find time for power boat to go from A to B given meeting time.
Find perimeter of triangle formed by line through incenter parallel to base.
Find probability that point (a,b) lies above parabola y=ax^2-bx.
Find edge length of square pyramid base with inscribed hemisphere.
Count colorings of pentagon vertices with diagonal color restriction.
Find area of triangle formed by tangency points of three circles.
Maximize x^2-6x+y^2 given |x+y|+|x-y|=2.
Find sum of two smallest N given elite status formula equals 19.
Find integer k such that f(100) is between 5000k and 5000(k+1).
Find N+c where N is largest n with nonempty domain of f_n.
Count 100-ray partitional points not 60-ray partitional in a square.
Find difference between max and min |b| given functional equation.
Find radius of largest circle inside quadrilateral with given sides.
Find angle CBA maximizing area of pentagon BCOIH in triangle.
Compute the difference of two fractions with arithmetic series.
Find minimum test score to raise average by 3 points.
Determine how much LeRoy must give Bernardo to share costs equally.
Find correct product after reversing digits of a two-digit number.
Find sum of digits of second smallest integer divisible by 1 through 6.
Find angle between two tangents given arc length ratio.
Maximize ratio of two two-digit numbers with mean 60.
Find speed given time difference between inside and outside track edges.
Find probability product of two random numbers from [-20,10] is positive.
Find angle AMD in rectangle with point M on side AB.
Find minimum jumps of length 5 from (0,0) to (1,0) on lattice.
Find probability dart lands in center square of regular octagon.
Find sum of possible largest of four integers given pairwise differences.
Find cosine of angle AVB for parabola with segment through focus.
Count two-digit factors of 2^24 - 1.
Find area of points inside rhombus closer to vertex B than others.
Find sum of digits of h_{2011}(1) for iterated function composition.
Find volume of cube inside pyramid with square base and equilateral faces.
Find maximum a such that y=mx+2 has no lattice points for 1/2 < m < a.
Find sum of distances from X to vertices of triangle ABC.
Find |x-y| given arithmetic and geometric means are digit reversals.
Find perimeter of last triangle in sequence from incircle tangency points.
Count integer points on paths of length ≤20 from A to B.
Find minimum perimeter of octagon with vertices as zeros of polynomial.
Find minimum probability that nearest integer equation holds for random n.
Evaluate the expression (20-(2010-201))+(2010-(201-20)).
Find total tourists on 6 ferry trips starting at 100 and decreasing by 1 each trip.
Find AB/AD given rectangle shares 50% area with square, square shares 20% with rectangle.
For x<0, determine which expression must be positive.
Find minimum n such that n consecutive bullseyes guarantee victory in archery tournament.
Find sum of digits of x where x and x+32 are three- and four-digit palindromes.
Find height of scale model water tower given volume ratio and actual height.
Find angle ACB in triangle with AB=2AC and equilateral triangle CFE.
Find volume of cube with 2x2 square holes through each face.
Find 2010th term of arithmetic sequence with terms p, 9, 3p-q, 3p+q.
Find base b such that solution of 7^(x+7)=8^x is x=log_b(7^7).
Determine number of frogs among four amphibians given truth-telling statements.
Count integer k for which circle x^2+y^2=k^2 and hyperbola xy=k do not intersect.
Find smallest possible perimeter of triangle with angle bisector AD=3, DC=8.
Find probability of heads given 4 flips have 1/6 chance of equal heads and tails.
Probability Bernardo's 3-digit number > Silvia's when picking distinct numbers from 1-9 and 1-8.
Find sum of possible r in equiangular hexagon where triangle ACE area is 70% of hexagon.
Count 16-step paths from (-4,-4) to (4,4) staying outside or on boundary of square [-2,2].
Find smallest n such that probability of stopping after n draws is less than 1/2010.
Find largest n such that arithmetic sequences a_n and b_n have integer terms and product 2010.
Find largest x where graph of y=x^6-10x^5+... lies above line y=bx+c except at three points.
Find minimum value of sum |x-1|+|2x-1|+...+|119x-1|.
Find last two nonzero digits of 90!.
Find number of disjoint open intervals in domain of f(x)=log(product sin(kπx)) on [0,1].
Count convex cyclic quadrilaterals with integer sides and perimeter 32, up to rotation/translation.
Find percent of 9-hour workday spent in two meetings totaling 135 minutes.
Find area of an L-shaped figure composed of two rectangles.
Find number of possible whole-number ticket prices given two total costs.
Find how many days of the week could start a 31-day month with equal Mondays and Wednesdays.
Find the number substituted for e so that ignoring parentheses gives the correct result.
Find difference between max and min possible percent of students who changed their answer.
Find minutes driven in rain given total distance and time with two speeds.
Find number of schools given median score and two teammates' ranks.
Find number of digits of smallest n divisible by 20 with n^2 a cube and n^3 a square.
Find x such that average of 1 through 99 and x equals 100x.
Find probability a random 4-digit palindrome is divisible by 7.
Solve logarithmic equation with multiple bases for x.
Find BC in triangle ABC given cos(2A-B)+sin(A+B)=2 and AB=4.
Minimize the maximum of adjacent sums of five positive integers totaling 2010.
Count ordered triples (x,y,z) under 20 with exactly two distinct values in set of complex powers.
Find probability that abc+ab+a is divisible by 3 for random a,b,c from 1 to 2010.
Count 3x3 arrays with digits 1-9 in increasing order in each row and column.
Find probability frog ends within 1 meter of start after three random 1-meter jumps.
Find total first-half points given geometric and arithmetic quarterly scores with 1-point win.
Find n such that a_n = 1+cos x in geometric sequence with sin x, cos x, tan x.
Find smallest a such that polynomial P with integer coefficients has given alternating values.
Find largest possible BD in cyclic quadrilateral with distinct integer sides under 15 and BC*CD=AB*DA.
Find sum of minimum values of monic quadratics P and Q given zeros of compositions.
Find sum of lengths of intervals where sum of three reciprocals is at least 1.
Find largest m such that 2010^m divides product of pow(n) for n=2 to 5300.
Kim's flight from Newark to Miami takes h hours and m minutes; find h+m.
Evaluate the continued fraction 1 + 1/(1 + 1/(1+1)).
Find the number one third of the way from 1/4 to 3/4.
Four coins from pennies, nickels, dimes, quarters; which total is impossible?
Cube dimensions changed by ±1; volume decreases by 5. Find original volume.
Given P=2^m and Q=3^n, express 12^{mn} in terms of P and Q.
First three terms of arithmetic sequence given; find n for nth term 2009.
Four congruent rectangles in a square; outer area 4× inner. Find rectangle side ratio.
Given f(x+3)=3x^2+7x+4 and f(x)=ax^2+bx+c, find a+b+c.
Quadrilateral ABCD with sides 5,17,5,9; BD integer. Find BD.
Sequence of diamond figures; find number of diamonds in F_20.
Positive integers less than 1000 that are 6 times the sum of their digits.
Ship sails 10 then 20 miles with turn 45-60°; find interval for AC².
Line y=mx divides triangle with vertices (0,0),(1,1),(6m,0) into equal areas.
Find n such that i+2i²+3i³+...+ni^n = 48+49i.
Circle tangent to axes and externally tangent to circle at (3,0) radius 1.
Two geometric series with same first term; sums equal common ratios. Find r1+r2.
I_k = 10...064 with k zeros; find max exponent of 2 in prime factorization.
Compare area between incircle and circumcircle of pentagon vs heptagon side 2.
Quadrilateral ABCD with AB=9, CD=12, AC=14; triangles AED and BEC equal area. Find AE.
Cubic p(x) with given zeros; find number of nonreal zeros of p(x^4).
Plane parallel to opposite faces cuts regular octahedron side 1; find intersection area.
Quadratic f and g with g(x)=-f(100-x); x-intercepts differ by 150. Find x4-x1.
Tower function T(n); find largest k such that log_2...log_2(B) is defined.
Sequence a1=1, a2=1/√3, a_{n+2}=(a_n+a_{n+1})/(1-a_n a_{n+1}); find |a_2009|.
Jane buys muffins and bagels for a week; total cost is a whole number of dollars.
Paint for 30 rooms lost 3 cans; now only enough for 25 rooms. Find cans used.
Twenty percent less than 60 is one-third more than what number?
Rectangular yard with two congruent isosceles right triangle flower beds; find fraction occupied.
Product of three ages (two twin brothers and Kiana) is 128; find sum.
Insert parentheses in 2×3+4×5 to get different values; count distinct results.
Gasoline price changes by given percentages; find the final percent decrease to return to original.
Bucket weights at two-thirds and one-half full; find weight when full in terms of a and b.
Find the area of a triangle with a vertex on a given line.
Find the fraction of the day a faulty clock shows the correct time.
Millie adds seeds daily; birds eat millet and other seeds; find when millet exceeds half.
Find the first term of a geometric sequence given two later terms.
Find the sum of the two possible lengths of the third side of a triangle.
Find the x-intercept of a line dividing a figure into equal areas.
Determine which exponential equation has the largest solution for x.
Find the length of a side of a trapezoid given angles and a ratio.
Each face of a cube gets a random stripe; find probability of a continuous stripe encircling the cube.
Two runners on a circular track; find probability both are in a photo taken during a random minute.
Find the sum of all prime values of a quartic polynomial for positive integers.
Find the number of edges of a polyhedron after truncating its vertices.
Find the number of ways ten women can reseat themselves with restrictions.
Count parallelograms with given area and vertices on specific lines.
Find the probability that a scaled and rotated point stays in a square.
Find the number of solutions to an equation with inverse trig functions.
Count squares with side at least 6 whose vertices are in a given set of lattice points.
A bakery machine completes one third of a job by 11:10 AM after starting at 8:30 AM. Find completion time.
Find the reciprocal of the sum 1/2 + 2/3.
Given 2/3 of 10 bananas equals 8 oranges, find how many oranges equal 1/2 of 5 bananas.
Compute the product of fractions from 8/4 to 2008/2004.
Determine which statement must be true about x if (2x/3 - x/6) is an integer.
Find the sticker price of a computer given discounts and rebates at two stores.
Find the slowest bailing rate to prevent a boat from sinking while rowing to shore.
Find the volume of a cube whose surface area is twice that of a unit cube.
Find the height of darkened strips on a TV screen when letterboxing a movie.
Find the equation for total time including lunch when two people paint a room together.
Maximize the sum of visible numbers on three stacked cubes made from a given net.
Find the domain and range of g(x)=1-f(x+1) given f has domain [0,2] and range [0,1].
Find the ratio of areas of two internally tangent circles with a 60-degree central angle.
Find the area of the region defined by |3x-18|+|2y+7| ≤ 3.
Find the units digit of k^2 + 2^k where k = 2008^2 + 2^2008.
Find n such that the 12th term of an arithmetic sequence of logs is log(b^n).
Count positive integers a1 ≤ 2008 where a1 is less than a2, a3, and a4 in a Collatz-like sequence.
Find the volume of tetrahedron OABC with vertices on positive axes and side lengths 5, 6, 7.
Find the coefficient of x^28 in the expansion of (1+x+...+x^27)(1+x+...+x^14)^2.
Find the ratio of inradii of two triangles formed by the angle bisector of the right angle in a 3-4-5 triangle.
Count permutations of (1,2,3,4,5) where a1+a2 < a4+a5.
Find the length x of rectangular placemats arranged around a round table of radius 4.
Find the area of the convex polygon whose vertices are the roots of z^4+4z^3i-6z^2-4zi-i=0.
Find the maximum possible value of tan(∠BAD) in triangle ABC with ∠C=60° and BC=4, D the midpoint of BC.
Find a1+b1 given a recurrence for points in the plane and (a100,b100)=(2,4).
Basketball player makes 5 baskets worth 2 or 3 points each; find number of possible total points.
Reverse rows of a 4x4 calendar block and find positive difference between diagonal sums.
Find maximum possible salary for one player given minimum salary and total team salary cap.
Find ratio of sector area to circle area given two angles on a diameter.
Find number of bouquets possible spending exactly $50 on $3 roses and $2 carnations.
Calculate miles walked given pedometer flips and final reading.
Evaluate custom operation a$b = (a-b)^2 for (x-y)^2$(y-x)^2.
Find fraction BC/AD given AB=4*BD and AC=9*CD on segment AD.
Find length AC where C is midpoint of minor arc AB on circle radius 5 with chord AB=6.
Find number of bricks in chimney given individual and combined work rates with distraction.
Find ocean depth at base of cone-shaped mountain given top 1/8 volume above water.
Find 2008th term of sequence where mean of first n terms is n.
Find area of region inside square and outside triangle with distance constraints from side.
Find log_a(b) given circle radius log(a^2) and circumference log(b^4).
Find area of region S minus region R formed by equilateral triangles on a square.
Find number of ordered pairs (a,b) for floor dimensions with 1-foot border occupying half area.
Find sum of digits of y-coordinate of C on y=x^2 forming right triangle with area 2008.
Find volume of pyramid with square base area 196 and given lateral face areas.
Minimize |alpha|+|gamma| for complex quadratic with f(1) and f(i) real.
Count meetings between Michael walking 5 ft/s and truck moving 10 ft/s stopping 30s at each pail.
Probability two unit circles with centers on parallel segments intersect.
Probability SUV requiring 2 adjacent spaces can park after 12 cars park randomly in 16 spaces.
Find n such that sum of base-10 logs of divisors of 10^n equals 792.
Find least n so that A_0A_n >= 100 for equilateral triangles on y=sqrt(x).
Find area of hexagon formed by angle bisectors in trapezoid with sides 11,5,19,7.
Susan buys 4 tickets at 25% off, Pam buys 5 at 30% off. How much more does Pam pay?
A brick is placed in an aquarium; find how much the water rises.
The larger of two consecutive odd integers is three times the smaller. Find their sum.
Kate rode 30 min at 16 mph then walked 90 min at 4 mph. Find overall average speed.
Mr. Public paid 20% federal then 10% state tax on remainder, total $10500. Find inheritance.
In isosceles triangles ABC and ADC, find angle BAD given angles ABC=40 and ADC=140.
Five consecutive terms in an arithmetic sequence sum to 30. Which term can be found?
A star polygon is drawn on a clock face by connecting each number to the fifth clockwise. Find vertex angle.
Yan walks to stadium or walks home then bikes to stadium in same time. Find ratio of distances.
A 3-4-5 triangle is inscribed in a circle of radius 3. Find its area.
A sequence of three-digit integers where each term's tens/units become next term's hundreds/tens. Find largest prime factor always dividing sum.
Integers a,b,c,d chosen from 0 to 2007. Find probability that ad-bc is even.
Mouse runs along line y=-5x+18; cheese at (12,10). Find a+b where mouse starts getting farther.
Distinct integers a,b,c,d,e satisfy (6-a)(6-b)(6-c)(6-d)(6-e)=45. Find a+b+c+d+e.
Set {3,6,9,10} augmented by n; median equals mean. Find sum of all possible n.
How many three-digit numbers with distinct digits have one digit equal to the average of the other two?
Given sin a + sin b = sqrt(5/3) and cos a + cos b = 1, find cos(a-b).
Polynomial f(x)=x^4+ax^3+bx^2+cx+d has real coefficients, f(2i)=f(2+i)=0. Find a+b+c+d.
Triangles ABC and ADE have areas 2007 and 7002. Find sum of all possible x-coordinates of A.
Corners sliced off a unit cube so faces become regular octagons. Find total volume of removed tetrahedra.
Sum of zeros, product of zeros, and sum of coefficients of f(x)=ax^2+bx+c are equal. Find common value.
For how many positive integers n does n + S(n) + S(S(n)) = 2007, where S(n) is sum of digits?
Square ABCD of area 36 has AB parallel to x-axis; vertices on y=log_a x, y=2log_a x, y=3log_a x. Find a.
For n>1, F(n) is number of solutions to sin x = sin(nx) on [0,pi]. Find sum from n=2 to 2007.
A set of integers is spacy if it contains no more than one out of any three consecutive integers. How many subsets of {1,...,12} are spacy?
Calculate total wall area to paint in three bedrooms, excluding doors and windows.
Find average gas mileage for a round trip with different fuel efficiencies.
Find angle ABC in a triangle given central angles of its circumcircle.
Determine how many oranges cost as much as 18 bananas given fruit price ratios.
Find minimum correct answers needed to score at least 100 points on a test.
Find distance BD where two bugs meet on triangle sides traveling opposite directions.
Find angle E in a pentagon with equal sides and two right angles.
Tom's age equals sum of his three children's ages; find ratio of his age to years ago.
Evaluate f(5) given f(3x-1) = x^2 + x + 1 for all real x.
Find initial number of girls given percentage changes after two leave and two boys arrive.
Quadrilateral angles satisfy proportional relationship; find measure of angle A rounded.
Find the common score of juniors given class average and seniors' average.
Find probability that traffic light changes color during a random 3-second interval.
Find side length of equilateral triangle given distances from interior point to sides.
Find a+r for a geometric series with given sums of all terms and odd-power terms.
Count distinguishable colorings of a regular tetrahedron's faces with three colors.
Find median of set {0,1,a,b,1/b} given equation ab^2 = log_10(b).
Find sum of digits of three-digit integer lying one-third between consecutive squares.
Find sin(angle ABC) when rhombus is rolled into a cylinder of given volume.
Minimize sum of positive integers a,b,c,d given areas of two parallelograms.
Count base-3 palindromes among the first 2007 positive integers.
Find ratio of area enclosed by midpoint of two particles moving on triangle edges.
Count non-congruent right triangles with integer legs where area equals 3 times perimeter.
Count coprime positive integer pairs (a,b) such that a/b + 14b/(9a) is integer.
Find area of triangle BDE in 3D space given segment lengths and right angles.
Cost of 5 sandwiches at $3 and 8 sodas at $2.
Evaluate h⊗(h⊗h) given x⊗y = x³−y.
Find Mary's age given ratio 3:5 and Alice is 30.
Largest possible sum of digits on a digital clock.
How much more Dave pays than Doug for pizza.
Find y so rectangle cut into hexagons forms a square.
Mary's age on next birthday given percentages and sum.
Number of sets of consecutive positive integers summing to 15.
Cost of one pencil and one eraser given 13 pencils and 3 erasers cost $1.
Number of real x such that sqrt(120−sqrt(x)) is an integer.
Describe the graph of (x+y)² = x²+y².
Distance from top of top ring to bottom of bottom ring.
Sum of areas of three externally tangent circles at triangle vertices.
Smallest positive debt resolvable with pigs and goats.
Smallest positive z given cos x = 0 and cos(x+z) = 1/2.
Length CD of common internal tangent of two circles.
Ratio r/s for circle tangent to square with given AF length.
Largest domain of f satisfying f(x)+f(1/x)=x.
Find b for common external tangent y=mx+b to two circles.
Probability bug visits every cube vertex exactly once in 7 moves.
Ratio of areas of S₂ to S₁ defined by log inequalities.
Radius r such that probability of seeing 3 hexagon sides is 1/2.
Find x given A^100(S) = 1/2^50 for S = (1,x,...,x^100).
Number of terms in simplified (x+y+z)^2006 + (x−y−z)^2006.
Number of non-empty subsets of {1,...,15} with no consecutive numbers and element ≥ size.
Sum of alternating powers of -1 from 1 to 2006.
Evaluate a custom-defined operation with nested parentheses.
Find the losing team's score given total and margin.
Estimate the percentage change from a $20 bill for five items.
Time for Bob to catch John walking east at different speeds.
Calories in 200g of lemonade given recipe and calorie counts.
Seating arrangements for a family of four with driver restriction.
Find a+b given two lines intersect at (1,2).
Count even three-digit numbers with strictly increasing digits.
Max perimeter of triangle with sides x, 3x, and 15.
Ratio of cream in Joe's vs JoAnn's coffee after different steps.
Find b for parabola with vertex (p,p) and y-intercept (0,-p).
Area of smaller rhombus similar to larger rhombus with area 24.
Cost of jam given sandwich ingredients and total cost $2.53.
Area of hexagon formed by two externally tangent circles and tangents.
Area of regular hexagon given coordinates of two vertices.
Probability of rolling sum 7 with weighted dice in ratio 1:2:3:4:5:6.
Number of distinct points reachable in 10 steps on a lattice.
Find which age is not among eight children given license plate clues.
Probability that floor(log10(4x)) equals floor(log10(x)) for x in (0,1).
Perimeter of rectangle with given area and ellipse through vertices.
Minimize trailing zeros in a!b!c! with a+b+c=2006.
Find a+b for side length s = sqrt(a + b sqrt(2)) in right isosceles triangle.
Area of region in [0,pi/2]^2 satisfying sin^2 x - sin x sin y + sin^2 y <= 3/4.
Number of a_2 values such that a_{2006}=1 in absolute difference sequence.
Two is 10% of x and 20% of y; find x minus y.
Two equations have the same solution; find the value of b.
Rectangle diagonal is x, length twice width; find area.
Buy 4 windows get 1 free; find savings buying together vs separately.
Average of 20 numbers is 30, of 30 numbers is 20; find overall average.
Josh and Mike bike toward each other; find how far Mike rode.
Square inside square with given side lengths; find inner square area.
Three-digit number times digit sum equals 2005; find the hundreds digit.
Quadratic has only one solution for two values of a; find their sum.
Painted cube cut into unit cubes; find n given fraction of red faces.
Three-digit numbers where middle digit is average of first and last.
Line through (1,1) and (100,1000); count integer points strictly between.
Five-pointed star with numbers; sums form arithmetic sequence; find middle term.
Dot removed from die, then rolled; probability top face has odd dots.
Diameter AB, point C on AB, D and E on circle; find ratio of triangle areas.
Three small circles tangent to axes and each other; find ratio r/s.
Unit cube cut into prisms then again; find volume of piece containing vertex W.
Prime-looking numbers composite not divisible by 2,3,5; count under 1000.
Odometer skips digit 4; reading 002005; find actual miles traveled.
Piecewise function f iterated 2005 times equals 1/2; count solutions in [0,1].
Ordered triples (a,b,c) with log_a b = c^2005 and a+b+c=2005; count them.
Rectangular box inscribed in sphere; surface area 384, edge sum 112; find radius.
Two distinct numbers from powers of 2; probability log base a of b is integer.
P(x)=(x-1)(x-2)(x-3); count quadratics Q such that P(Q(x)) = P(x)R(x).
Points with coordinates from {0,1,2}; count equilateral triangles with vertices in set.
Profit from buying 1000 candy bars at five for $2 and selling at two for $1.
Find x such that x% of x equals 4.
Fraction of money left after buying all CDs given one fifth buys one third.
Maximum number of remaining quizzes Lisa can score below an A.
Shaded area of tiled bathroom floor with quarter-circle patterns.
Find BD in triangle ABC with AC=BC=7, AB=2, and CD=8.
Area enclosed by the graph of |3x|+|4y|=12.
Number of a such that y=x+a passes through vertex of y=x^2+a^2.
Difference between mean and median score on an exam with given percentages.
2005th term of sequence where each term is sum of cubes of digits of previous.
Probability sum of two random bills from envelope is $20 or more.
Find n/p given quadratic x^2+mx+n has roots twice those of x^2+px+m.
Product x1*x2*...*x124 given 4^x1=5, 5^x2=6, ..., 127^x124=128.
Radius of circle centered at (0,k) tangent to y=x, y=-x, and y=6.
Digit not used among eight digits of four two-digit numbers summing to 221.
Radius of smallest sphere centered at origin containing eight unit spheres.
Number of rational quadruples (a,b,c,d) satisfying log equation equal to 2005.
Area of region R of points C making triangle ABC acute with A(2,2), B(7,7).
Find x+y+m given x and y are two-digit reversals and x^2-y^2=m^2.
Minimum possible value of (a+b+c+d)^2+(e+f+g+h)^2 from given set.
Greatest k such that 7^k divides n, where n has 60 divisors and 7n has 80.
Number of possible z0 given z_{n+1}=i z_n / conjugate(z_n) and z_{2005}=1.
Find a+b given x^3+y^3 = a*10^{3z}+b*10^{2z} with log constraints.
Sum of x-coordinates of equilateral triangle vertices on y=x^2 with side slope 2.
Probability six ants on octahedron vertices move to adjacent vertices without collision.
Alicia earns $20 per hour; 1.45% is deducted for local taxes. Find cents per hour deducted.
Charlyn leaves 8 of 25 problems unanswered; find how many correct to score at least 100.
Find number of ordered positive integer pairs (x,y) satisfying x + 2y = 100.
Bertha has 6 daughters; some have 6 daughters. Total 30 women. Find how many have no daughters.
Given graph of line y=mx+b, determine which inequality about mb is true.
Given expressions U through Z involving powers of 2004, find which difference is largest.
Three players with tokens; each round the leader gives one token to each other and discards one. Find number of rounds.
Two overlapping right triangles share side AB; find difference in areas of triangles ADE and BDC.
Cylindrical jar diameter increased 25% without changing volume; find percent height decrease.
Sum of 49 consecutive integers is 7^5; find their median.
Average value of coins in purse is 20 cents; adding a quarter makes average 21. Find number of dimes.
Points A(0,9) and B(0,12); lines AA' and BB' intersect at C(2,8); A',B' on y=x. Find A'B' length.
Set S of points (a,b) with a,b in {-1,0,1}. Count distinct lines through at least two points of S.
Arithmetic progression with first term 9; adding 2 to second and 20 to third yields geometric progression. Find smallest possible third term of geometric progression.
Brenda and Sally run opposite directions on circular track from opposite points; find track length.
Find smallest x such that the nested logarithm expression is defined.
Function f defined by f(1)=1 and f(2n)=n*f(n); find f(2^100).
Square ABCD side 2; semicircle on AB inside square; tangent from C meets AD at E. Find CE length.
Three externally tangent circles A(radius 1), B, C; internally tangent to circle D. Find radius of B.
Select a,b in [0,1] randomly; let c=a+b. A,B,C are a,b,c rounded to nearest integer. Find P(A+B=C).
Infinite sum of cos^(2n)(theta) equals 5; find cos(2theta).
Three unit spheres on plane; sphere radius 2 rests on them. Find distance from plane to top of larger sphere.
Polynomial with real coefficients, 2004 distinct complex zeros; given sum of real parts equals sum of imaginary parts. Find which quantity can be nonzero.
Plane contains points A,B with AB=1; S is union of all unit disks covering AB. Find area of S.
For n>=4, a_n = 0.overline{133}_n (base n). Find product a_4*a_5*...*a_99 expressed as m/n! with minimal n; find m.
Jenny doubles free throws each practice; fifth practice she makes 48. Find first practice count.
Maximize c·a^b - d using digits 0,1,2,3 each once.
Find x+y given 2^x * 3^y = 1296 with positive integers x,y.
Probability a two-digit integer from 10-99 has at least one digit 7.
Isabella exchanges US to Canadian dollars; find sum of digits of initial amount.
Find distance between two cities given distances and directions from airport.
Area of union of a square and a circle centered at a vertex.
Number of rows in a can display where each row has two more cans than above.
Coordinates after rotating point 90° clockwise then reflecting over y=x.
Find area of annulus in terms of tangent segment length a.
Smallest class size given five 100s, all ≥60, mean 76.
Find 2004th term of sequence defined by subtracting previous from sum of two before.
Find a+b given f(x)=ax+b and f^{-1}(x)=bx+a with a,b real.
Area of pentagon formed by perpendiculars from points on legs of right triangle.
Difference in ages when Jack's age digits reverse Bill's; in 5 years Jack twice Bill.
Number of complex z with |z|=5 and f(z)=i*conjugate(z)=z.
Find a given cubic with three positive roots; sum of base-2 logs of roots is 5.
Length of segment AB on parabola y=4x^2+7x-1 with origin as midpoint.
Radius of sphere tangent to top, bottom, and lateral surface of truncated cone.
Probability cube can be placed so four vertical faces same color.
Sum of max and min of y/x over points on ellipse in first quadrant.
Sum of possible values of g in multiplicative magic square with positive integers.
Number of possible n for cubic with integer coefficients and three distinct positive roots.
Area of isosceles triangle given tangents form geometric and arithmetic progressions.
Number of powers of 2 from 2^0 to 2^2003 with first digit 4.
Difference between sum of first 2003 even and odd numbers
Number of soccer league members given total cost
Percent of original volume removed from box corners
Average speed for round trip uphill and downhill
Sum of digits A+M+C from sum of two 5-digit numbers
Which statement about a custom absolute value operation is false
Number of non-congruent triangles with integer sides and perimeter 7
Probability a random positive factor of 60 is less than 7
Smallest number of points in a set symmetric about origin and axes
Fraction of candy unclaimed after three people take wrong shares
Ratio of areas of circles circumscribed about square and triangle
Sum of numbers on middle three alternating color cards
Number of positions to attach a square to form a cube missing one face
Area of square formed by outer vertices of four equilateral triangles
Area of lune formed by two semicircles
Probability triangle ABP has greatest area among three subtriangles
Distance from intersection point of two circles to side of square
Number of 5-digit numbers where quotient plus remainder is divisible by 11
Graph of sum of reflected and translated parabolas
Number of 15-letter arrangements with restrictions on positions of letters
Which coefficient of a quintic with five distinct x-intercepts cannot be zero
Probability two objects moving randomly on grid meet
Number of perfect square divisors of product of factorials 1! through 9!
Largest possible value of sum of two log expressions
Number of real a such that domain and range of sqrt(ax^2+bx) are equal
Simplify a fraction with alternating signs in numerator and denominator.
Find the cost of one green pill given total cost for two weeks.
Minimize cost of planting flowers in rectangular regions of a flower bed.
Find time to mow a rectangular lawn with overlapping swath.
Find horizontal length of a TV screen given diagonal and aspect ratio.
Find a possible first term of a geometric sequence given two terms.
Find the largest integer dividing (n+1)(n+3)(n+5)(n+7)(n+9) for all even n.
Find the ratio of cone height to radius if melted ice cream fills the cone.
Linear function f satisfies f(6) - f(2) = 12; find f(12) - f(2).
Count non-congruent figures made by attaching two equilateral triangles to a regular pentagon in two of five positions.
Find a+b+c+d for the minimum x satisfying 7x^5 = 11y^13.
Find probability second term is 2 in random permutation of 1-5 with first term not 1.
Find the ratio of cone height to radius given ice cream sphere melts to fill cone.
Find area of triangle formed by intersecting lines in a rectangle.
Find area of rectangle inside a regular octagon of unit area.
Find shaded area inside large semicircle but outside three smaller semicircles.
Find minimum c so system 2x+y=2003, y=|x-a|+|x-b|+|x-c| has exactly one solution.
Find probability all three pairwise distances on a circle are less than the radius.
Probability that second term is 2 in random permutation of 1-5 with first term not 1.
Find coefficient b of cubic given graph with roots at -1, 0, 1.
Probability that distance AC is less than 7 given random turn angle.
Minimum distance from point on rhombus side to intersection of perpendiculars to diagonals.
Number of x-intercepts of sin(1/x) in interval (0.0001, 0.001).
Minimum c such that system with absolute values has exactly one solution.
Probability all three pairwise distances on a circle are less than the radius.
Sum of all roots of (2x+3)(x-4)+(2x+3)(x-6)=0
Find correct result after reversing subtraction and division steps
Number of distinct values from different parenthesizations of 2^2^2^2
Find angle whose complement is 25% of its supplement
Area of shaded region in concentric circles with tangent small circles
Number of positive integers m with n such that m*n ≤ m+n
Ratio of areas of two circles given equal arc lengths
Compare areas of blue triangles, white squares, and red square in flag
Minimum number of disks to store files of given sizes
Fraction of cream in first cup after mixing coffee and cream
Speed needed to arrive exactly on time given early/late data
Number of possible k such that quadratic has both roots prime
Sum of two positive numbers each differing from reciprocal by 1
Evaluate N = f(11)+f(13)+f(14) with f(n)=log_{2002} n^2
Largest possible integer in set of eight with mean, median, mode, range 8
Probability Sergio's number exceeds sum of Tina's two distinct numbers
Smallest possible sum of primes using each nonzero digit once
Length of common external tangent segment between two circles
Number of solutions to f(f(x))=6 from piecewise linear graph
Number of possible denominators for 0.overline{ab} in lowest terms
Smallest n such that sum of Fibonacci-like digit sequence exceeds 10000
Probability that BD > 5√2 for random point P in right triangle
Area of triangle ABD given AD=9, DC=7, with perpendicular bisector and angle bisector
Number of ordered pairs (a,b) such that (a+bi)^2002 = a-bi
Identify graph of polynomial P and Q where coefficients replaced by mean
Find the missing digit in the arithmetic mean of nine numbers consisting of repeated 9s.
Evaluate an algebraic expression at x=4 by simplifying or substituting.
Count positive integers n for which n^2-3n+2 is prime.
Determine which statement about n is false given the sum is an integer.
Find the middle term of an arithmetic sequence of pentagon angles summing to 540.
Find the pair (a,b) given that a and b are roots of x^2+ax+b=0.
Find the sum of squares of three consecutive positive integers with given product-sum relation.
Determine which weekday must appear five times in August given July has five Mondays.
Find a/d given a,b,c,d form an increasing arithmetic and a,b,d a geometric sequence.
Count distinct sums of three distinct members from the set {1,4,7,...,19}.
Determine the nature of the sum of four primes A, B, A-B, A+B.
Count integers n for which n/(20-n) is a perfect square.
Find the smallest perfect square sum of 18 consecutive positive integers.
Find the maximum number of intersection points among four distinct circles.
Count four-digit numbers N where removing the leftmost digit gives N/9.
Find probability that product of an octahedral and a six-sided die roll is a multiple of 3.
Determine who finishes mowing first given lawn areas and mower speeds.
Find probability a point in a rectangle is closer to the origin than to (3,1).
Find abc given a(b+c)=152, b(c+a)=162, c(a+b)=170.
Find XY in a right triangle given distances from vertices to midpoints of legs.
Sum a_n for n<2002 where a_n depends on divisibility by 11,13,14.
Compute b-c where b and c are sums of reciprocals of logs base n of 2002.
Find BC in triangle ABC where median from A equals BC, AB=1, AC=2.
Find perimeter of convex quadrilateral with interior point P and given distances.
Find area of region defined by f(x)+f(y)≤0 and f(x)-f(y)≤0 where f(x)=x^2+6x+1.
Two numbers sum to S; add 3 to each, double each, find new sum.
Two-digit number N equals product plus sum of its digits; find units digit.
Find annual income given a piecewise tax rate equals a flat percentage.
Mean is 10 more than least and 15 less than greatest; median is 5; find sum.
Find expression for product of all positive odd integers less than 10000.
Phone number with decreasing digits in each part; find A given sum condition.
140 tickets sold for $2001; full and half price; find full-price ticket revenue.
Cone formed from a 252° sector of radius 10; find slant height and radius.
Function f(xy)=f(x)/y for positive reals; f(500)=3; find f(600).
Plane tiled with squares and pentagons; find percent enclosed by pentagons.
5 chips (3 red, 2 white) drawn without replacement; probability last chip is white.
Count positive integers ≤2001 that are multiples of 3 or 4 but not 5.
Parabola reflected about horizontal line through vertex; find sum of coefficients.
Regular 9-gon; count distinct equilateral triangles with at least two vertices from set.
Shortest path on tetrahedron surface from midpoint of edge to opposite edge midpoint.
Spider puts on sock then shoe on each of 8 legs; count possible orders.
Random point in pentagon; probability angle APB is obtuse.
Two externally tangent circles of radii 1 and 4; find radius of circle tangent to both and common external tangent.
Cubic with average of zeros, product of zeros, sum of coefficients equal; y-intercept 2; find b.
Quadrilateral ABCD in first quadrant; midpoints form a square; find sum of coordinates of D.
Four positive integers with product 8! satisfy three equations; find a-d.
Rectangle area 70; points E,F,G on sides; find area of triangle EHJ.
Degree-4 polynomial with leading coefficient 1, integer coefficients, two integer zeros; which complex number can be a zero?
Triangle ABC with angle ABC=45°, D on BC with 2·BD=CD, angle DAB=15°; find angle ACB.
Sequence: each term after first is 1 less than product of neighbors; find how many x make 2001 appear.
Find largest sum of three distinct positive integers whose product is 2001.
Simplify the expression 2000(2000^{2000}).
Find original number of jellybeans given 20% eaten each day and 32 left after two days.
Find which digit is last to appear in the units place of Fibonacci numbers.
If |x-2|=p and x<2, find x-p in terms of p.
Find which number could be pq-(p+q) for two primes between 4 and 18.
Count positive integers b such that log_b(729) is a positive integer.
Find number of unit squares in figure 100 of a pattern.
Find last score entered given each partial average was an integer.
Find coordinates after reflecting, rotating, and translating a 3D point.
Find possible value of a/b + b/a - ab given ab = a - b.
Maximize AMC+AM+MC+AC given A+M+C=12 with nonnegative integers.
Find number of family members given Angela drank 1/4 milk and 1/6 coffee.
Find sum of all x such that mean, median, mode form an arithmetic progression.
Find sum of z satisfying f(3z)=7 given f(x/3)=x^2+x+1.
Find sum of numbers that are the same in row-major and column-major numbering.
Find OC in terms of theta given tangent and angle bisector in a circle.
Find day of week for 100th day of year N-1 given conditions on Tuesdays.
Find area of triangle ADE where D is midpoint and E is foot of angle bisector.
Find xyz given three equations relating x, y, z and their reciprocals.
Find ratio of area of small triangle to square in a right triangle with parallel lines.
Find smallest among five expressions involving a quartic polynomial from its graph.
Find probability winning ticket has same property: sum of logs of six numbers is integer.
Find circumference of circle tangent to two circular arcs and a line segment.
Count distinguishable colorings of a regular octahedron with 8 colors.