AMC 8 Problems

Percent of a 4x4 grid covered by an eight-pointed star.

Interpret Egyptian hieroglyphs to find the represented number.

Find cards per player when 2 more friends join a 4-player game.

Find the 10th number when counting backward by 7 from 100.

Shortest route in blocks from F to A to B to C and back to F.

Which number from 15-19 is erased so the sum of the rest is a multiple of 4.

Number of students scoring at least 80% and less than 90%.

Volume of a cube given the area of its net is 18.

Average of the averages of opposite numbers on a clock.

Total area covered by two overlapping rectangles after a 90-degree rotation.

Identify the two other tetrominoes when an S tile covers a 3x4 rectangle.

Area of the largest circle that fits inside a 24-square region.

Histogram of remainders when even numbers 2 to 50 are divided by 7.

Find N so that the mean of the list is twice the median.

Least and greatest number of gold-on-gold pairs when folding a 6x6 grid.

Sum of ten chosen numbers from 1-20 with no pair differing by 10.

Number of people working in city A given fractions commuting between cities.

Radius R of a circle where one quarter of the ring equals the full ring of a unit circle.

Meeting point of two cars driving toward each other with changing speed limits.

Fraction of cheese Sarika eats in total when each person eats half of what remains.

Sum of grades assigned to pods C, E, F given adjacency constraints.

Number of different coat counts that allow equal spacing on 35 hooks.

Four-digit numbers ending in 99, one less than a perfect square, product of two primes.

Number of non-congruent trapezoids with integer sides, 60-degree angles, perimeter 30.

Sum of areas between all NE/NW paths and the right side of a 5x5 diamond grid.

Find the units digit of a long subtraction expression.

Compute the sum of three fractions in decimal form.

Find the area of the visible gray region in a diagram of four aligned squares.

Find the number left out when a sum of 1 to 9 becomes a square.

Find which sum cannot occur when the product of two dice is a multiple of 6.

Order four skating paths from shortest to longest.

Find the minimum number of 1x1 tiles needed to cover a 3x7 rectangle.

Count different dollar amounts possible after three days of adding or doubling.

Find which total number of marbles is possible given ratios of red, green, and blue.

Estimate the CO2 level in 2030 given a starting value and annual increase.

Find the y-coordinate of a triangle vertex given the area and base.

Find the number of guppies in the fourth tank given a total and differences.

Count sequences of 6 hops up and down that start and end on the ground.

Find the shortest route from A to Z on a one-way road network.

Find the sum of two 3-digit numbers from a repeating-digit equation.

Minimize rows and columns with a product divisible by 3 in a 9x9 grid.

Count ways to place two non-attacking kings on a 3x3 grid.

Find the central angle so shaded and unshaded areas of concentric circles are equal.

Find the least possible fraction of red high-top sneakers given totals.

Count equilateral triangles containing vertex P in a cube.

Find the difference between green and yellow frogs after a move changes the ratio.

Estimate the length of tape unrolled from a roll with given diameters and thickness.

Count grid cells intersected by a line segment from (2000,3000) to (5000,8000).

Find the height h where two right-triangle mountains intersect given total area.

Find probability a couple gets adjacent seats in a plane with 8 passengers already seated.

Evaluate the expression (8 × 4 + 2) - (8 + 4 × 2).

Determine the unfolded shape after folding and cutting a square paper.

Calculate wind chill given air temperature and wind speed.

Count primes among four numbers on a diagonal in a spiral grid.

Find total fish in a lake given trout count and sample ratio.

Maximize expression by placing digits 2,0,2,3 into boxes.

Count points on a rectangle that lie on two given lines.

Determine Tiyo's win-loss record in a ping pong tournament.

Find total seconds Malaika's elevation is between 4 and 7 meters.

Calculate fraction of pie remaining after three successive eatings.

Estimate rover's average speed in mph given distance and time.

Find fraction of large white circle's interior that is shaded.

Find race length given positions of water and repair stations.

Maximize number of stamps to make exactly $7.10 in postage.

Find speed needed to reach school on time after a detour.

Count P, Q, R letters in a 20x20 table with a repeating pattern.

Identify which numbered face ends up to the right of Q on an octahedron.

Find fewest jumps for a grasshopper to reach pad 2023 pads right.

Find ratio of trapezoid area to inner triangle area in an equilateral triangle.

Find maximum sum of two numbers inserted to double range without changing mode or median.

Count ways to divide numbers 1-9 into three groups with equal sums.

Find first term of a sequence where each term after second is product of previous two.

Find probability a 3x3 tiling contains a large gray diamond in a 2x2 subgrid.

Find height h of isosceles triangle given heights of unshaded portions.

Find sum of digits of a_14 given constraints on equally spaced integers.

Find the area of a multiplication symbol logo on a grid of 1-inch squares.

Evaluate the expression (5 blacklozenge 3) bigstar 6 using defined operations.

Count ways to choose three positive integers a<b<c whose product is 100.

Identify the resulting image after reflecting the letter M over two lines.

Find how many years older Anna is than Bella given ages and a kitten.

Find the smallest of three equally spaced positive integers with middle 15.

Calculate minutes to download a 4.2 MB song at 56 kilobits per second.

Compute the product of fractions from 1/3 to 20/22.

Find water temperature after 15 minutes if temperature difference halves every 5 minutes.

Select the graph showing distance from home during a hike with two driving speeds.

Find original length of pasta if 10 pieces total 17 inches after 3-inch bites.

Find probability that 10A+B is a perfect square using two spinners.

Count how many positive integers can fill the blank in the sentence.

Count rearrangements of BEEKEEPER with no two Es adjacent.

Find the weight of pepper with lowest price per ounce from a scatter plot.

Find average of first and last numbers given averages of pairs.

Find units digit of sum of double factorials from 2!! to 2022!!.

Find area of rectangle given midpoints of its sides.

Find minimum students who got 5 extra points to raise median to 85.

Find smallest possible x in a 3x3 grid with equal row and column sums.

Find how many more baskets Candace scored in second half than first.

Find minutes until Zia boards the bus given speeds and waiting rules.

Count 3x3 grids with three triangles and three circles in a line.

Find volume of triangular prism formed by folding a polygon net.

Find probability cricket returns to starting leaf after 4 hops among 4 leaves.

Luka makes lemonade with 4 times as much water as sugar and twice as much sugar as lemon juice. He uses 3 cups of lemon juice. How many cups of water does he need?

Four friends earn $15, $20, $25, and $40. They split earnings equally. How much does the friend who earned $40 give to the others?

Carrie has a 6 ft by 8 ft garden. She plants 4 strawberry plants per square foot, each yielding 10 strawberries. How many strawberries will she harvest?

Three hexagons of increasing size are shown. The dot pattern continues with one more band of dots per hexagon. How many dots are in the next hexagon?

Three-fourths of a pitcher is filled with juice. It is poured equally into 5 cups. What percent of the total capacity did each cup receive?

Five people sit in a train with five cars. Maren is last. Aaron is directly behind Sharon. Darren is in front of Aaron. At least one person sits between Karen and Darren. Who sits in the middle car?

How many integers between 2020 and 2400 have four distinct digits arranged in increasing order?

Ricardo has 2020 coins, some pennies and some nickels. He has at least one of each. What is the difference between the greatest and least possible amounts of money?

A 4x4x4 cake has icing on the top and four sides. It is cut into 64 unit cubes. How many small cubes have icing on exactly two sides?

Zara has 4 marbles: Aggie, Bumblebee, Steelie, Tiger. She wants to arrange them in a row but not put Steelie and Tiger next to each other. How many ways?

Maya bikes and Naomi takes a bus to the beach 6 miles away. The graph shows their journeys. What is the difference in their average speeds in mph?

For positive integer n, n! is the product from n to 1. What value of N satisfies 5! * 9! = 12 * N!?

Jamal has 6 green, 18 purple, and 12 orange socks. After adding more purple socks, the probability of picking a purple sock is 60%. How many purple socks did he add?

The bar chart shows populations of 20 cities. The dashed line is the average population. What is the total population of all 20 cities?

15% of x equals 20% of y. What percentage of x is y?

Points A-F represent digits 1-6. The digits along each of five lines are added, totaling 47. What digit is B?

How many positive integer factors of 2020 have more than 3 factors?

Rectangle ABCD is inscribed in a semicircle with diameter FE. DA=16, FD=AE=9. What is the area of ABCD?

A flippy number has alternating distinct digits. How many five-digit flippy numbers are divisible by 15?

A scientist recorded heights of 5 trees. Each tree is either twice or half as tall as the one to its right. The average height ends in .2. What is the average height?

A marker starts at P on a checkerboard. Each step moves to an adjoining white square in the row above. How many 7-step paths are there from P to Q?

A machine outputs N/2 if N is even, 3N+1 if N is odd. After 6 steps starting from N, the final output is 1. What is the sum of all such N?

Five different awards are given to three students. Each student receives at least one award. In how many ways can the awards be distributed?

A large square is paved with n^2 gray tiles, each with a border of width d. When n=24, the tiles cover 64% of the area. What is d/s?

Rectangles R1, R2 and squares S1, S2, S3 combine to form a rectangle 3322 wide and 2020 high. What is the side length of S2?

Ike and Mike buy sandwiches and drinks with $30.

Find area of rectangle formed by three identical rectangles.

Order three fractions from least to greatest.

Find area of rhombus given perimeter and one diagonal.

Select graph matching tortoise and hare race description.

Probability line from center to random point is symmetry line.

Find lowest possible score on one test to average 81.

Find percentage of marbles left after three sequential gifts.

Find ratio of volumes of two cylindrical cat food cans.

Describe change in mean and median after correcting Wednesday's count.

Find number of students taking only math class.

Find color of face opposite aqua on painted cube.

Find sum of digits of least 3-digit non-palindrome sum of three 2-digit palindromes.

Find day of week Isabella redeems first coupon.

Find probability person wearing sunglasses also wears a cap.

Find additional miles needed to average 50 mph overall.

Evaluate product of fractions from 1 to 98.

Find probability sum of two special dice is even.

Find greatest possible points for each of top three teams.

Find number of real solutions to (x^2-5)^2 = 16.

Find area of triangle formed by three lines.

Find percent increase and decrease that results in 84% of original.

Find total points scored by other 7 team members.

Find area of triangle EBF given triangle ABC area 360.

Number of ways to share 24 apples among three people with each getting at least 2.

Scale model height given real height and ratio 1:20.

Compute product of fractions (1+1/n) from n=1 to 6.

Counting game in a circle; last person standing.

Area of a 12-sided figure on graph paper.

Sum of odd numbers minus sum of even numbers up to 2019.

Total travel time given speeds and distances.

Find remainder when 5-digit number divisible by 9 is divided by 8.

Mean number of exercise days from a bar graph.

Number of tiles for border and inner floor of a room.

Compute harmonic mean of 1, 2, and 4.

Probability two friends sit adjacent in a 2x3 grid.

Actual time given a fast car clock and accurate watch.

Possible last test score given average and first four equal scores.

Greatest 5-digit number with digit product 120; sum of digits.

Area of shaded region in three tangent circles.

Arrangements of books keeping Arabic and Spanish books together.

Number of steps Bella takes until meeting Ella.

Number of positive factors of 23,232.

Number of bottom row sign patterns giving a plus at top of pyramid.

Ratio of area of quadrilateral CDEF to triangle ABC.

Count three-digit integers with given remainders mod 6, 9, 11.

Area of square given area of quadrilateral AFED.

Probability triangle from octagon vertices shares a side with octagon.

Ratio of cross-section area to face area in a cube.

Count perfect cubes between 2^8+1 and 2^18+1 inclusive.

Evaluate arithmetic expressions to find the largest value.

Use a pie chart to find total votes from a given percentage.

Simplify a nested radical expression involving square roots.

Estimate the product of a decimal and a large integer.

Compute the value of a fraction with factorial numerator and sum denominator.

Find the largest angle of a triangle given a ratio.

Determine which number must be a factor of a 6-digit repeating number.

Find the units digit of a house number given three true statements.

Find the smallest possible number of yellow marbles given fractions and a count.

Find probability that 4 is the largest card drawn from five cards.

Find total square tiles given the number on both diagonals.

Find the smallest integer >1 with remainder 1 when divided by 4, 5, 6.

Find Kyler's wins given total wins and losses in a chess tournament.