AMC 8 Math Concepts Quiz

Ike and Mike have $30.00 to spend on sandwiches and soft drinks. Each sandwich costs $4.50 and each soft drink costs $1.00. They want to buy as many sandwiches as possible and then use the remaining money for soft drinks. The question asks for the total number of items they will buy.

Three identical rectangles are arranged to form a larger rectangle ABCD. The shorter side of each smaller rectangle is 5 feet long. The problem asks for the area of the larger rectangle ABCD.

The question asks for the order of the fractions 15/11, 19/15, and 17/13 from least to greatest.

A rhombus ABCD has a perimeter of 52 meters and a diagonal AC with a length of 24 meters. The problem asks for the area of the rhombus.

A tortoise and a hare race. The hare runs quickly at first, then takes a nap, allowing the tortoise to slowly but steadily win the race. The question asks for the graph that best represents this scenario.

In a square grid with 81 points, one point (P) is at the center, and another (Q) is chosen randomly from the remaining points. The problem asks for the probability that line PQ is a line of symmetry for the square.

Shauna took five tests, each worth 100 points. Her scores on the first three tests were 76, 94, and 87. She aims to average 81 across all five tests. The question asks for the lowest possible score she could get on one of the remaining two tests.

Gilda has a bag of marbles. She gives 20%, 10%, and 25% of her marbles to three different friends. The question asks for the percentage of marbles Gilda has left for herself.

Alex and Felicia have cylindrical cat food cans with different dimensions. Alex's cans have a 6 cm diameter and 12 cm height, while Felicia's have a 12 cm diameter and 6 cm height. The question asks for the ratio of the volume of Alex's can to the volume of Felicia's can.

There are 93 eight-graders, with 70 taking math, 54 taking a foreign language, and some taking both. The question asks for the number of eighth-graders who take only math and not a foreign language.

A cube has faces painted different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown. The problem asks for the color of the face opposite the aqua face.

A palindrome is a number that is the same forward and backward, like 12321. The problem asks for the least three-digit number that is not a palindrome but is the sum of three distinct two-digit palindromes, and then the sum of digits of that number.

Isabella has 6 coupons for free ice cream, and she plans to use one every 10 days. She wants to avoid Sundays. The problem asks for the day of the week she will redeem her first coupon.

On a beach, 50 people wear sunglasses, 35 wear caps, and some wear both. The probability that someone wearing a cap also wears sunglasses is 2/5. The question asks for the probability that someone wearing sunglasses also wears a cap.

Qiang travels 15 miles at 30 mph. The problem asks how many more miles he needs to drive at 55 mph to achieve a 50 mph average speed for the whole trip.

The provided expression involves a series with alternating signs and a specific pattern. You need to evaluate the final value of the product.

Two fair dice are numbered 1, 2, 3, 5, 7, and 8. The problem asks for the probability of getting an even sum when both dice are rolled.

Six teams play each other twice in a tournament. Each win earns 3 points, a draw earns 1 point, and a loss earns 0 points. The top three teams have the same number of points. The question asks for the maximum possible points for each of the top three teams.

The question asks to find the area of the triangle formed by the lines y = 5, y = 1 + x, and y = 1 - x.

A store increases a shirt's price by a certain percentage and then decreases it by the same percentage. The final price is 84% of the original. The problem asks for the percentage by which the price was increased and decreased.

In a basketball game, Alexa scored 1/4 of the team's points, Brittany scored 2/7, and Chelsea scored 15. The remaining 7 team members scored no more than 2 points each. The question asks for the total points scored by these 7 members.

Alice has 24 apples. The problem asks for the number of ways she can share these apples with Becky and Chris, ensuring each person gets at least 2 apples.

The expression involves the product of several terms. You need to compute the final value of the product.

Students in a circle count numbers. When the number contains a 7 or is a multiple of 7, the student leaves the circle. The question asks for the last student present.

The expression involves a series of consecutive odd numbers with a pattern and a series of consecutive even numbers with a pattern. The question asks for the value of the difference.

Anh drove 50 miles on the highway and 10 miles on a coastal road. His highway speed was three times his coastal road speed. He spent 30 minutes on the coastal road. The question asks for the total time of his trip in minutes.

A five-digit number 2018U is divisible by 9. The question asks for the remainder when this number is divided by 8.

The harmonic mean is defined as the reciprocal of the average of the reciprocals of a set of numbers. The problem asks for the harmonic mean of the numbers 1, 2, and 4.

Six students are arranged in two rows of three in a random order. The problem asks for the probability that Abby and Bridget sit next to each other in the same row or column.

Sri's car clock gains time at a constant rate. His watch is accurate, and his car clock is 5 minutes ahead after a 30-minute shopping trip. The car clock shows 7:00. The problem asks for the actual time.

Laila took five math tests, each worth 100 points. She scored the same on the first four tests and higher on the fifth. Her average score is 82. The question asks for the number of possible scores for her fifth test.

The problem asks for the greatest five-digit number whose digits have a product of 120 and the sum of the digits of that number.

Two smaller circles are inside a larger circle, with each smaller circle's diameter equal to the larger circle's radius. The smaller circles have a combined area of 1 square unit. The problem asks for the area of the shaded region.

Professor Chang has nine language books to arrange: two Arabic, three German, and four Spanish. Books of the same language must be kept together. The problem asks for the number of ways to arrange the books.

Bella and Ella are traveling towards each other, Bella walking and Ella biking five times faster. The distance between their houses is 2 miles (10,560 feet), and Bella takes 2.5 feet per step. The question asks for the number of steps Bella takes before meeting Ella.

The problem asks for the number of positive factors of 23,232.

A sign pyramid with four levels is filled either with '+' or '-'. A cell gets '+' if both cells below it have the same sign and '-' if they have different signs. The question asks for the number of possible ways to fill the bottom row with signs to produce a '+' at the top.

The problem asks for the number of three-digit integers that leave certain remainders when divided by 6, 9, and 11.

Point E is the midpoint of CD in square ABCD, and BE intersects diagonal AC at F. The area of AFED is 45. The question asks for the area of ABCD.

In a regular octagon, a triangle is formed by randomly connecting three vertices. The question asks for the probability that at least one side of the triangle is also a side of the octagon.

The question asks for the number of perfect cubes between 2⁸ + 1 and 2¹⁸ + 1, inclusive.

The number of students at soccer practice is given for each weekday. The mean and median were calculated, but then an error in the Wednesday count is corrected. The question asks how the mean and median change.

In a cube with opposite vertices C and E, midpoints J and I are marked on edges FB and HD respectively. The question asks for the square of the ratio of the area of cross-section EJCI to the area of a cube face.

In triangle ABC, point D divides AC such that AD:DC = 1:2. E is the midpoint of BD, and F is the intersection of BC and AE. The area of ABC is 360. The question asks for the area of AEBF.

Point E is the midpoint of CD in square ABCD, and BE intersects diagonal AC at F. The area of AFED is 45. The question asks for the area of ABCD.

In triangle ABC, E is on AB with AE = 1 and EB = 2. D is on AC such that DE || BC, and F is on BC such that EF || AC. The question asks for the ratio of the area of CDEF to the area of ABC.

Students in a health class reported the number of days they exercised for at least 30 minutes last week. The results are presented in a bar graph. The question asks for the mean number of days, rounded to the nearest hundredth.