Competition · AMC preparation · step 4 of 4

AMC 8 2019: all 25 problems

Each problem has a solution worked from first principles and the first grade (by CCSS standards) that can solve it.

AMC 8 2019 #1 grade 5+ arithmetic
Ike and Mike go into a sandwich shop with a total of $30.00 to spend. Sandwiches cost $4.50 each and soft drinks cost $1…
AMC 8 2019 #2 grade 4+ geometry-2d
Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length…
AMC 8 2019 #3 grade 4+ arithmetic
Which of the following is the correct order of the fractions 15/11,19/15, and 17/13, from least to greatest?
AMC 8 2019 #4 grade 8+ geometry-2d
Quadrilateral ABCD is a rhombus with perimeter 52 meters. The length of diagonal AC is 24 meters. What is the area in sq…
AMC 8 2019 #5 grade 8+ rate-ratio, algebra
A tortoise challenges a hare to a race. The hare eagerly agrees and quickly runs ahead, leaving the slow-moving tortoise…
AMC 8 2019 #6 grade 7+ geometry-2d, probability
There are 81 grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges.…
AMC 8 2019 #7 grade 6+ arithmetic
Shauna takes five tests, each worth a maximum of 100 points. Her scores on the first three tests are 76 , 94 , and 87 .…
AMC 8 2019 #8 grade 6+ arithmetic
Gilda has a bag of marbles. She gives 20% of them to her friend Pedro. Then Gilda gives 10% of what is left to another f…
AMC 8 2019 #9 grade 8+ geometry-3d, rate-ratio
Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high…
AMC 8 2019 #10 grade 6+ arithmetic
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and…
AMC 8 2019 #11 grade 2+ counting, logic
The eighth grade class at Lincoln Middle School has 93 students. Each student takes a math class or a foreign language c…
AMC 8 2019 #12 geometry-3d, logic
The faces of a cube are painted in six different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple…
AMC 8 2019 #13 grade 4+ number-theory
A palindrome is a number that has the same value when read from left to right or from right to left. (For example, 12321…
AMC 8 2019 #14 grade 4+ number-theory, logic
Isabella has 6 coupons that can be redeemed for free ice cream cones at Pete's Sweet Treats. In order to make the coupon…
AMC 8 2019 #15 grade 6+ probability
On a beach 50 people are wearing sunglasses and 35 people are wearing caps. Some people are wearing both sunglasses and…
AMC 8 2019 #16 grade 6+ rate-ratio, algebra
Qiang drives 15 miles at an average speed of 30 miles per hour. How many additional miles will he have to drive at 55 mi…
AMC 8 2019 #17 grade 5+ arithmetic, pattern
What is the value of the product ((1·3)/(2·2))((2·4)/(3·3))((3·5)/(4·4))…((97·99)/(98·98))((98·100)/(99·99))?
AMC 8 2019 #18 grade 7+ probability, counting
The faces of each of two fair dice are numbered 1, 2, 3, 5, 7, and 8. When the two dice are tossed, what is the probabil…
AMC 8 2019 #19 grade 4+ logic, counting
In a tournament there are six teams that play each other twice. A team earns 3 points for a win, 1 point for a draw, and…
AMC 8 2019 #20 grade 6+ algebra
How many different real numbers x satisfy the equation (x²-5)²=16?
AMC 8 2019 #21 grade 6+ geometry-2d, algebra
What is the area of the triangle formed by the lines y=5, y=1+x, and y=1-x?
AMC 8 2019 #22 grade 7+ rate-ratio, algebra
A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount.…
AMC 8 2019 #23 grade 6+ number-theory, algebra
After Euclid High School's last basketball game, it was determined that 1/4 of the team's points were scored by Alexa an…
AMC 8 2019 #24 grade 8+ geometry-2d
In triangle △ ABC, point D divides side AC so that AD:DC=1:2. Let E be the midpoint of BD and let F be the point of inte…
AMC 8 2019 #25 grade 6+ counting
Alice has 24 apples. In how many ways can she share them with Becky and Chris so that each of the three people has at le…

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