Competition · AMC preparation · step 4 of 4

AMC 8 2015: 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 2015 #1 grade 5+ geometry-2d
Onkon wants to cover his room's floor with his favourite red carpet. How many square yards of red carpet are required to…
AMC 8 2015 #2 grade 6+ geometry-2d
Point O is the center of the regular octagon ABCDEFGH, and X is the midpoint of the side AB. What fraction of the area o…
AMC 8 2015 #3 grade 6+ rate-ratio
Jack and Jill are going swimming at a pool that is one mile from their house. They leave home simultaneously. Jill rides…
AMC 8 2015 #4 grade 4+ counting
The Blue Bird High School chess team consists of two boys and three girls. A photographer wants to take a picture of the…
AMC 8 2015 #5 grade 6+ arithmetic
Billy's basketball team scored the following points over the course of the first 11 games of the season. If his team sco…
AMC 8 2015 #6 grade 8+ geometry-2d
In bigtriangleup ABC, AB=BC=29, and AC=42. What is the area of bigtriangleup ABC?
AMC 8 2015 #7 grade 7+ probability
Each of two boxes contains three chips numbered 1, 2, 3. A chip is drawn randomly from each box and the numbers on the t…
AMC 8 2015 #8 grade 6+ geometry-2d
What is the smallest whole number larger than the perimeter of any triangle with a side of length 5 and a side of length…
AMC 8 2015 #9 grade 3+ arithmetic, pattern
On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widge…
AMC 8 2015 #10 grade 5+ counting
How many integers between 1000 and 9999 have four distinct digits?
AMC 8 2015 #11 grade 7+ probability
In the small country of Mathland, all automobile license plates have four symbols. The first must be a vowel (A, E, I, O…
AMC 8 2015 #12 grade 4+ geometry-3d, counting
How many pairs of parallel edges, such as AB and GH or EH and FG, does a cube have?
AMC 8 2015 #13 grade 7+ arithmetic, counting
How many subsets of two elements can be removed from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} so that the mean (avera…
AMC 8 2015 #14 grade 4+ algebra, number-theory
Which of the following integers cannot be written as the sum of four consecutive odd integers?
AMC 8 2015 #15 grade 6+ arithmetic, logic
At Euler Middle School, 198 students voted on two issues in a school referendum with the following results: 149 voted in…
AMC 8 2015 #16 grade 6+ rate-ratio
In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No…
AMC 8 2015 #17 grade 8+ rate-ratio, algebra
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can…
AMC 8 2015 #18 grade 4+ algebra, pattern
An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous…
AMC 8 2015 #19 grade 6+ geometry-2d
A triangle with vertices as A=(1,3), B=(5,1), and C=(4,4) is plotted on a 6×5 grid. What fraction of the grid is covered…
AMC 8 2015 #20 grade 6+ algebra, arithmetic
Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, som…
AMC 8 2015 #21 grade 8+ geometry-2d
In the given figure, hexagon ABCDEF is equiangular, ABJI and FEHG are squares with areas 18 and 32 respectively, △ JBK i…
AMC 8 2015 #22 grade 6+ number-theory
On June 1, a group of students is standing in rows, with 15 students in each row. On June 2, the same group is standing…
AMC 8 2015 #23 grade 6+ logic, arithmetic
Tom has twelve slips of paper which he wants to put into five cups labeled A, B, C, D, E. He wants the sum of the number…
AMC 8 2015 #24 grade 7+ algebra, number-theory
A baseball league consists of two four-team divisions. Each team plays every other team in its division N games. Each te…
AMC 8 2015 #25 grade 6+ geometry-2d
One-inch squares are cut from the corners of this 5 inch square. What is the area in square inches of the largest square…

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