2025 AMC 8 Problems

2025 AMC 8 (Answer Key) Printable versions: • AoPS Resources • PDF

Instructions This is a 25-question, multiple choice test. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct. You will receive 1 point for each correct answer. There is no penalty for wrong answers. No aids are permitted other than plain scratch paper, writing utensils, ruler, and erasers. In particular, graph paper, compass, protractor, calculators, computers, smartwatches, and smartphones are not permitted. Rules Figures are not necessarily drawn to scale. You will have 40 minutes working time to complete the test.

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Problem 1

Solution

The eight-pointed star, shown in the figure below, is a popular quilting pattern. What percent of the entire \(4\times4\) grid is covered by the star?

\[ \begin{array}{c} \text{{\begin{asy} // Draws a 4x4 grid with an eight-pointed star in the center size(5cm);

// Draw grid lines for (int i = 0; i <= 4; ++i) {

   draw((i,0)--(i,4), gray);
   draw((0,i)--(4,i), gray);

}

// Define star points pair A = (1,1), B = (2,1), C = (3,1); pair D = (1,2), E = (2,2), F = (3,2); pair G = (1,3), H = (2,3), I = (3,3);

// Fill star filldraw(E--B--F--cycle, gray); filldraw(E--D--F--cycle, gray); filldraw(E--H--F--cycle, gray); filldraw(E--G--F--cycle, gray); filldraw(E--B--D--cycle, gray); filldraw(E--D--G--cycle, gray); filldraw(E--H--I--cycle, gray); filldraw(E--F--I--cycle, gray);

// Draw star outline draw(A--C); draw(D--I); draw(G--I); draw(A--G); draw(A--E); draw(B--H); draw(F--H); draw(F--E); \end{asy}}} \end{array} \]

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

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Problem 10

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Problem 11

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Problem 12

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Problem 13

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Problem 14

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Problem 15

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Problem 16

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Problem 17

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Problem 18

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Problem 19

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Problem 20

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Problem 21

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Problem 22

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Problem 23

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Problem 24

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Problem 25

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See Also

AMC 8

AMC 8 Problems and Solutions

Mathematics Competition Resources