Difference between revisions of "2025 AMC 8 Problems"

Revision as of 18:44, 29 January 2025

2025 AMC 8 (Answer Key) Printable versions: Wiki • 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?

$\textbf{(A)}\ 40 \qquad \textbf{(B)}\ 50 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 80$

Solution

Problem 2

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

@@ Line 7: / Line 7: @@
 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?
-\[
-\begin{array}{c}
-\text{{\begin{asy}
-// Draws a 4x4 grid with an eight-pointed star in the center
-size(5cm);
-// Draw grid lines
-for (int i = 0; i <= 4; ++i) {
-    draw((i,0)--(i,4), gray);
-    draw((0,i)--(4,i), gray);
-}
-// Define star points
-pair A = (1,1), B = (2,1), C = (3,1);
-pair D = (1,2), E = (2,2), F = (3,2);
-pair G = (1,3), H = (2,3), I = (3,3);
-// Fill star
-filldraw(E--B--F--cycle, gray);
-filldraw(E--D--F--cycle, gray);
-filldraw(E--H--F--cycle, gray);
-filldraw(E--G--F--cycle, gray);
-filldraw(E--B--D--cycle, gray);
-filldraw(E--D--G--cycle, gray);
-filldraw(E--H--I--cycle, gray);
-filldraw(E--F--I--cycle, gray);
-// Draw star outline
-draw(A--C);
-draw(D--I);
-draw(G--I);
-draw(A--G);
-draw(A--E);
-draw(B--H);
-draw(F--H);
-draw(F--E);
-\end{asy}}}
-\end{array}
-\]
 <math>\textbf{(A)}\ 40 \qquad \textbf{(B)}\ 50 \qquad \textbf{(C)}\ 60 \qquad \textbf{(D)}\ 75 \qquad \textbf{(E)}\ 80</math>

2025 AMC 8 (Problems • Answer Key • Resources)
Preceded by 2024 AMC 8	Followed by 2026 AMC 8
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All AJHSME/AMC 8 Problems and Solutions

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Difference between revisions of "2025 AMC 8 Problems"

Revision as of 18:44, 29 January 2025

Contents

Problem 1

Solution

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

See Also