2025 AMC 10A Problems: Difference between revisions

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2025 AMC 10A (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 6 points for each correct answer, 2.5 points for each problem left unanswered if the year is before 2006, 1.5 points for each problem left unanswered if the year is after 2006, and 0 points for each incorrect answer. No aids are permitted other than scratch paper, graph paper, ruler, compass, protractor and erasers (and calculators that are accepted for use on the SAT if before 2006. No problems on the test will require the use of a calculator). Figures are not necessarily drawn to scale. You will have 75 minutes working time to complete the test.
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Problem 1

Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at 1:30 traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at 2:30, traveling due east at a steady 12 miles per hour. At what time will they be exactly the same distance from their common starting point?

$\textbf{(A) } 3{:}30 \qquad\textbf{(B) } 3{:}45 \qquad\textbf{(C) } 4{:}00 \qquad\textbf{(D) } 4{:}15 \qquad\textbf{(E) } 4{:}30$

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Suppose $a$ and $b$ are real numbers. When the polynomial $x^3+x^2+ax+b$ is divided by $x-1$ , the remainder is $4$ . When the polynomial is divided by $x-2$ , the remainder is $6$ . What is $b-a$ ?

$\textbf{(A) } 14 \qquad\textbf{(B) } 15 \qquad\textbf{(C) } 16 \qquad\textbf{(D) } 17 \qquad\textbf{(E) } 18$

Solution

Problem 8

Agnes writes the following four statements on a blank piece of paper.

At least one of these statements is true. At least two of these statements are true. At least two of these statements are false. At least one of these statements is false. Each statement is either true or false. How many false statements did Agnes write on the paper?

Answer Choices:

A. 0

B. 1

C. 2

D. 3

E. 4

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Six chairs are arranged around a round table…

Correct ans: 1/5

Solution: 6 choose 2 times 4 choose 2 times 6 * 3 times 2 factorial squared/

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

This is a problem that's easier than problem 1 but being put to problem 22 to mess up our points

Problem 23

Triangle $\triangle ABC$ has side lengths $AB = 80$ , $BC = 45$ , and $AC = 75$ . The bisector $\angle B$ and the altitude to side $\overline{AB}$ intersect at point $P$ . What is $BP$ ?

$\textbf{(A)}~18\qquad\textbf{(B)}~19\qquad\textbf{(C)}~20\qquad\textbf{(D)}~21\qquad\textbf{(E)}~22$

@@ Line 4: / Line 4: @@
 Andy and Betsy both live in Mathville. Andy leaves Mathville on his bicycle at 1:30 traveling due north at a steady 8 miles per hour. Betsy leaves on her bicycle from the same point at 2:30, traveling due east at a steady 12 miles per hour. At what time will they be exactly the same distance from their common starting point?
-<imath>\textbf{(A) } 3{:}30 \qquad\textbf{(B) } 3:45 \qquad\textbf{(C) } 4:00 \qquad\textbf{(D) } 4:15 \qquad\textbf{(E) } 4:30</imath>
+<imath>\textbf{(A) } 3{:}30 \qquad\textbf{(B) } 3{:}45 \qquad\textbf{(C) } 4{:}00 \qquad\textbf{(D) } 4{:}15 \qquad\textbf{(E) } 4{:}30</imath>
 ==Problem 2==

2025 AMC 10A (Problems • Answer Key • Resources)
Preceded by 2024 AMC 10B Problems	Followed by 2025 AMC 10B Problems
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All AMC 10 Problems and Solutions

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