2025 AMC 10B Problems: Difference between revisions

Revision as of 23:49, 9 November 2025

2025 AMC 10B (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

What is the value of

$\sqrt{6-2{\sqrt{5}}}+\sqrt{6+2{\sqrt{5}}}$

$\textbf{(A)} ~2 \qquad\textbf{(B)} ~\sqrt{5} \qquad\textbf{(C)} ~2\sqrt{5} \qquad\textbf{(D)} ~4\sqrt{5} \qquad\textbf{(E)} ~12$

Solution

Problem 2

Zane is a three-year-old who wants to find the roots of the cubic $ax^3-bx^2+cx-d$ , but doesn't know how to, so he randomly factors the equation into $(x+a)(x-b)(x+c)$ . For how many polynomials is the equation equal to Zach's factoring?

@@ Line 13: / Line 13: @@
 ==Problem 2==
-Zane is a three-year-old who wants to find the roots of the cubic <imath>ax^3-bx^2+cx-d</imath>, but doesn't know how to, so he randomly factors the equation into <imath>(x+a)(x-b)(x+c)</imath>. For <imath>a=1</imath>, <imath>b<\infty</imath>, and <imath>c<\infty</imath>, what is the probability that the expansion of Zane's factoring is equal to the original cubic?
+Zane is a three-year-old who wants to find the roots of the cubic <imath>ax^3-bx^2+cx-d</imath>, but doesn't know how to, so he randomly factors the equation into <imath>(x+a)(x-b)(x+c)</imath>. For how many polynomials is the equation equal to Zach's factoring?
 ==Problem 3==

2025 AMC 10B (Problems • Answer Key • Resources)
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2025 AMC 10B Problems: Difference between revisions

Revision as of 23:49, 9 November 2025

Contents

Problem 1

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