art of problem solving amc 10 practice tests

2021 Fall AMC 10B Problems

1 Problem 1
2 Problem 2
3 Problem 3
4 Problem 4
5 Problem 5
6 Problem 6
7 Problem 7
8 Problem 8
9 Problem 9
10 Problem 10
11 Problem 11
12 Problem 12
13 Problem 13
14 Problem 14
15 Problem 15
16 Problem 16
17 Problem 17
18 Problem 18
19 Problem 19
20 Problem 20
21 Problem 21
22 Problem 22
23 Problem 23
24 Problem 24
25 Problem 25
26 See also

$1234+2341+3412+4123?$

Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris's. What is the expected number of balls that occupy their original positions after these two successive transpositions?

$(\textbf{A})\: 1.6\qquad(\textbf{B}) \: 1.8\qquad(\textbf{C}) \: 2.0\qquad(\textbf{D}) \: 2.2\qquad(\textbf{E}) \: 2.4$

AMC 10 Problems and Solutions
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AMC 10 Problems

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Mathematical Association of America

Sample competition: 2022 amc 10 a.

Test out your creative problem-solving skills! Try your hand at these problems from the 2022 American Mathematics Competition (AMC) 10 A competition. This mathematical competition is for students in grades 10 and below.

Interested in more? You can purchase collections of past competitions from our store or participate in our next MAA AMC competition .