Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus
AMC 10 CLASSES
AoPS has trained thousands of the top scorers on AMC tests over the last 20 years in our online AMC 10 Problem Series course.
CHECK SCHEDULE

Difference between revisions of "2021 Fall AMC 10A Problems"
Line 2: Line 2:
  
 
==Problem 1==
 
==Problem 1==
 +
What is the value of <math>\frac{(2112-2021)^2}{169}</math>?
 +
 +
<math>\textbf{(A) } 7 \qquad\textbf{(B) } 21 \qquad\textbf{(C) } 49 \qquad\textbf{(D) } 64 \qquad\textbf{(E) } 91</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 1|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 1|Solution]]
  
 
==Problem 2==
 
==Problem 2==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 2|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 2|Solution]]
  
 
==Problem 3==
 
==Problem 3==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 3|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 3|Solution]]
  
 
==Problem 4==
 
==Problem 4==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 4|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 4|Solution]]
  
 
==Problem 5==
 
==Problem 5==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 5|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 5|Solution]]
  
 
==Problem 6==
 
==Problem 6==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 6|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 6|Solution]]
  
 
==Problem 7==
 
==Problem 7==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 7|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 7|Solution]]
  
 
==Problem 8==
 
==Problem 8==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 8|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 8|Solution]]
  
 
==Problem 9==
 
==Problem 9==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 9|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 9|Solution]]
  
 
==Problem 10==
 
==Problem 10==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 10|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 10|Solution]]
  
 
==Problem 11==
 
==Problem 11==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 11|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 11|Solution]]
  
 
==Problem 12==
 
==Problem 12==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 12|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 12|Solution]]
  
 
==Problem 13==
 
==Problem 13==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 13|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 13|Solution]]
  
 
==Problem 14==
 
==Problem 14==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 14|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 14|Solution]]
  
 
==Problem 15==
 
==Problem 15==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 15|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 15|Solution]]
  
 
==Problem 16==
 
==Problem 16==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 16|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 16|Solution]]
  
 
==Problem 17==
 
==Problem 17==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 17|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 17|Solution]]
  
 
==Problem 18==
 
==Problem 18==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 18|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 18|Solution]]
  
 
==Problem 19==
 
==Problem 19==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 19|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 19|Solution]]
  
 
==Problem 20==
 
==Problem 20==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 20|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 20|Solution]]
  
 
==Problem 21==
 
==Problem 21==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 21|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 21|Solution]]
  
 
==Problem 22==
 
==Problem 22==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 22|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 22|Solution]]
  
 
==Problem 23==
 
==Problem 23==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 23|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 23|Solution]]
  
 
==Problem 24==
 
==Problem 24==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 24|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 24|Solution]]
  
 
==Problem 25==
 
==Problem 25==
 +
 +
<math>\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }</math>
  
 
[[2021 Fall AMC 10A Problems/Problem 25|Solution]]
 
[[2021 Fall AMC 10A Problems/Problem 25|Solution]]

Revision as of 17:43, 22 November 2021

2021 Fall AMC 10A (Answer Key)
Printable versions: Wiki • Fall AoPS Resources • Fall PDF

Instructions

  1. 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.
  2. 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.
  3. 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).
  4. Figures are not necessarily drawn to scale.
  5. You will have 75 minutes working time to complete the test.
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Problem 1

What is the value of $\frac{(2112-2021)^2}{169}$?

$\textbf{(A) } 7 \qquad\textbf{(B) } 21 \qquad\textbf{(C) } 49 \qquad\textbf{(D) } 64 \qquad\textbf{(E) } 91$

Solution

Problem 2

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 3

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 4

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 5

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 6

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 7

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 8

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 9

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 10

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 11

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 12

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 13

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 14

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 15

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 16

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 17

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 18

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 19

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 20

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 21

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 22

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 23

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 24

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

Problem 25

$\textbf{(A) } \qquad\textbf{(B) } \qquad\textbf{(C) } \qquad\textbf{(D) } \qquad\textbf{(E) }$

Solution

See also

2021 AMC 10A (Problems • Answer Key • Resources)
Preceded by
2020 AMC 10B 		Followed by
2021 AMC 10B
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2021_Fall_AMC_10A_Problems&oldid=165025"