Difference between revisions of "2021 AMC 12A Problems"

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{{AMC12 Problems|year=2021|ab=A}}
 
{{AMC12 Problems|year=2021|ab=A}}
 
==Problem 1==
 
==Problem 1==
These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.
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TWhat is the value of<cmath>2^{1+2+3}-(2^1+2^2+2^3)?</cmath>
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<math>\textbf{(A) }0 \qquad \textbf{(B) }50 \qquad \textbf{(C) }52 \qquad \textbf{(D) }54 \qquad \textbf{(E) }57</math>
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[[2021 AMC 12A Problems/Problem 1|Solution]]
 
[[2021 AMC 12A Problems/Problem 1|Solution]]

Revision as of 15:34, 11 February 2021

2021 AMC 12A (Answer Key)
Printable version: Wiki | AoPS ResourcesPDF

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 test 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

TWhat is the value of\[2^{1+2+3}-(2^1+2^2+2^3)?\] $\textbf{(A) }0 \qquad \textbf{(B) }50 \qquad \textbf{(C) }52 \qquad \textbf{(D) }54 \qquad \textbf{(E) }57$


Solution

Problem 2

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 3

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 4

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 5

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 6

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 7

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 8

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 9

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 10

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 11

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 12

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 13

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 14

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 15

A choir director must select a group of singers from among his $6$ tenors and $8$ basses. The only requirements are that the difference between the numbers of tenors and basses must be a multiple of $4$, and the group must have at least one singer. Let $N$ be the number of groups that could be selected. What is the remainder when $N$ is divided by $100$?

$\textbf{(A) } 47\qquad\textbf{(B) } 48\qquad\textbf{(C) } 83\qquad\textbf{(D) } 95\qquad\textbf{(E) } 96\qquad$

Solution

Problem 16

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 17

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 18

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 19

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 20

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 21

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 22

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 23

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 24

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

Problem 25

These problems will not be posted until the 2021 AMC12A is released on Thursday, February 4, 2021.

Solution

See also

2021 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
2020 AMC 12B Problems
Followed by
2021 AMC 12B Problems
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 12 Problems and Solutions

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

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