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Difference between revisions of "2024 AMC 12A Problems"

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{{AMC12 Problems|year=2024|ab=A}}
  
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==Problem 1==
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What is the value of <math>9901\cdot101-99\cdot10101?</math>
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<math>\textbf{(A)}~2\qquad\textbf{(B)}~20\qquad\textbf{(C)}~200\qquad\textbf{(D)}~202\qquad\textbf{(E)}~2020</math>
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[[2024 AMC 12A Problems/Problem 1|Solution]]
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==Problem 2==
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A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form <math>T=aL+bG,</math> where <math>a</math> and <math>b</math> are constants, <math>T</math> is the time in minutes, <math>L</math> is the length of the trail in miles, and <math>G</math> is the altitude gain in feet. The model estimates that it will take <math>69</math> minutes to hike to the top if a trail is <math>1.5</math> miles long and ascends <math>800</math> feet, as well as if a trail is <math>1.2</math> miles long and ascends <math>1100</math> feet. How many minutes does the model estimates it will take to hike to the top if the trail is <math>4.2</math> miles long and ascends <math>4000</math> feet?
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<math>\textbf{(A) }240\qquad\textbf{(B) }246\qquad\textbf{(C) }252\qquad\textbf{(D) }258\qquad\textbf{(E) }264</math>
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[[2024 AMC 12A Problems/Problem 2|Solution]]
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==Problem 3==
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[[2024 AMC 12A Problems/Problem 3|Solution]]
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==Problem 4==
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[[2024 AMC 12A Problems/Problem 4|Solution]]
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==Problem 5==
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[[2024 AMC 12A Problems/Problem 5|Solution]]
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==Problem 6==
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[[2024 AMC 12A Problems/Problem 6|Solution]]
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==Problem 7==
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[[2024 AMC 12A Problems/Problem 7|Solution]]
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==Problem 8==
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[[2024 AMC 12A Problems/Problem 8|Solution]]
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==Problem 9==
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[[2024 AMC 12A Problems/Problem 9|Solution]]
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==Problem 10==
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[[2024 AMC 12A Problems/Problem 10|Solution]]
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==Problem 11==
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[[2024 AMC 12A Problems/Problem 11|Solution]]
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==Problem 12==
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[[2024 AMC 12A Problems/Problem 12|Solution]]
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==Problem 13==
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[[2024 AMC 12A Problems/Problem 13|Solution]]
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==Problem 14==
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[[2024 AMC 12A Problems/Problem 14|Solution]]
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==Problem 15==
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[[2024 AMC 12A Problems/Problem 15|Solution]]
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==Problem 16==
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[[2024 AMC 12A Problems/Problem 16|Solution]]
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==Problem 17==
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[[2024 AMC 12A Problems/Problem 17|Solution]]
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==Problem 18==
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[[2024 AMC 12A Problems/Problem 18|Solution]]
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==Problem 19==
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[[2024 AMC 12A Problems/Problem 19|Solution]]
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==Problem 20==
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[[2024 AMC 12A Problems/Problem 20|Solution]]
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==Problem 21==
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[[2024 AMC 12A Problems/Problem 21|Solution]]
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==Problem 22==
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[[2024 AMC 12A Problems/Problem 22|Solution]]
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==Problem 23==
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[[2024 AMC 12A Problems/Problem 23|Solution]]
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==Problem 24==
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[[2024 AMC 12A Problems/Problem 24|Solution]]
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==Problem 25==
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[[2024 AMC 12A Problems/Problem 25|Solution]]
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==See also==
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{{AMC12 box|year=2024|ab=A|before=[[2023 AMC 12B Problems]]|after=[[2024 AMC 12B Problems]]}}
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* [[AMC 12]]
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* [[AMC 12 Problems and Solutions]]
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* [[Mathematics competitions]]
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* [[Mathematics competition resources]]

Revision as of 17:06, 8 November 2024

2024 AMC 12A (Answer Key)
Printable versions: Wiki • AoPS Resources • 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 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

What is the value of $9901\cdot101-99\cdot10101?$

$\textbf{(A)}~2\qquad\textbf{(B)}~20\qquad\textbf{(C)}~200\qquad\textbf{(D)}~202\qquad\textbf{(E)}~2020$

Solution

Problem 2

A model used to estimate the time it will take to hike to the top of the mountain on a trail is of the form $T=aL+bG,$ where $a$ and $b$ are constants, $T$ is the time in minutes, $L$ is the length of the trail in miles, and $G$ is the altitude gain in feet. The model estimates that it will take $69$ minutes to hike to the top if a trail is $1.5$ miles long and ascends $800$ feet, as well as if a trail is $1.2$ miles long and ascends $1100$ feet. How many minutes does the model estimates it will take to hike to the top if the trail is $4.2$ miles long and ascends $4000$ feet?

$\textbf{(A) }240\qquad\textbf{(B) }246\qquad\textbf{(C) }252\qquad\textbf{(D) }258\qquad\textbf{(E) }264$

Solution

Problem 3

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

Problem 11

Solution

Problem 12

Solution

Problem 13

Solution

Problem 14

Solution

Problem 15

Solution

Problem 16

Solution

Problem 17

Solution

Problem 18

Solution

Problem 19

Solution

Problem 20

Solution

Problem 21

Solution

Problem 22

Solution

Problem 23

Solution

Problem 24

Solution

Problem 25

Solution

See also

2024 AMC 12A (Problems • Answer Key • Resources)
Preceded by
2023 AMC 12B Problems 		Followed by
2024 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
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