AMC 12 Number Theory Practice Exam

AMC 12 Number Theory Practice Exam

This is a comprehensive practice exam featuring 41 authentic AMC 12 Number Theory questions spanning from 2000 to 2023. All questions are multiple choice with detailed solutions.

Exam Information

How to Use This Exam

Try solving each problem on your own before revealing hints or solutions. The problems are arranged by difficulty level, with intermediate questions first.

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• Complete Intermediate Problems (1-14)

  Harder problems from #17-#25 range
• Complete Introductory Problems (15-41)

  Foundation number theory problems
• Review all solutions

  Understand the solution methods
• Identify weak areas

  Focus on problem types you struggled with

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Part I: Intermediate Number Theory

These 14 problems represent the more challenging number theory questions (typically problems #17-#25).

Problem 1 - AMC 12A 2023 #17

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Problem 2 - AMC 12A 2023 #22

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Problem 3 - AMC 12A 2022 #23

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Problem 4 - AMC 12A 2022 #25

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Problem 5 - Fall AMC 12B 2021 #25

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Problem 6 - AMC 12A 2021 #25

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Problem 7 - AMC 12B 2018 #17

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Problem 8 - AMC 12B 2017 #19

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Problem 9 - AMC 12B 2017 #21

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Problem 10 - AMC 12B 2016 #22

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Problem 11 - AMC 12B 2014 #23

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Problem 12 - AMC 12A 2010 #23

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Problem 13 - AMC 12A 2009 #18

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Problem 14 - AMC 12B 2004 #25

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Part II: Introductory Number Theory

These 27 problems cover fundamental number theory topics.

Problem 15 - AMC 12B 2023 #16

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Problem 16 - AMC 12B 2018 #15

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Problem 17 - AMC 12B 2016 #16

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Problem 18 - AMC 12B 2013 #9

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Problem 19 - AMC 12B 2013 #14

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Problem 20 - AMC 12B 2013 #15

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Problem 21 - AMC 12B 2012 #11

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Problem 22 - AMC 12B 2011 #15

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Problem 23 - AMC 12A 2010 #11

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Problem 24 - AMC 12A 2007 #11

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Problem 25 - AMC 12A 2007 #12

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Problem 26 - AMC 12A 2007 #22

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Problem 27 - AMC 12A 2006 #4

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Problem 28 - AMC 12A 2006 #9

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Problem 29 - AMC 12A 2006 #14

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Problem 30 - AMC 12A 2005 #18

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Problem 31 - AMC 12A 2003 #8

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Problem 32 - AMC 12A 2003 #12

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Problem 33 - AMC 12B 2002 #3

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Problem 34 - AMC 12B 2002 #11

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Problem 35 - AMC 12B 2002 #12

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Problem 36 - AMC 12B 2002 #15

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Problem 37 - AMC 12A 2002 #20

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Problem 38 - AMC 12 2000 #6

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Problem 39 - AMC 12 2000 #13

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Problem 40 - AMC 12 2000 #16

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Problem 41 - AMC 12 2000 #18

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Summary and Review

Key Number Theory Topics Covered

Difficulty Distribution

The exam is designed with a mix of difficulties:

• Intermediate (34%): Typically AMC 12 problems #17-#25, requiring deeper insights
• Introductory (66%): Foundation problems that test core number theory concepts

This mirrors the actual AMC 12 exam structure where later problems are significantly harder.

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Topic Index

By Mathematical Concept

Modular Arithmetic & CRT:

• Problems 3, 5, 8, 9, 21, 25

Prime Factorization & Divisibility:

• Problems 2, 6, 11, 12, 18, 22, 24, 33

Diophantine Equations:

• Problems 4, 15, 28, 29

GCD/LCM Applications:

• Problems 3, 29

Number Bases:

• Problems 21

Combinatorics & Counting:

• Problems 16, 17, 30, 31

Probability:

• Problems 1, 25, 31

Sequences:

• Problems 19, 26

Special Topics:

• Frobenius numbers (15)
• Repeating decimals (10, 37)
• Factorial trailing digits (12, 13)
• Power of 2 properties (14, 22)

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Study Recommendations

Next Steps

After completing this exam:

1. Review any problems you struggled with
2. Try solving them again without looking at the solution
3. Look for similar problems in past AMC 12 exams
4. Focus on the specific topics where you need more practice

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Exam compiled from authentic AMC 12 competitions (2000-2023) All solutions verified and detailed for learning