American Mathematics Competitions Syllabus 2026: AMC 8, AMC 10 and AMC 12 Topics

The American Mathematics Competitions (AMC) are designed to help students build mathematical reasoning and problem-solving skills through challenging questions. Organised by the Mathematical Association of America (MAA), the AMC program includes competitions for students at different school levels.

The AMC syllabus 2026 varies depending on the competition. The AMC 8 syllabus focuses on middle school mathematics, while the AMC 10 syllabus covers elementary high school mathematics. The AMC 12 syllabus includes the full high school mathematics curriculum, except calculus.

Knowing the American Mathematics Competition syllabus can help students understand what topics to prepare, choose the right competition, and plan their preparation more effectively.

American Mathematics Competitions Syllabus 2026

There is no single syllabus for all AMC exams. The topics depend on whether a student is taking the AMC 8, AMC 10, or AMC 12.

The MAA does not provide a traditional chapter-by-chapter syllabus. Instead, it describes the mathematical content and skills tested in each competition.

AMC 8 Syllabus 2026

The AMC 8 syllabus is designed for middle school students and focuses on mathematical concepts that students typically encounter through Grade 8.

The competition includes 25 questions to be solved in 40 minutes.

AMC 8 Syllabus Topics

The major AMC 8 topics include:

• Counting and probability

• Estimation

• Proportional reasoning

• Elementary geometry

• Pythagorean theorem

• Spatial visualization

• Graphs and tables

• Basic arithmetic

• Beginning algebra

• Linear functions

• Quadratic functions

• Coordinate geometry

The later questions can be more challenging and may require students to combine multiple concepts or use creative problem-solving approaches.

AMC 8 Mathematics Topics Explained

Counting and Probability: Students may encounter basic counting techniques and probability-based problems.

Estimation: Questions can test whether students can make reasonable estimates and work efficiently with numbers.

Proportional Reasoning: Ratios, proportions, rates, and related applications are important areas.

Geometry: Students should be comfortable with elementary geometric concepts, including shapes, angles, areas, volumes, and the Pythagorean theorem.

Graphs and Tables: Students may need to interpret information presented through graphs, tables, or diagrams.

Beginning Algebra: Some questions may involve linear or quadratic functions and coordinate geometry.

AMC 10 Syllabus 2026

The AMC 10 syllabus is intended for students in Grade 10 and below. It contains 25 multiple-choice questions and has a 75-minute time limit.

The AMC 10 covers elementary mathematics topics and problem-solving techniques.

AMC 10 Syllabus Topics

The major topics include:

• Elementary algebra

• Basic geometry

• Area and volume

• Elementary number theory

• Probability

• Counting

• Arithmetic

• Ratios and proportions

• Coordinate geometry

• Functions

The AMC 10 does not include advanced topics such as trigonometry, advanced algebra, or advanced geometry.

Elementary Algebra

Students should have a strong understanding of basic algebraic concepts, including equations, expressions, functions, and algebraic manipulation.

Geometry

The syllabus includes basic geometric concepts, along with area and volume formulas. Students should also be comfortable solving geometry problems using logical reasoning.

Number Theory

Elementary number theory is another important part of the AMC 10 syllabus. Students may need to work with factors, multiples, divisibility, prime numbers, and related properties.

Probability and Counting

Students should understand basic probability and counting principles and be able to apply them to unfamiliar problems.

AMC 12 Syllabus 2026

The AMC 12 syllabus covers a broader range of high school mathematics than AMC 10.

The AMC 12 consists of 25 multiple-choice questions with a 75-minute time limit.

It covers the full high school mathematics curriculum, including more advanced concepts.

AMC 12 Syllabus Topics

The main areas include:

• Algebra

• Advanced algebra

• Geometry

• Advanced geometry

• Trigonometry

• Number theory

• Probability

• Counting

• Functions

• Coordinate geometry

Calculus is excluded from the AMC 12.

Algebra

AMC 12 preparation should include strong knowledge of algebraic expressions, equations, inequalities, functions, sequences, and other high school algebra concepts.

Geometry

Students should prepare for both elementary and advanced geometry. Problems can involve angles, triangles, circles, polygons, coordinate geometry, area, volume, and geometric relationships.

Trigonometry

Unlike the AMC 10, the AMC 12 includes trigonometry. Students should be familiar with fundamental trigonometric concepts and their applications.

Number Theory

Number theory problems can involve divisibility, primes, factors, remainders, modular reasoning, and other properties of integers.

Probability and Counting

Students should understand fundamental counting principles and probability and be prepared to apply them to unfamiliar competition-style problems.

AMC 10 vs AMC 12 Syllabus

The AMC 10 and AMC 12 have several topics in common, but the AMC 12 covers more advanced mathematics.

The key difference is that AMC 12 covers the full high school mathematics curriculum, including trigonometry, while AMC 10 excludes advanced algebra, advanced geometry, and trigonometry.

Is There an AMC Mathematics Syllabus PDF?

Students looking for an AMC mathematics syllabus PDF should note that MAA describes the content of each AMC competition rather than providing one conventional chapter-wise syllabus PDF.

Students can use the official MAA AMC information and past competition problems to understand the topics and difficulty level. Past papers are particularly useful because AMC questions are designed to test problem-solving ability rather than simple memorisation.

AMC Syllabus Topics Students Should Prioritise

While preparing for AMC, students should focus on both mathematical concepts and problem-solving techniques.

1. Build Strong Fundamentals

Before attempting difficult AMC problems, make sure the basics of arithmetic, algebra, geometry, probability, and number theory are clear.

2. Practice Non-Routine Problems

AMC questions often require students to look at familiar concepts in unfamiliar ways. Regular practice with competition-style questions can help develop this skill.

3. Work on Speed and Accuracy

AMC competitions have strict time limits. Students need to solve problems efficiently while avoiding careless mistakes.

For AMC 8, students have 40 minutes for 25 questions, while AMC 10 and AMC 12 students have 75 minutes for 25 questions.

4. Learn From Previous AMC Problems

Solving previous AMC questions can help students understand the style, difficulty, and types of reasoning expected in the competition.

5. Practice Different Topics Together

Instead of studying only one topic at a time, students should eventually practice mixed-topic problem sets. AMC questions can require students to combine concepts from different areas of mathematics.

Understanding the American Mathematics Competitions syllabus for 2026 can help students prepare for the right level of AMC and focus their practice on the most relevant mathematical concepts. AMC 8 emphasises middle school mathematics, while AMC 10 focuses on elementary high school topics. AMC 12 goes further by covering advanced algebra, geometry, and trigonometry, while excluding calculus.

Students should not rely only on textbook exercises. Regular practice with previous AMC problems, timed tests, and non-routine questions can help develop the speed, accuracy, and mathematical reasoning needed to perform well in the competition.

Related Resources:

• AMC Exam Dates 2026-27

• American Mathematics Olympiad

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