What's Actually on the AMC 12: A Complete Topic Breakdown

If you're moving up from AMC 10—or jumping straight into AMC 12—you need to know exactly what's different.

Here's everything that's covered.

The Short Version

AMC 12 covers the full high school math curriculum. That means everything on AMC 10, plus trigonometry, logarithms, and complex numbers. Still no calculus.

The format is identical to AMC 10: 25 questions, 75 minutes, multiple choice. But the problems go deeper, and the additional topics open up new problem types entirely.

Test Basics

One thing worth noting: the AIME cutoff for AMC 12 is lower than AMC 10. About 5% of AMC 12 takers qualify, compared to 2.5% of AMC 10 takers.

AMC 12 = AMC 10 + More

AMC 12 includes everything from AMC 10:

• Algebra (through Algebra II)
• Geometry
• Number Theory
• Counting & Probability

Plus these additional topics:

• Trigonometry
• Logarithms
• Complex Numbers
• Advanced Algebra
• Advanced Geometry

About 40-60% of problems (10-15 questions) overlap between AMC 10 and AMC 12 each year. The rest are AMC 12 exclusive.

The Additional Topics

These are what set AMC 12 apart.

Trigonometry

This is the biggest addition. You need solid command of trig, not just memorized formulas.

What you need to know:

• Unit circle and radian measure
• All six trig functions and their graphs
• Pythagorean identities
• Sum and difference formulas
• Double angle and half angle formulas
• Law of Sines and Law of Cosines
• Solving triangles
• Inverse trig functions
• Trig equations

Competition-level applications:

• Using trig to solve geometry problems (often faster than synthetic methods)
• Trig substitutions in algebra
• Roots of unity connections

Logarithms

Logarithms appear both as standalone problems and as tools for solving other problems.

What you need to know:

• Definition and properties of logarithms
• Change of base formula
• Logarithmic equations
• Exponential and logarithmic functions
• Natural logarithm (basic)

Competition-level applications:

• Manipulating complex logarithmic expressions
• Using logs to compare large numbers
• Functional equations involving logs

Complex Numbers

Complex numbers are a major topic on AMC 12. They connect algebra, geometry, and trigonometry in powerful ways.

What you need to know:

• Arithmetic with complex numbers
• Complex plane and geometric representation
• Modulus and argument
• Polar form (r·cis θ)
• De Moivre's Theorem
• Roots of unity
• Complex conjugates

Competition-level applications:

• Using complex numbers to solve geometry problems
• Finding roots of polynomials
• Connecting to trigonometric identities

Advanced Algebra

AMC 12 pushes algebra further than AMC 10.

Additional topics:

• Polynomial theory (degree, roots, coefficients)
• Rational functions
• Partial fractions (basic)
• Inequalities (AM-GM, Cauchy-Schwarz at basic level)
• Functional equations (more complex)
• Sequences and series (more advanced)

Advanced Geometry

Geometry on AMC 12 can use tools unavailable in AMC 10.

Additional approaches:

• Trigonometric solutions to geometry problems
• Complex number geometry
• More sophisticated coordinate geometry
• Conic sections (basic)
• Three-dimensional geometry (more complex)

Why These Topics Matter

Here's something important: the additional AMC 12 topics don't just add new problem types. They give you more powerful tools for solving problems.

Many AMC 10 geometry problems require clever auxiliary lines or creative insights. The same problems often have straightforward solutions using trigonometry. If you know trig, you have options.

Complex numbers turn many geometry problems into algebra. Logs simplify problems involving large exponents. These tools expand what you can do.

AMC 10 vs AMC 12: Side by Side

What's Still NOT on AMC 12

Even AMC 12 has limits:

• Calculus (no derivatives, integrals, limits)
• Linear algebra (matrices beyond basics)
• Advanced statistics
• College-level topics

The MAA keeps AMC 12 within pre-calculus bounds. The difficulty comes from creative problem-solving, not advanced topics.

Strategic Considerations

Should you take AMC 10 or AMC 12?

Arguments for AMC 12:

• Lower AIME cutoff percentage (5% vs 2.5%)
• The additional topics are useful for AIME anyway
• More powerful problem-solving tools
• Better signal to colleges if you score well

Arguments for AMC 10:

• Smaller topic range to prepare
• Can take AMC 12 later with more preparation
• Some students score higher on AMC 10

If you're comfortable with trig, logs, and complex numbers, AMC 12 often makes sense. If those topics are still shaky, strengthen them first.

Preparation Priorities for AMC 12

If you're coming from AMC 10 preparation:

The additional topics aren't just "extra material." They become essential tools for solving harder problems efficiently.

The Real Challenge

AMC 12 isn't harder just because it covers more topics. It's harder because:

1. Problems assume you can combine multiple advanced concepts
2. Later problems require genuine insight, not just technique
3. Time pressure is intense—75 minutes for 25 problems
4. The competition is strong—everyone taking AMC 12 is serious about math

Knowing the topics is table stakes. Applying them creatively under pressure is the real test.

AMC 12 doesn't just test more math. It tests whether you can think flexibly with a larger toolkit.