The AMC 10 is the gateway to AIME. But what exactly gets tested, and how has it changed?

I analyzed 6 years of AMC 10 data (2020-2025), covering both the A and B versions. The patterns are clear—and different from what most prep advice suggests.

The Big Picture: What Dominates?

Let's start with the overall topic distribution.

![amc10_total_distribution.png]

Algebra dominates at 42%. That's nearly half the test. If your algebra is weak, AIME qualification is a distant dream.

But here's the surprise: Number Theory is now #2 at 22%. Five years ago, it was the least tested topic. More on this below.

Year-by-Year Trends

The yearly breakdown reveals important shifts.

Key observations:

1. Algebra is stable but heavy. Consistently 9-11 problems per test. This won't change.
2. Number Theory surged. From 3 problems in 2020 to 5-6 problems now. This is the fastest-growing topic.
3. Geometry is declining slightly. From 6 problems to 4. Still important, but less dominant than in AMC 8.
4. Counting stays constant. About 5 problems per test, every year. Predictable.

The Rising Star: Number Theory

This deserves its own section.

Number Theory went from 3 problems (12%) in 2020 to 5-6 problems (22%) in recent years. That's an 83% increase.

Why does this matter? Because most school curricula barely cover number theory. Topics like:

• Modular arithmetic
• Prime factorization techniques
• Diophantine equations
• Number bases
• Divisibility properties

These are not taught in typical Algebra 1/2 classes. If you don't study them separately, you're giving up ~5 problems.

Hard Problems: Q21-25 Analysis

AIME qualification often comes down to the last 5 questions. What topics appear there?

Unlike AMC 8 where geometry dominates hard problems, AMC 10 hard problems are evenly distributed.

This means you can't afford to be weak in any area. A single topic weakness could cost you 1-2 hard problems—enough to miss the AIME cutoff.

Recent trend: Algebra and Number Theory are appearing more in Q21-25, while Geometry is declining in the hard section.

AIME Cutoff Trends

What score do you need to qualify for AIME?

Key insights:

• Cutoffs are volatile, ranging from 88.5 to 105
• 10A and 10B can differ by 10+ points
• Taking both A and B doubles your chances
• Average cutoff is around 100 (roughly 14 correct + 4 blank)

2024 Awards (for reference):

How to Prepare: Topic-by-Topic

Based on the data, here's how to prioritize.

Priority 1: Algebra (42% of test)

This is non-negotiable. You must be fast and accurate.

Key subtopics:

• Quadratic equations and factoring
• Systems of equations
• Functions and graphs
• Sequences (arithmetic, geometric)
• Inequalities
• Polynomials

How to train:

• AoPS Introduction to Algebra + Intermediate Algebra
• AMC 10 past problems sorted by topic
• Focus on speed drills—algebra problems should be automatic

Priority 2: Number Theory (22%, RISING)

The highest-ROI topic to study. Most competitors are weak here.

Key subtopics:

• Modular arithmetic (remainders, congruences)
• Prime factorization and divisibility
• GCD/LCM applications
• Number bases
• Diophantine equations
• Digit problems

How to train:

• AoPS Introduction to Number Theory (essential)
• Practice converting between bases
• Master mod arithmetic through repetition
• AMC 10/12 number theory problem sets

Priority 3: Counting & Probability (20%)

Consistent and predictable. Systematic methods win.

Key subtopics:

• Combinations and permutations
• Complementary counting
• Casework
• Expected value
• Probability with conditions

How to train:

• AoPS Introduction to Counting & Probability
• Practice "no gaps, no overlaps" counting
• Work on problems requiring multiple techniques

Priority 4: Geometry (16%)

Still important, but less dominant than in AMC 8.

Key subtopics:

• Similar triangles and ratios
• Circles (inscribed angles, power of a point)
• Coordinate geometry
• 3D visualization
• Area methods

How to train:

• AoPS Introduction to Geometry
• Focus on problems combining multiple concepts
• Learn coordinate bash as a backup technique

Topic Ranking at a Glance

![amc10_topic_ranking.png]

AMC 10 vs AMC 8: Key Differences

If you're transitioning from AMC 8:

The biggest shift: AMC 8 rewards geometry specialists. AMC 10 requires balanced mastery across all topics.

Strategic Recommendations

For AIME Qualification (Score ~100+)

1. Master Q1-15 first. These should be nearly automatic. Target 14-15 correct.
2. Get 2-3 from Q16-20. This is where preparation shows.
3. Attempt 1-2 from Q21-25. Even partial progress helps.
4. Leave strategic blanks. Wrong answers cost 0.5 points.

For Distinction (Score ~110+)

1. Q1-15 must be perfect or near-perfect.
2. Get 4-5 from Q16-20.
3. Solve 2-3 from Q21-25.
4. Time management is critical. Practice under test conditions.

For Honor Roll (Score ~135+)

1. Near-perfect on Q1-20.
2. Solve 3-4 from Q21-25.
3. This requires deep mastery across all topics.
4. AIME-level problem practice is essential.

The Bottom Line

AMC 10 is harder than AMC 8, but the data shows clear priorities:

1. Algebra is king. 42% of the test. No shortcuts here.
2. Number Theory is rising fast. From 12% to 22%. Study it separately.
3. Hard problems are balanced. You can't have weak areas.
4. Take both A and B. Cutoffs vary significantly.
5. Speed matters. 75 minutes for 25 problems is tight.

Stop studying randomly. Let the data guide your preparation.

Targeting AIME but not sure where you stand? Drop a comment with your recent practice test score and I'll help you build a targeted study plan.