Introduction
The AMC (American Mathematics Competitions) series helps students transition from school math to true mathematical problem-solving. While AMC 8 introduces middle school students to creative thinking, AMC 10 takes this challenge to the next level — testing algebra, geometry, and logical reasoning at a high-school level. In this article, we’ll compare AMC 10 vs AMC 8, explore what makes AMC 10 harder than school math, and share how students can prepare effectively.
🧭 New to AMC 8? Read our AMC 8 Preparation Guide for a 12-week study plan and formula checklist.
AMC 10 vs AMC 8: Key Differences
The AMC series has multiple levels:
- AMC 8: for students in Grade 8 or below (under age 14.5)
- AMC 10: for students in Grade 10 or below (under age 17.5)
Both contests are organized by the Mathematical Association of America (MAA) and consist of 25 multiple-choice questions, but the depth, scoring, and test strategies differ significantly.
Exam Format & Scoring Comparison
| Feature | AMC 8 | AMC 10 |
| Grade Limit | ≤ 8 | ≤ 10 |
| Age Limit | < 14.5 | < 17.5 |
| Duration | 40 minutes | 75 minutes |
| Questions | 25 | 25 |
| Scoring | +1 for correct, 0 for wrong or blank | +6 for correct, +1.5 for blank, 0 for wrong |
| Max Score | 25 | 150 |
Strategy Difference:
AMC 8 encourages students to attempt every problem — there’s no penalty for guessing.
AMC 10, on the other hand, rewards accuracy and strategic decision-making, as skipping hard questions can yield a higher score than random guessing.
Exam Content and Topic Scope
The AMC 8 focuses on middle school math — arithmetic, proportions, simple algebra, and introductory geometry.
AMC 10 builds upon this foundation and adds Algebra I, Geometry, Number Theory, and Counting & Probability with far greater complexity.
AMC 10 Topic Overview
| Domain | Key Concepts & Focus Areas |
| Algebra & Functions | Linear & quadratic equations, inequalities, exponents, functional relationships, sequences |
| Number Theory | Divisibility, primes, modular arithmetic, remainders, Diophantine equations |
| Geometry & Coordinate Geometry | Triangles, circles, polygons, 3D geometry, coordinate systems |
| Counting & Probability | Permutations, combinations, expected value, complementary counting |
| Advanced Problem Solving & Logic | Multi-step reasoning, pattern recognition, proof-style thinking |
To illustrate this, let’s look at an example:
2023 AMC 8, Question 24
In short:
AMC 8 measures understanding of math concepts.
AMC 10 measures how creatively and efficiently students apply them.
Question Difficulty and Preparation Time
The last 5 questions of AMC 8 are roughly as hard as the first 10 of AMC 10.
From Q18 to Q25, AMC 10 problems become multi-layered and abstract — requiring algebraic modeling, casework, or geometric proof techniques.
Preparation Timeline
- AMC 8: 6–12 months (for middle school math readiness)
- AMC 10: 18–36 months (for high-school algebra and geometry mastery)
Students often need to bridge content gaps before attempting AMC 10, especially if they haven’t yet completed formal Algebra I or Geometry in school.
AMC 10 vs School Math
Many students who score A’s in school math are surprised when they find AMC 10 far more challenging.
That’s because school math emphasizes procedure, while contest math demands creativity and logical depth.
| Skill Area | In-School Math | AMC 10 Math |
| Algebra | Formula-based computation | Multi-variable and parametric reasoning |
| Geometry | Recall of properties | Integration of geometry, algebra, and logic |
| Number Theory | Rarely covered | Frequent, conceptual, and abstract |
| Probability | Simple dice problems | Multi-case or combinatorial analysis |
Example:
A school question might ask students to find the sum of two dice outcomes.
AMC 10 could ask for the probability that seven dice yield a total divisible by 5 — requiring combinatorial counting and modular reasoning.
Why the Transition Matters
The move from AMC 8 to AMC 10 is more than just a jump in difficulty — it marks the shift from middle school math to high-school mathematical thinking.
Students learn to:
- Break complex problems into manageable steps
- Apply reasoning beyond formulas
- Develop perseverance in problem-solving
Preparing for AMC 10 Effectively
To prepare for AMC 10, students should:
- Review core Algebra and Geometry concepts.
- Practice with past AMC 10A / 10B papers under timed conditions.
- Analyze mistakes carefully to identify weak areas.
- Study Number Theory and Probability concepts beyond school curriculum.
Prepare Smarter for AMC 10 with Think Academy Canada
Think Academy Canada offers AMC 8 & AMC 10 Booster Programs designed for students bridging middle and high school math contests.
Our courses cover:
- Key topic review by domain
- Problem-solving drills by difficulty
- Full-length timed mock tests
- Personalized evaluation reports
Start with a Free Evaluation Test to discover your child’s AMC level and study plan.
