AMC 8
American Mathematics Competition for Middle School
Competition Format
The AMC 8 is a 25-question, 40-minute multiple choice examination designed to promote the development of problem-solving skills. It’s the first level of the AMC series that can eventually lead to the International Math Olympiad.
- Each problem is worth 1 point (no partial credit)
- Problems increase in difficulty from 1 to 25
- No calculators allowed
- Perfect score: 25 points
Key Topics Covered
- Number Theory: Divisibility, primes, GCD/LCM
- Algebra: Linear equations, sequences, patterns
- Geometry: Area, perimeter, angles, similar figures
- Counting & Probability: Permutations, combinations, basic probability
- Logic & Word Problems: Critical thinking and problem interpretation
What Makes It Unique
Pathway to Glory: High scorers can qualify for MATHCOUNTS and eventually the International Math Olympiad
- Most prestigious middle school math competition in the US
- Nationally recognized and valued by top schools
- Problems emphasize creative problem-solving over computation
- Perfect training for high school competitions (AMC 10/12)
How to Prepare
Practice Past Tests
Work through 10+ previous AMC 8 exams to understand question patterns and difficulty progression.
Build Speed
Practice under timed conditions. Aim for 90 seconds per problem on average.
Master Fundamentals
Ensure strong foundation in all middle school math topics before attempting advanced problems.
Learn Shortcuts
Study clever techniques and shortcuts that save time on computation-heavy problems.
MATHCOUNTS
National Middle School Mathematics Competition
Competition Structure
MATHCOUNTS features four distinct competition rounds throughout the season:
- Sprint Round: 30 problems, 40 minutes (no calculator)
- Target Round: 8 problems in pairs, 6 minutes per pair (calculator allowed)
- Team Round: 10 problems, 20 minutes (team of 4, calculator allowed)
- Countdown Round: Head-to-head competition for top students
Competition Levels
- School Competition: January (qualify 4 students + 2 alternates)
- Chapter Competition: February (top teams advance)
- State Competition: March (top 4 students per state advance)
- National Competition: May in Washington D.C.
What Makes It Unique
Team Spirit: The only major competition that emphasizes teamwork alongside individual performance
- Multiple rounds test different skills (speed, accuracy, collaboration)
- Combines individual achievement with team dynamics
- Intense countdown round creates exciting pressure situations
- National recognition and scholarship opportunities
- Season-long commitment builds lasting skills
How to Prepare
Speed Drills
Practice mental math and calculation speed. The sprint round demands rapid problem-solving.
Team Practice
Form study groups to practice team rounds. Learn to communicate solutions efficiently.
Calculator Skills
Master calculator techniques for target round. Know your calculator’s functions inside out.
Pressure Training
Simulate countdown round conditions. Practice solving problems with time pressure and audience.
Mathematical Olympiad for Elementary & Middle Schools (MOEMS)
Monthly Problem-Solving Competition
Competition Format
Math Olympiad consists of 5 monthly contests held between November and March. Each contest features 5 non-routine problems.
- Each problem worth 1 point (show all work)
- Problems require written explanations
- Emphasis on creative thinking over computation
- Cumulative scoring across all 5 contests (max 25 points)
Problem Types
- Logic Puzzles: Deductive reasoning and pattern finding
- Number Theory: Properties of numbers and sequences
- Geometry: Spatial reasoning and visual problems
- Combinatorics: Counting and arrangements
- Creative Thinking: Problems requiring “aha!” moments
What Makes It Unique
Beginner-Friendly: Excellent introduction to competitive math with manageable difficulty and monthly rhythm
- More forgiving format – 5 opportunities to score throughout the year
- Problems emphasize creativity over speed
- Great for younger students (4th-6th grade)
- Monthly contests prevent cramming, encourage consistent practice
- Less intense than single high-stakes competitions
How to Prepare
Monthly Practice
Work on 1-2 past olympiad problems weekly to stay sharp between contests.
Show Your Work
Practice writing clear explanations. Partial credit available for well-reasoned attempts.
Think Creatively
Focus on problem-solving strategies: draw diagrams, work backwards, find patterns.
Review Solutions
Study official solutions after each contest to learn new techniques and approaches.
Math Kangaroo
International Mathematics Competition
Competition Format
Math Kangaroo is an international competition with over 6 million participants from 90+ countries. Students compete in grade-level divisions with problems tailored to their level.
- 30 multiple choice problems
- Problems divided into three difficulty levels (easy, medium, hard)
- Calculator allowed for some divisions
- Heavy emphasis on visual reasoning and logic
Scoring System
- Problems 1-10: 3 points each
- Problems 11-20: 4 points each
- Problems 21-30: 5 points each
- No penalty for wrong answers or blanks
National and international rankings are published after the competition, with medals and certificates for top performers.
What Makes It Unique
International Flavor: Compare your performance with students from 90+ countries around the world
- Emphasis on “aha!” moments and clever tricks
- Heavy focus on visual/spatial reasoning
- Problems reward creativity over calculation
- More time per problem (2.5-3 minutes average)
- Accessible yet challenging for all levels
How to Prepare
Think Visually
Practice spatial reasoning puzzles, tangrams, and geometry problems.
Logic Puzzles
Work on KenKen, Sudoku, and other logic-based challenges.
Past Problems
Review previous Math Kangaroo contests to understand the unique problem style.
Pattern Recognition
Focus on identifying patterns and looking for clever shortcuts.
Competition Comparison
| Competition | Best For | Difficulty | Time Commitment | Key Skills |
|---|---|---|---|---|
| AMC 8 | Students seeking prestigious recognition | Intermediate | One-time, 40 min | Problem-solving, all topics |
| MATHCOUNTS | Team-oriented competitors | Intermediate-Advanced | Multiple rounds, season-long | Speed, teamwork, pressure |
| Math Olympiad | Beginners, young students | Beginner-Intermediate | 5 monthly contests, 30 min each | Strategic thinking, creativity |
| Math Kangaroo | Visual/logical thinkers | Intermediate | One-time, 75 min | Pattern recognition, logic |
Other Notable Competitions
Purple Comet! Math Meet
Format: Free, online team competition
When: April
Who: Middle and high school students
A challenging team-based competition with 25 problems in 90 minutes. Great for schools without access to other team competitions.
AIME (American Invitational Mathematics Examination)
Format: 15 problems, 3 hours
When: February-March
Who: High AMC 8/10/12 scorers (by invitation only)
The next level after AMC competitions, featuring challenging problems requiring integer answers from 000 to 999.
MathWorks Math Modeling Challenge
Format: 14-hour team challenge
When: Early March
Who: High school students (grades 9-12)
Apply math modeling to solve real-world problems. Focuses on teamwork, research, and presentation.
Caribou Contests
Format: Online, 6 contests per year
When: October-May
Who: Grades K-12
Interactive online competition with puzzles and problem-solving. Worldwide participation with instant results.
How to Prepare for Success
Create a Preparation Timeline
6 Months Before: Build foundational skills in all topic areas
3-4 Months Before: Take practice tests to identify weak areas
1-2 Months Before: Intensive practice, focus on weak topics
1 Week Before: Light review, rest, and mental preparation
Essential Practice Resources
- Past Competition Tests: The single best preparation tool
- Art of Problem Solving (AoPS): Books, online courses, and Alcumus practice
- Beast Academy: For younger students (grades 2-5)
- Competition Math Books: Topic-specific workbooks
- YaniPrep: AI-powered practice with YaniCoach guidance
Key Topics to Master
Number Theory
Primes, divisibility, GCD/LCM, modular arithmetic
Algebra
Equations, sequences, patterns, word problems
Geometry
Area, perimeter, angles, triangles, circles
Counting
Permutations, combinations, probability, casework
Build Competition Skills
- Time Management: Practice under timed conditions regularly
- Strategic Guessing: Learn when to skip and when to persist
- Mental Math: Develop quick calculation abilities
- Problem Recognition: Identify problem types quickly
- Test-Taking Strategy: Learn to maximize your score
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