Why Competition Mathematics?
Develop problem-solving skills that last a lifetime
Critical Thinking
Competition math develops deep analytical skills and creative problem-solving abilities that extend far beyond mathematics into every aspect of life and career.
Strategic Approach
Learn proven strategies and techniques used by top performers in international mathematics competitions to tackle complex problems efficiently.
Academic Excellence
Success in math competitions opens doors to prestigious universities, scholarships, and STEM career opportunities around the world.
Practice Problems with Solutions
Real competition-style problems to sharpen your skills
We know that \( (x + y)^2 = x^2 + 2xy + y^2 \)
Therefore: \( x^2 + y^2 = (x + y)^2 - 2xy \)
Substituting the given values:
\( x^2 + y^2 = (10)^2 - 2(21) = 100 - 42 = 58 \)
Answer: 58
Step 1: Find integers divisible by 7:
Numbers divisible by 7 less than 1000: \( \lfloor 999/7 \rfloor = 142 \)
Step 2: Find integers divisible by 14 (these are also divisible by 7):
Numbers divisible by 14 less than 1000: \( \lfloor 999/14 \rfloor = 71 \)
Step 3: Subtract to get numbers divisible by 7 but not 14:
\( 142 - 71 = 71 \)
Answer: 71
Step 1: Find the side of the square:
Area of square = \( s^2 = 144 \), so \( s = 12 \)
Step 2: Find perimeter of square:
Perimeter = \( 4 \times 12 = 48 \)
Step 3: Find side of hexagon:
A regular hexagon has 6 equal sides. If perimeter = 48:
Side length = \( 48 \div 6 = 8 \)
Answer: 8 units
Step 1: Count total arrangements:
MATHEMATICS has 11 letters: M(2), A(2), T(2), H(1), E(1), I(1), C(1), S(1)
Total arrangements = \( \frac{11!}{2! \cdot 2! \cdot 2!} = \frac{39,916,800}{8} = 4,989,600 \)
Step 2: Count arrangements with M's together:
Treat MM as one unit: 10 objects with A(2), T(2), and others
Arrangements = \( \frac{10!}{2! \cdot 2!} = \frac{3,628,800}{4} = 907,200 \)
Step 3: Subtract:
\( 4,989,600 - 907,200 = 4,082,400 \)
Answer: 4,082,400
We need to test values systematically:
\( n = 8: 2^8 - 8^2 = 256 - 64 = 192 < 1000 \) ❌
\( n = 9: 2^9 - 9^2 = 512 - 81 = 431 < 1000 \) ❌
\( n = 10: 2^{10} - 10^2 = 1024 - 100 = 924 < 1000 \) ❌
\( n = 11: 2^{11} - 11^2 = 2048 - 121 = 1927 > 1000 \) ✓
Since exponential growth (\(2^n\)) eventually dominates polynomial growth (\(n^2\)), and we've found the first value where the inequality holds:
Answer: n = 11
Step 1: Find the position of each hand:
Minute hand at 15 minutes: \( 15 \times 6° = 90° \) from 12 o'clock
Hour hand at 3:15: \( 3 \times 30° + 15 \times 0.5° = 90° + 7.5° = 97.5° \) from 12 o'clock
(Each hour = 30°, each minute moves hour hand 0.5°)
Step 2: Find the angle between them:
\( |97.5° - 90°| = 7.5° \)
Answer: 7.5°
Major Mathematics Competitions
Prepare for prestigious national and international math competitions
Singapore and Asian Schools Math Olympiad - A premier mathematics competition for students across Singapore and Asia, emphasizing problem-solving and mathematical reasoning.
Levels: Primary 1-6, Secondary 1-4, Junior College
Format: Multiple choice and short answer
Difficulty: Progressive from basic to olympiad-level
American Mathematics Competitions - The first step toward the International Math Olympiad (IMO) for US students. Highly respected worldwide.
AMC 8: Middle School (25 questions, 40 min)
AMC 10/12: High School (25 questions, 75 min)
Recognition: Top scorers advance to AIME
MATHCOUNTS Competition - National middle school mathematics competition that builds problem-solving skills and positive attitudes toward mathematics.
Level: 6th-8th grade
Rounds: Sprint, Target, Team, Countdown
Prestige: Highly competitive US national competition
International Mathematical Olympiad - The most prestigious mathematics competition for high school students worldwide, featuring the toughest problems.
Level: High School (pre-university)
Format: 6 problems over 2 days (4.5 hours each)
Participants: National teams from 100+ countries
Math Kangaroo Competition - International competition with over 6 million participants annually from more than 80 countries, fostering mathematical thinking.
Levels: Grade 1-12 (multiple levels)
Format: Multiple choice (24-30 questions)
Focus: Logical thinking and creative problem-solving
American Regions Mathematics League - Prestigious team competition bringing together top math students from across North America for collaborative problem-solving.
Format: Team, Power, Individual, Relay Rounds
Level: High School
Emphasis: Teamwork and communication
Competition Math Topics
Master these essential areas for competition success
Essential Resources
Tools and platforms to accelerate your math competition journey
SASMO Singapore
Official site of the Singapore and Asian Schools Math Olympiad. Register for competitions, access past papers, and join Asia's premier math olympiad community.
Visit SASMO.sg →Math Calculators
Comprehensive collection of mathematical calculators for algebra, geometry, calculus, statistics, and more. Verify your solutions and understand the steps.
Browse Math Calculators →Practice Problems
Thousands of competition-style problems with detailed solutions. Start with easier problems and progressively build to olympiad-level challenges.
Start Practicing →Competition Success Strategies
Proven techniques from top performers
1. Master the Fundamentals
Build a rock-solid foundation in arithmetic, algebra, and geometry before attempting advanced topics. Competition math rewards deep understanding over superficial knowledge.
2. Practice Consistently
Solve 5-10 problems daily across different topics. Consistency beats cramming. Review your mistakes and understand why your approach didn't work.
3. Learn from Solutions
After attempting a problem, study the official solution even if you got it right. There may be more elegant approaches you haven't considered.
4. Time Management
Practice under timed conditions. Learn to quickly identify problem types and allocate your time wisely during actual competitions.
5. Study Past Papers
Review past competition papers from AMC, MATHCOUNTS, SASMO, and others. Recognize patterns and frequently tested concepts.
6. Join Study Groups
Collaborate with peers who share your passion for mathematics. Explaining concepts to others deepens your own understanding.