5.1 Contest Math
Learn the key techniques and train hard for contest math.
Algebra
Geometry
Combinatorics
Number Theory
Math Requires Creativity
Diagnostic: Ratios and Percentages
Diagnostic: Simple Equations
Sequences and Series
Equations with Ratios
Non-numeric Geometric Ratios
Equations Practice Quiz 1
Equations Practice Quiz 2
Diagnostic: Data
Data Measures
Changing Data Sets
Determine the Set
Multiple Possibilities
Data Practice 1
Data Practice Quiz 2
Diagnostic: Measures
Diagnostic: Angle Hunting
Polygon Angle Hunting
Special Right Triangles
Creating Right Triangles
Measures Practice Quiz 1
Measures Practice Quiz 2
Diagnostic: Similarity
Scaling
Exploring Similarity
Applying Similarity
Coordinate Geometry
Similarity Practice Quiz 1
Similarity Practice Quiz 2
Diagnostic: Composites
Lunes & Leaves
Inscribed Figures
Ratios Meet Geometry
Working in 3D
Composites Practice Quiz 1
Composites Practice Quiz 2
Diagnostic: Counting
Venn Diagrams
Branch Diagrams
Over-Counting
Symmetry
Counting Practice Quiz 1
Counting Practice Quiz 2
Diagnostic: Probability
Probability by Outcomes
PIE and Complements
Choosing
Symmetry and Conditional
Probability Practice Quiz 1
Probability Practice Quiz 2
Diagnostic: Efficiency
Calculations
Exponents
Roots
What's the Number?
Efficiency Practice Quiz 1
Efficiency Practice Quiz 2
Diagnostic: Factorization
Number of Divisors
GCD and LCM
Factorials
Cryptograms
Factorization Practice Quiz 1
Factorization Practice Quiz 2
Core Topics
Reframing Problems
Key Strategies
Color Cube Assembly
Autobiographical Numbers
Systems of Equations
Rates and Ratios
Quadratics
Exponents
Special Functions
Logarithms
Basic Inequalities
AM-GM
Cauchy-Schwarz
Roots
Equations
Vieta's Formulas
Transformations
Arithmetic Sequences
Geometric Sequences
Telescoping Series
Prime Factorization
GCD/LCM
Counting Factors
System of Congruences
Fractions
Units Digit
Euler's Theorem
Pythagorean Theorem
Triangle Areas
Similar Triangles
Angle Bisector Theorem
Power of a Point
Cyclic Quadrilaterals
Circles
Coordinate Geometry
Conics
Mass Points
Complex Number Geometry
Trigonometric Functions
Law of Cosines
Law of Sines
Trigonometric Identities
Roots of Unity
Constructive Counting
Complementary Counting
Binomial Coefficients
Principle of Inclusion-Exclusion
Balls and Urns
Probability
Conditional Probability
Expected Value
Recursion
Linearity of Expectation
Events with States
Casework
Extreme Cases and Invariants
Generalization
Using Symmetry
Eliminating Choices
Simplifications
Course description
Via intriguing problems and competition-style practice, we’ll guide you through your training from start to finish. Improve your speed and accuracy while gaining an appreciation for how fun math can be. Upon completion, you’ll have perfected your algebra, geometry, probability, and number sense game, and have the tools needed to successfully tackle math competitions at the level of MATHCOUNTS and the AMC8.
Topics covered
- Angle Hunting
- Composite Figures
- Counting Strategies
- Factorials
- Mean, Median, Mode
- Probability
- Problem Solving
- Prime Factorization
- Sequences and Series
- Similarity
- Venn Diagrams
Prerequisites and next steps
You should have some familiarity with basic mathematical concepts, such as simple algebra and geometry, and foundational operations. We recommend starting with Mathematical Fundamentals if these are unfamiliar to you!