## 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!