Empower Your Academic Journey

Session I: Algebra and Introductory Counting (16 hours, $600)

Focus: Basic concepts in algebra and the first half of counting techniques. Targeting younger students and beginners (grades 4-5)

Goal: Establishes a solid foundation in algebra and basic counting principles, essential for beginners to build confidence and skills for initial competitions like MathCounts and AMC 8

Algebra (10 hours)
1. Variables and Equations (2 hours)
Variables, Consecutive Integers, d=rt, Harmonic Mean, Moles Digging Holes
2. Linear Equations (2 hours)
Slope, Intercepts, Slope-Intercept Form, Point-Slope Form, Standard Form, Parallel/Perpendicular Lines, Horizontal and Vertical Lines
3. Systems of Equations (1.5 hours)
Substitution, Elimination, Common Word Problems, Cheating the System
4. Ratios, Proportions, and Percents (1.5 hours)
Ratios, Proportions, Percents, and Percent of Change
5. Distribution (1 hour)
The Distributive Property, Difference of Squares and Perfect Squares, Sum of the Reciprocals
6. Quadratics (1 hour)
Perfect Squares, Difference of Squares, Factoring By Grouping, Solving Quadratics by Factoring, The Quadratic Formula, Word Problems, Sum and Product of the Roots
7. Exponents and Radicals (1 hour)
Multiplying, Dividing, Raising a Power to a Power, Fractional Exponents, Square Roots
8. Statistics (1 hour)
Mean, Median, Mode and Range
9. Sequences and Series (1 hour)
Arithmetic Sequences and Series, Geometric Sequences and Series
10. More Substitution (1 hour)
Nested Square Roots, Continued Fractions

Counting (6 hours)
1. Basics (1 hour)
Simple Counting Techniques
2. Venn Diagrams (1 hour)
Two and Three-Set Venn Diagrams
3. Bowling Pins and Handshakes (1 hour)
Triangular Number Patterns
4. Counting Outcomes (1 hour)
The Fundamental Counting Principle
5. Casework (1 hour)
Keeping Organized
Review (1 hour)
Review and practice problems