This course consists of two sections - Algebra and Counting & Probability.

Algebra section covers exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, quadratics, and complex numbers. Our textbook is Art of Problem Solving Introduction to Algebra by Richard Rusczyk. The philosophy of this course is that students develop more by learning to solve problems they have not seen before, as opposed to offering repeated drills that students can memorize their way through.

Counting & Probability includes basic and intermediate counting concepts, including case-work, multiplication, permutations, combinations, Pascal’s triangle, probability, combinatorial identities, and the Binomial Theorem. Our textbook is Introduction to Counting & Probability by David Patrick.

**Course Syllabus**

WEEK 1 - Introduction

WEEK 2 - Follow the Rules

WEEK 3 - Fractional Exponents, Radicals, and Variables (Pt. 1)

WEEK 4 - Fractional Exponents, Radicals, and Variables (Pt. 2)

WEEK 5 - Linear Equations

WEEK 6 - More Variables

WEEK 7 - Linear Equations with Multiple Variables

WEEK 8 - Ratio and Percent

WEEK 9 - More Ratios and Proportion

WEEK 10 - Common Errors and Challenging Problems

WEEK 11 - Graphing Lines (Pt. 1)

WEEK 12 - Graphing Lines (Pt. 2) and Introduction to Inequalities

WEEK 13 - Graphing Inequalities

WEEK 14 - Quadratic Equations (Pt. 1)

WEEK 15 - Special Factorizations

WEEK 16 - Simon’s Favorite Factoring Trick and Complex Numbers

WEEK 17 - Quadratic Equations (Pt. 2)

WEEK 18 - Lists, Venn Diagrams, Addition, Multiplication

WEEK 19 - Casework, Constructions, and Restriction

WEEK 20 - Overcounting and Combinations

WEEK 21 - Combinations and Distinguishability

WEEK 22 - Challenging Problems

WEEK 23 - Introduction to Probability

WEEK 24 - Probability and Arithmetic

WEEK 25 - Geometric Probability, Think About It!, and Expected Value

WEEK 26 - Pascal’s Triangle and Identities

WEEK 27 - The Hockey Stick Identity

WEEK 28 - The Binomial Theorem

WEEK 29 - More Challenging Problems and Review