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
