Pre-Calculus
The comprehensive preparation for calculus. Master every function class, develop deep facility with trigonometry and identities, and get the first real look at limits.
9 units and 44 lessons, for Grade 11 to Grade 12. Free on Slate.
Unit 1: Functions and Their Graphs
Build the most complete picture of functions as mathematical objects before specializing in specific families.
- Functions, Transformations, and the Library of Parent Functions (10 min)
- Composition of Functions (10 min)
- Inverse Functions and One-to-One Functions (10 min)
- Piecewise and Step Functions (10 min)
- Modeling with Functions (10 min)
Unit 2: Polynomial and Rational Functions
Develop a thorough understanding of polynomial and rational functions at the pre-calculus level of depth.
Unit 3: Exponential and Logarithmic Functions
Deepen mastery of exp/log with data modeling and the full properties of logarithms.
Unit 4: Trigonometry: Angles and Functions
Build a complete and rigorous understanding of the trigonometric functions from the unit circle.
- Angles and Radian Measure (10 min)
- The Unit Circle: Complete Mastery (10 min)
- Trigonometric Functions of Any Angle (10 min)
- Graphing Trig Functions and Their Transformations (10 min)
- Inverse Trigonometric Functions (10 min)
- Solving Trigonometric Equations (10 min)
Unit 5: Trigonometric Identities and Equations
Prove and apply the full suite of trig identities, one of the highest-leverage skills for calculus and physics.
- Fundamental Identities (10 min)
- Sum and Difference Formulas (10 min)
- Double-Angle and Half-Angle Formulas (10 min)
- Verifying Trigonometric Identities (10 min)
- Solving Trig Equations: General Solutions (10 min)
Unit 6: Applications of Trigonometry
Apply trigonometry to triangles, vectors, and polar and parametric representations.
- Law of Sines: Complete Treatment (10 min)
- Law of Cosines and Area Formulas (10 min)
- Vectors: Introduction and Operations (10 min)
- The Dot Product and Angle Between Vectors (10 min)
- Polar Coordinates and Graphs (10 min)
- Parametric Equations (10 min)
Unit 7: Limits: An Introduction to Calculus
Develop the intuition and some algebra of limits that forms the backbone of calculus.
- The Concept of a Limit (10 min)
- Evaluating Limits Algebraically (10 min)
- One-Sided Limits and Limits at Infinity (10 min)
- Continuity and the Intermediate Value Theorem (10 min)
- Preview of the Derivative (10 min)
- Preview of the Integral (10 min)
Unit 8: Sequences, Series & Mathematical Induction
Formalize sequences and series and introduce rigorous proof by induction.
- Arithmetic and Geometric Sequences and Series (10 min)
- Mathematical Induction (10 min)
- Binomial Theorem and Pascal's Triangle (10 min)
- Introduction to Power Series (10 min)
Unit 9: Matrices and Linear Systems
Solve systems algebraically with matrices and understand linear transformations.
- Matrix Operations (10 min)
- Determinants (10 min)
- Solving Systems with Gaussian Elimination (10 min)
- Cramer's Rule (10 min)