## Math 12 Pre-Calculus

*It is recommended that students complete: Pre-Calculus 11.*

** View the complete Learning Outcomes for this course**: Pre-Calculus Math 12 Integrated Resource Package

This course is suited for students who will continue their studies in math and science at a post-secondary institution.

Students use headphones/speakers to hear narration and explanation while the material is presented online. Students have complete control over the pace at which they learn the lesson – lessons can be paused, resumed, and repeated using simple navigation buttons. Examples are interactive with animated step-by-step flash and video whiteboard solutions.

### Unit 1: Transformations

Functions and Their Graphs, Domain and Range**Lesson 1:**Translating Graphs of Functions**Lesson 2:**Reflecting Graphs of Functions**Lesson 3:**Compressing and Expanding Graphs of Functions**Lesson 4:**Combining Transformations of Functions**Lesson 5:**Finding the Coordinates of Ordered Pairs after Transformations**Lesson 6:**

### Unit 2: Graphing Radicals and Rationals

Transformations of Radical Functions**Lesson 1:**Square Root of a Function**Lesson 2:**Graphical Solutions to Radical Equations**Lesson 3:**Transformations of Rational Functions**Lesson 4:**Analysing Rational Functions**Lesson 5:**Equations and Graphs of Rational Functions**Lesson 6:**

### Unit 3: Polynomials

The Remainder Theorem**Lesson 1:**The Factor Theorem**Lesson 2:**Factoring Polynomials**Lesson 3:**Solving Polynomial Equations**Lesson 4:**Graphs of Polynomial Functions**Lesson 5:**

### Unit 4: Exponents and Logarithms

Review the Exponent Law**Lesson 1:**Solving Equations Involving Exponents**Lesson 2:**Defining a Logarithm and Logarithmic Restrictions**Lesson 3:**Law of Logarithms**Lesson 4:**Solving Exponential and Logarithmic Equations**Lesson 5:**Introduction to Exponential Functions**Lesson 6:**Applications of Exponential Functions Part I**Lesson 7:**Applications of Exponential Functions Part II**Lesson 8:**Graphs of Exponential Functions**Lesson 9:**Graphing Logarithmic Functions**Lesson 10:**

### Unit 5: Circular Functions

Radian Measure – Angles in Standard Position**Lesson 1:**Sine, Cosine and Tangent Functions of Angles in Standard Position**Lesson 2:**Sine, Cosine and Tangent Functions of Special Angles**Lesson 3:**Graphing Sine and Cosine Functions**Lesson 4:**Transformations of Trigonometric Functions Part I**Lesson 5:**Transformations of Trigonometric Functions Part II**Lesson 6:**Sinusoidal Functions with Rational Periods**Lesson 7:**Applications of Sinusoidal Functions**Lesson 8:**Graphing the Tangent Function**Lesson 9:**Graphing the Trigonometric Reciprocal Functions (Enrichment)**Lesson 10:**

### Unit 6: Trigonometric Equations and Identities

Solving Trigonometric Equations using a Graphing Calculator**Lesson 1:**Solving Trigonometric Equations for Exact Values**Lesson 2:****Lesson 3:**Reciprocal and Pythagorean IdentitiesMore Trigonometric Identities**Lesson 4:**Sum and Difference Identities**Lesson 5:**Double Angle Identities**Lesson 6:**

### Unit 7: Permutations and Combinations

The Fundamental Counting Principles**Lesson 1:**Permutations Involving Different Objects**Lesson 2:**Permutations Involving Identical Objects**Lesson 3:**Combinations**Lesson 4:**Pascal’s Triangle and the Binomial Theorem**Lesson 5:**

### Unit 8: Function Notation and Operations

Function Notation**Lesson 1:**Sums and Difference of Functions**Lesson 2:**Products and Quotients of Functions**Lesson 3:**Compositions of Functions**Lesson 4:**

### Assessment

**First Assignment: 1 (5 %)**

**Assignments: 9 (25%)**

**Tests: 4 (70%)**** **

**Required Resource:** Access to a computer with speakers/headphones and internet