**Important Information**

Course Outline

Ministry of Education Math Pre-Calculus 12 curriculum (2008)

Link to recommended practice from the textbook.

**Chapter 1 – Transformations and Functions**

By the end of this chapter, you will be able to…

- 1A – translate the graphs of functions
- 1B – reflect the graphs of functions
- 1C – expand or compress the graphs of functions
- 1D – transform the graph of functions by combining translations, reflections, expansions, or compressions
- 1E – graph the inverse of a function

By the end of this chapter, you will be able to…

- 2A – graph the function y = SQRT(x)
- 2B – state the domain and range of a radical function
- 2C – transform the graph of a radical function by combining translations, reflections, and expansions
- 2D – determine the restrictions of a radical equation
- 2E – solve radical equations
- 2F – apply radical equations to solve problems

**Chapter 3 – Polynomial Functions**

By the end of this chapter, you will be able to…

- 3A – define a polynomial function
- 3B – determine the properties of polynomial functions
- 3C – divide polynomials using synthetic division
- 3D – use the Remainder Theorem to determine remainder in a polynomial division statement
- 3E – use the Factor Theorem to determine factors of a polynomial expression
- 3F – sketch the graph of a polynomial function

**Chapter 4 – Trigonometry and the Unit Circle**

By the end of this chapter, you will be able to…

- 4A – convert degree measures to radian measures and vice versa
- 4B – understand the nature of sine, cosine, and tangent functions using the unit circle
- 4C – solve trigonometric equations with and without graphing calculators

**Chapter 5 – Trigonometric Functions and Graphs**

By the end of this chapter, you will be able to…

- 5A – understand the nature of a periodic graph
- 5B – graph the sine, cosine, and tangent functions using radians
- 5C – determine the period, amplitude, range, and domain of the trigonometric functions
- 5D – apply transformation techniques to sketch trigonometric graphs
- 5E – use graphing calculators to investigate transformations on the trigonometric functions

**Chapter 6 – Trigonometric Identities**

By the end of this chapter, you will be able to…

- 6A – recognize and apply the Pythagorean, reciprocal, and quotient identities
- 6B – recognize and apply the sum and difference identities
- 6C – recognize and apply the double angle identities
- 6D – solve trigonometric equations using trigonometric identities

**Chapter 7 – Exponential Functions**

By the end of this chapter, you will be able to…

- 7A – describe the characteristics of an exponential function
- 7B – describe the characteristics of the graph of an exponential function
- 7C – transform the graph of exponential functions by combining translations, reflections, and expansions
- 7D – solve exponential equations

**Chapter 8 – Logarithmic Functions**

By the end of this chapter, you will be able to…

- 8A – graph and analyze logarithmic functions
- 8B – transform the graph of logarithmic functions by combining translations, reflections, and expansions
- 8C – apply laws of logarithms
- 8D – solve exponential and logarithmic equations using the laws of logarithms

**Chapter 9 – Rational Functions**

By the end of this chapter, you will be able to…

- 9A – determine the non-permissible values of a rational expression
- 9B – analyze a rational function
- 9C – transform the graph of rational functions by combining translations, reflections, and expansions
- 9D – solve a rational equation
- 9E – apply a rational equation to solve problems

**Chapter 10 – Function Operations**

By the end of this chapter, you will be able to…

- 10A – analyze and graph the sum or difference of two functions
- 10B – analyze and graph the product or quotient of two functions
- 10C – analyze and graph the composition of two functions

**Chapter 11 – Permutations, Combinations, and the Binomial Theorem**

By the end of this chapter, you will be able to…

- 11A – apply the Fundamental Counting Principle
- 11B – describe the similarities and differences between permutations and combinations
- 11C – apply permutations to count the number of possible outcomes
- 11D – apply combinations to count the number of possible outcomes
- 11E – apply Pascal’s Triangle as a counting principle
- 11F – apply the Binomial Theorem