## Math 12 Pre-Calculus

**Unit 01 Functions and Relations**

**Functions – Review**

difference between equations and functions (video)

evaluating with function notation (video)

how to evaluate a function given its formula – example (video)

how to evaluate a function given its graph – example (video)

function notation in context – example (video)

**Domain and Range of Functions – Review**

domain and range of a relation (video)

domain and range of a function (video)

**Operations with Functions**

how to combine functions by adding them (video)

how to combine functions by subtracting them (video)

how to combine functions by multiplying them (video)

how to combine functions by dividing them (video)

**Composition of Functions**

introduction to function composition (video)

how to evaluate a composite function given the formulas of the composed functions – example (video)

**Inverse of a Relation**

introduction to function inverses (video)

inputs and outputs of function inverses (video)

how to graph the inverse of a linear function given the graph of the function – example (video)

how to find the inverse of a linear function – example (video)

how to find the inverse of a quadratic function – example (video)

how to find the inverse of a quadratic function – example (video)

**Unit 02 Polynomial Functions and Equations**

**Long Division and Synthetic Division of Polynomials**

introduction to long division of polynomials (video)

how to divide a quadratic expression by a linear expression using long division – example (video)

introduction to synthetic division of polynomials (video)

how to divide polynomials using synthetic division – example (video)

why synthetic division works (video)

**Remainder Theorem and Polynomial Factoring**

introduction to the remainder theorem (video)

how to find the remainder of a polynomial division using the remainder theorem – example (video)

**Unit 03 Transformations**

**Shifting Functions**

shifting and reflecting functions (video)

**Stretching Functions**

shifting and stretching functions (video)

**Unit 04 Exponents and Logarithmic Functions**

**Exponential Functions**

introduction to exponential functions (video)

solving exponential equations (video)

**Logarithmic Functions**

comparing exponential and logarithmic functions (video)

graphing logarithmic functions (video)

matching functions to their graphs (video)

graphs of logarithmic functions (video)

solving logarithmic equations (1) (video)

solving logarithmic equations (2) (video)

**Unit 05 Radical and Rational Functions**

**Radical Equations and Functions
**

solving radical equations (video)

extraneous solutions to radical equations (video)

solving radical equations 1 (video)

solving radical equations 2 (video)

solving radical equations 3 (video)

flipping and shifting radical functions (video)

**Rational Equations and Functions
**

how to solve an equation with one rational expression – example (video)

how to solve an equation with a rational expression that needs simplification – example (video)

how to solve an equation with two rational expressions – example (video)

how to solve a rational equation with an extraneous solution – example (video)

analyzing end behavior and discontinuities of rational functions (video)

how to graph a rational function – example 1 (video)

how to graph a rational function – example 2 (video)

how to graph a rational function – example 3 (video)

how to graph a rational function – example 4 (video)

**Unit 06 Trigonometry 01 (Functions and Graphs)**

**Radian and Degree Angular Measure**

introduction to radians (video)

rotation by radians and quadrants (video)

**Trigonometric Ratios and the Unit Circle**

the basics of trigonometry (video)

introduction to the unit circle (video)

unit circle manipulative (video)

matching ratios to trig functions (video)

solving triangle in unit circle (video)

finding trig functions of special angles – example (video)

**Graphs of Trigonometric Functions**

midline, amplitude and period of a function (video)

graph of sine function (video)

**Transformations of Trigonometric Functions**

amplitude and period transformations – example (video)

amplitude and period cosine transformations – example (video)

determining the equation of a trig function (video)

**Modelling Sinusoidal Functions**

modeling annual temperature variation with trigonometry (video)

modeling temperature through the day (video)

**Unit 07 Trigonometry 02 (Equations and Identities)**

**First and Second Degree Trigonometric Equations
**

solving first degree trigonometric equations (video)

solving first degree trigonometric equations (video)

solving second degree trigonometric equations by isolation (video)

solving second degree trigonometric equations by isolation (video)

**Trigonometric Equations Involving Multiple Angles**

solving trigonometric equations involving multiple angles (video)

**Pythagorean Identity**

pythagorean trig identity from soh cah toa (video)

pythagorean trig identity from unit circle (video)

using the pythagorean trig identity (video)

using pythagorean identities to simplify trigonometric expressions – examples (video)

**Sum and Difference Identities**

sum and difference identities (for sine) (video)

sum ad difference identities (for cosine) (video)

**Double Angle Identities**

double angle identities (video)

**Trigonometric Identities**

trigonometry identities 1 (video)

trigonometric identities 2 (video)

trigonometric identities 3 (video)

**Using Identities to Solve Equations**

using trigonometric identities to solve equations (video)

using trigonometric identities to solve equations (video)

**Unit 08 Combinatorics**

**Permutations**

factorial and counting seat arrangements (video)

possible three letter words (video)

example – ways to arrange colours (video)

example – ways to pick officers (video)

**Combinations**

introduction to combinations (video)

handshaking combinations (video)

9 card hands – example (video)

**Binomial Theorem and ****Polynomial Functions **

pascal’s triangle for binomial theorem (video)

determining coefficient in binomial expansion (video)

**Possible Useful Software**

virtual graphing calculator software: click to download and install 90 day trial software…

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