MATH 12 (P/C)

Math 12 Pre-Calculus

Unit 01 Functions and Relations

Functions – Review

what is a function (video)

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 of a function (video)

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)

how to find the formula of 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)

how to check if a linear expression is a factor of a polynomial using the remainder theorem – example (video)

how to determine the coefficients of a polynomial so it has a certain factor 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)

radians and degrees (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)

graph of cosine (video)

graph of tangent (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)

permutation formula (video)

possible three letter words (video)

zero factorial (video)

example – ways to arrange colours (video)

example – ways to pick officers (video)

Combinations

introduction to combinations (video)

combinations formula (video)

handshaking combinations (video)

9 card hands – example (video)

Binomial Theorem and Polynomial Functions

binomial theorem (video)

pascal’s triangle for binomial theorem (video)

determining coefficient in binomial expansion (video)

Possible Useful Software

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