Lesson 1: Quick Review of Exponents

• Zero exponents

• Negative exponents

• Negative exponents with fractions as base

• Exponent laws

• Exponents as fractions

  • Solutions to examples explained

• Solving exponent equations

  • Steps to solving

  • Solutions to increasingly difficult examples explained

Lesson 2: Adding, Subtracting and Multiplying Polynomials

• Steps to adding polynomials

  • Solutions to examples explained

• Steps to subtracting polynomials

  • Solutions to examples explained

• Multiplying a monomial and a polynomial

  • The distributive property

  • Solutions to examples explained

• Multiplying a binomial and a binomial

  • Solutions to examples explained

• Multiplying two polynomials

  • Solution to an example explained

Lesson 3: Factoring Polynomials

• Common factoring

  • Tips for finding factors

  • Solutions to examples explained

• Difference of squares factoring

  • Examples explained

• Perfect square trinomial factoring

  • How to recognize a perfect square trinomial

  • Solutions to examples explained

  • Product / sum method of factoring (a = 1)

  • Decomposition method (a > 1)

  • Examples with increasing difficulty explained

Lesson 4: Simplifying Rational Expressions

• Some key definitions

  • Restrictions

  • 4 steps for finding restrictions

  • Examples with increasing difficulty explained

Lesson 1: Domain and Range

• Key definitions

• Determining domain and range

  • Simple examples explained

  • Increasingly difficult examples

  • Important tip to know

• Types of functions

  • Domain and range of linear functions

  • Domain and range of quadratic functions

  • Importance of transformation of quadratic functions

  • Domain and range of square root functions

  • Domain and range of cubic functions

  • Domain and range of reciprocal functions

  • Domain and range of absolute functions

  • Domain and range of exponential functions

Lesson 2: Vertical and Horizontal Translations

• Definition of a vertical translation

  • Functional representation

  • Example illustrated

• Definition of a horizontal translation

  • Functional representation

  • Example illustrated

• Vertical and horizontal translations of 7 parent functions

• Reflections of functions

  • Definitions of reflections in the x – and y- axis

• Reflections in the x- and y – axis of 7 different functions

• Vertical stretch and compression

  • Functional representations

  • Examples illustrated

• Horizontal stretch and compression

  • Functional representations

  • Examples illustrated

• Graphical illustrations of vertical stretch and compression

• Graphical illustrations of horizontal stretch and compression

• Vertical and horizontal stretch and compression of 7 parent functions

Lesson 3: Combinations of Transformations

• Description of general equation

  • Explanation of a solved example

• Inverse of a function

• Difference of squares factoring

  • Definition and functional representation

  • Table of value representation of a linear example

  • Graphical representation of a linear example

• Inverse notation

• Characteristics of an inverse function

  • Test for functionality of an inverse function

• Domain and range of an inverse function explained

• Finding the inverse of a function

  • 3 steps for finding the inverse of a function

  • Solutions to examples explained

Lesson 1: Primary Trigonometric Ratios

• Key definitions and review of right-angled triangles

  • Sine formula: SOH

  • Cosine formula: CAH

  • Tan formula: TOA

• Finding trigonometric ratios

• Finding inverse trigonometric ratios

• Examples solved to the nearest degree

• Strategies for solving triangles

• Review of geometrical terms

• Solving application type word problems

Lesson 2: Sine and Cosine of Angles > 90°

• Key definitions

  • Standard position and component parts

• Sine and cosine of angles in each quadrant

• Examples using various points on the terminal arm

• Supplementary angle relations

• Evaluating solutions based on quadrant locations

• Evaluating angles within limits

Lesson 3: The Sine and Cosine Rule

• The Sine rule

  • The Sine formula

  • 2 conditions for Sine rule

  • Solving triangles using Sine rule

• The Cosine rule

  • The Cosine formula

  • 2 conditions for Cosine rule

  • Solving triangles using Cosine rule

• Deciding when to apply

  • 5 key questions to ask

Lesson 1: Trigonometric Ratios of Any Angle

• Review of key definitions and explanations

  • Standard position

  • Initial arm

  • Terminal arm

• Trigonometric ratios on Cartesian Plane

  • Trigonometric ratios in each quadrant

  • The CAST rule

• Signs of trigonometric ratios on the Cartesian Plane

• Special triangles

  • Exact values

• Special triangles and quadrant relationship

• Solving for exact values of trigonometric ratios

  • Steps to finding exact values of trigonometric ratios

Lesson 2: Graphing Trigonometric Functions

• Primary Sine function

• Explanation of key components:

  • Domain, range, period, minimum, maximum, x- & y- intercepts

• Primary Cosine function

• Explanation of key components:

  • Domain, range, period, minimum, maximum, x- & y- intercepts

• Period of Sine & Cosine functions

  • Definition of period

  • Explanation of horizontal compression / stretch

  • Explanation of negative “k”

• Solutions to examples explained

Lesson 3: Amplitude of Sine and Cosine Functions

• Defining amplitude

• Amplitude formula

• Amplitude symbol

• Vertical compression / stretch, and reflection

• Graphing of functions explained

• Calculating maximum & minimum, domain & range, y-intercept

• Graphing combination of “k” factor and amplitude functions

• Vertical translation of/sine & Cosine functions

• Horizontal translation of/sine & Cosine functions

• Calculating components for both functions

• Combining transformations

  • General equations for Sine and Cosine explained

• 5 Steps to graph combined transformation functions

• Example of graphing a combined transformation function

• Given the equation of a function, how to find the characteristics

Lesson 4: Reciprocal Trigonometric Functions

• Recall Primary trigonometric ratios

• Reciprocal trigonometric ratios explained

• Summary of angles of Special Triangles

• CAST rule for reciprocal trigonometric functions

• Examples of solving for exact values

• Solving more difficult reciprocal trigonometric ratios

• Trigonometric Identities

  • Defining an identity

• Common trigonometric identities:

  • Pythagorean identity

  • Quotient identity

  • Reciprocal identities

• Proving Trigonometric Identities:

  • Main goal

  • 3 steps to use

• Solutions for examples proving trigonometric identities

Lesson 1: Sequences

• Defining a Sequence and a Term

• Worked examples determining a sequence, given the formula

• Worked examples for generating a formula for the nth term

  • Examples for finding the nth term

• Recursive Sequences

• Defining a recursive sequence

• Solutions to finding recursive sequences

Lesson 2: Arithmetic Sequence

• Defining an Arithmetic Sequence

• General formula for an arithmetic sequence:

  • Terms explained

• Examples solving various types of arithmetic sequences questions:

  • Solving for the next n terms, given the first set of terms

  • Solving for the first n terms, given arithmetic sequence

  • Solving for the formula for the nth term

  • Solving for the number of terms in an arithmetic sequence

  • Solving for the first term and formula for the nth term

Lesson 3: Geometric Sequences

• Defining a Geometric Sequence

• General formula

  • Explanation of terms

• Examples of solutions to geometric sequences questions

  • Solving for Common Ratio and next 3 terms

  • Solving for first 4 terms, given formula for the nth term

• Solving for tη

Lesson 4: Arithmetic Series

• Defining arithmetic series

• Differentiating between arithmetic sequences & arithmetic series

• General formula for arithmetic series

  • Explanation of terms

• Examples of solutions to arithmetic series questions:

  • Solving for the sum of the first n terms

  • Solving for the sum of an arithmetic series

Lesson 5: Geometric Series

• Defining geometric series

• Differentiating between geometric sequences & geometric series

• General formula for geometric series

  • Explanation of terms

• Examples of solutions to geometric series questions:

  • Solving for the sum of the first n terms

  • Solving for the sum of a geometric series

Lesson 6: Binomial Expansion

• Pascal’s triangle and its interpretation

• Relationship of a cubic binomial with Pascal’s Triangle

• General relationship of (x + y)n to Pascal's Triangle

• 4 properties of a Binomial Expansion of the form (x+y)n

• Examples of expanding binomials using Pascal’s Triangle