Lesson 1: Quick Review

• Adding and subtracting integers

• Multiplying and dividing integers

• BEDMAS

• The distributive property

• The distributive property – simplifying fractions

• Factoring expressions

Lesson 2: Linear Systems

• Introduction to linear systems

• Solution of a linear system

• Graphing and solving linear systems (using x- and y- intercepts)

• Graphing and solving linear systems (using slope / y - intercept)

• How to check solutions

• Solving linear systems by substitution

• Solving linear systems by elimination

Lesson 3: Polynomials

• Review of factors

• Multiplying polynomials

• Multiplying a binomial by a monomial

• Multiplying two binomials

• Multiplying a trinomial by a binomial (vice versa)

Lesson 4: Factoring Trinomials of the Form ax² + bx + c

• Factoring trinomials (when “a” = 1)

• Factoring trinomials (when “a” ≠ 1), examples where “a” is factorable

• Factoring trinomials (when “a” = a negative)

• Factoring trinomials (when “a” ≠ 1, “a” is not factorable)

Lesson 5: Solving Trinomials, ax² + bx + c = 0

• Recognition of trinomials

• Strategies for solving trinomials

• Recognizing difference of squares

• Factorizing difference of squares

• Solving difference of squares

Lesson 1: Introduction to Linear Analytic Systems

• Quick recap:

  • Pythagorean Theorem

  • Slopes of parallel and perpendicular lines

  • Slope / y- intercept and standard forms

• Some definitions to know:

  • Cartesian coordinate system

  • Line segments

  • Mid-point, Median, Perpendicular Bisector

• Explanations how to find:

  • The mid-point

  • The equation of a line

  • The equation of a median

  • The equation of a perpendicular bisector

Lesson 2: Length of a Line Segment

• Defining a line segment

• Formula for a line segment

• Calculating the length of a line segment

• Equation of a line

• Equation of a circle with centre (0, 0)

• Word problems with a circle with centre (0, 0)

Lesson 3: Clarifying Figures on a Coordinate Grid

• Review of types of triangles and their properties

• Types of quadrilaterals and their properties

• Steps involved in solving word problems

• Classifying types of quadrilaterals

Lesson 4: Exploring Properties of Geometric Figures

• Understanding the Centroid of a triangle

  • Review of the Mid-point

  • 3 steps to finding the Centroid of a triangle

• Understanding the Circumcentre of a triangle

  • Review of perpendicular bisector

  • 3 steps to finding the Circumcentre of a triangle

Lesson 5: Solving Problems Using Coordinates

• Review area of a triangle

• Solutions explained for problems to solve for:

  • Slope; equation of the line

  • Slope of the altitude from a point

  • Equation of the altitude line from that point

  • Point of intersection for a line and the altitude from that point

  • Length of the altitude

Lesson 1: Quadratic Relations

• Some important definitions:

  • Quadratic relation in standard form; parabola

  • Degree of a Quadratic Relation

  • First and second differences

• Opening of a parabola

• Properties of graphs of quadratic relations

  • Axis of symmetry; equation of the axis of symmetry

  • Vertex

  • Maximum and minimum

  • Zeros or roots; optimal value

• Example finding the properties of a quadratic relation

Lesson 2: Factored Form of a Quadratic Relation

• Characteristics of quadratic relations in standard form

• Finding the y- intercepts of quadratic relations in standard form

• Finding the x- intercepts of quadratic relations in standard form

• Finding the axis of symmetry of quadratic relations in standard form

• Finding the equation of the axis of symmetry

• Finding the vertex

• Word problems involving quadratic relations in standard form

• Expanding quadratic relations

• Perfect squares

• Review of difference of squares

• Characteristics of perfect square trinomials

• Identifying perfect square trinomials

Lesson 3: Vertex Form of a Quadratic Relation

• Vertex formula and its components

• Converting standard form to vertex form:

  • 4 steps

• Worked examples explained

• The quadratic formula

  • Its use and when

• The Discriminant

  • 3 scenarios

• Application of the discriminant

Lesson 1: Transformations of Quadratic Relations

• The parent equation and its properties

• Graph of the parent equation

• Reflection in the x – axis

• Vertex form and its properties

• Vertical stretch and its characteristics

• Vertical compression and its characteristics

• General rules relating to vertical stretch and compression

• Horizontal shift and its characteristics

• Graph of horizontal shift

• Vertical shift and its characteristics

• Graph of vertical shift

Lesson 2: Graphing Quadratic Relations

• Review of direction and shape of a parabola

• The Step Pattern

• Use of Step Pattern for graphing quadratic relations

• Problems involving the Step Pattern

• Determining the equation in 3 formats given the graph

Lesson 1: Similar Triangles

• Characteristics of similar triangles

  • Expressing similar triangles

  • Proportional triangles and their expressions

  • Conditions for similarity

• Types of similarities

  • SSS

  • SAS

  • AA

• Congruent triangles

  • Identifying congruent triangles

  • Characteristics of congruent triangles

  • Conditions for congruence

• Types of Congruence

  • SSS

  • SAS

  • ASA

Lesson 2: Triangles and Their Relationships

• Triangles and angle relationships

• Properties of triangles and relationships

  • Complementary

  • Isosceles; Supplementary; and External angles

  • Transversal and parallel lines

• Corresponding and Co-interior angles

Lesson 3: Introduction to Trigonometry

• Investigating right triangles

  • Pythagorean Theorem

  • Primary trigonometric ratios

  • Relating the opposite and adjacent with an angle

  • Identifying SOH, CAH, and TOA

• Solving questions using trigonometric ratios

  • Solving for a side

  • Solving for an angle (use of sin-1, cos-1, and tan-1)

  • Technique for solving these questions

  • Caution to ensure accuracy (proper use of calculator)

Lesson 4: Non- Right Angle Triangles

• The sine rule (method 1)

  • Understanding sides and angles in relation to angles

  • Sine rule formula

  • Two conditions for sine rule

  • Solving application questions with sine rule

  • Drawing diagrams to represent questions

  • Caution for final answers

• The cosine rule (method 2)

  • The cosine rule formula

  • Understanding the pattern of the formula

  • Key to remembering the formula

  • Two conditions for cosine rule

  • Understanding the “joining” angle

  • Solving for unknown side using cosine rule

  • Solving for unknown angle using cosine rule

  • Applying cosine rule for triangles PQR or MNO etc.