4) Secondary 4 Elementary Mathematics (yearly access)

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Course Description

In this secondary 3, 4 and 5 elementary mathematics course, you will be learning

Numbers and their operations
Equations and inequalities
Functions and graphs
Congruence and Similarity
Properties of Circles
Pythagoras’ Theorem and Trigonometry
Arc Lengths and Sector Areas
Coordinate Geometry

Set Language and Notation
Matrices
Vectors in two dimensions
Probability
Data Handling and Analysis

Course Content

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1) Numbers and their operations 39 Topics Sample Lesson

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Let’s talk about a^n, where n is a positive integer

Let’s talk about a^-n, where n is a positive integer

Let’s talk about a^(1 divided by n), where n is a positive integer

Let’s talk about a^0

Let’s talk about a^(m divided by n)

Laws of Indices Part 1

Laws of Indices Part 2

Laws of Indices Summary

Practice Question 1a – Laws of Indices

Practice Question 1b – Laws of Indices

Practice Question 1c – Laws of Indices

Practice Question 1d – Laws of Indices

Practice Question 1e – Laws of Indices

Practice Question 1f – Laws of Indices

Practice Question 1g – Laws of Indices

Practice Question 1h – Laws of Indices

Practice Question 1i – Laws of Indices

Practice Question 1j – Laws of Indices

Practice Question 1k – Laws of Indices

Practice Question 1l – Laws of Indices

Practice Question 1m – Laws of Indices

Practice Question 1n – Laws of Indices

Comparing Indices

Practice Question 2a – Comparing Indices

Practice Question 2b – Comparing Indices

Practice Question 2c – Comparing Indices

Practice Question 2d – Comparing Indices

Standard Form

Standard Form , Let’s Explain Part 1

Standard Form , Let’s Explain Part 2

Standard Form – Special Names for powers of 10

Practice Question 3a – Standard Form

Practice Question 3b – Standard Form

Practice Question 3c – Standard Form

Practice Question 3d – Standard Form

Practice Question 3e – Standard Form

Practice Question 3f – Standard Form

Practice Question 3g – Standard Form

Practice Question 3h – Standard Form

2) Equations and inequalities 43 Topics

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Factorisation Method

Practice Question 1a – Factorisation Method

Practice Question 1b – Factorisation Method

Practice Question 1c – Factorisation Method

Practice Question 1d – Factorisation Method

Graphical Method

Practice Question 2a – Graphical Method

Practice Question 2b – Graphical Method

Practice Question 2c – Graphical Method

Practice Question 2d – Graphical Method

Completing The Square Method

Practice Question 3a – Completing The Square Method

Practice Question 3b – Completing The Square Method

Practice Question 3c – Completing The Square Method

Quadratic Formula

Practice Question 4a – Quadratic Formula

Practice Question 4b – Quadratic Formula

Practice Question 4c – Quadratic Formula

Practice Question 4d – Quadratic Formula

Practice Question 4e – Quadratic Formula

Fractional Equations

Practice Question 5a – Fractional Equations

Practice Question 5b – Fractional Equations

Practice Question 5c – Fractional Equations

Practice Question 5d – Fractional Equations

Problems Involving Quadratic Equations

Practice Question 6a – Problems Involving Quadratic Equations

Refresher on Basic Inequalities

Basic Properties of Inequalities Part 1

Basic Properties of Inequalities Part 2

Basic Properties of Inequalities Part 3

Basic Properties of Inequalities Part 4

Practice Question 7a – Basic Properties of Inequalities

Practice Question 7b – Basic Properties of Inequalities

Linear Inequalities In One Variable

Practice Question 8a – Linear Inequalities In One Variable

Practice Question 8b – Linear Inequalities In One Variable

Simultaneous Linear Inequalities

Practice Question 9a – Simultaneous Linear Inequalities

Practice Question 9b – Simultaneous Linear Inequalities

Practice Question 9c – Simultaneous Linear Inequalities

Applications of Linear Inequalities

Practice Question 10a – Applications of Linear Inequalities

3) Functions and graphs 34 Topics

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Graph of y=(x-h)^2 + k

Graph of y=-(x-h)^2 + k

Intuitions for the graph of y=(x-h)^2 + k and y=-(x-h)^2 + k

Steps to sketch the graph of y=(x-h)^2 + k and y=-(x-h)^2 + k

Practice Question 1a – Graph of y=(x-h)^2 + k

Practice Question 1b – Graph of y=-(x-h)^2 + k

Practice Question 1c – Graph of y=(x-h)^2 + k

Practice Question 1d – Graph of y=-(x-h)^2 + k

Practice Question 1e – Graph of y=(x-h)^2 + k

Practice Question 1f – Graph of y=-(x-h)^2 + k

Graph of y=(x-a)(x-b)

Graph of y=-(x-a)(x-b)

Steps to sketch the graph of y=(x-a)(x-b) and y=-(x-a)(x-b)

Practice Question 2a – Graph of y=(x-a)(x-b)

Practice Question 2b – Graph of y=-(x-a)(x-b)

Practice Question 2c – Graph of y=(x-a)(x-b)

Practice Question 2d – Graph of y=-(x-a)(x-b)

Graphs of Power Functions

Graphs of Power Functions , n=0

Graphs of Power Functions , n=1

Graphs of Power Functions , n=2

Graphs of Power Functions , n=3

Practice Question 3a – Graphs of Power Functions , n=3

Graphs of Power Functions , n=-1

Practice Question 3b – Graphs of Power Functions , n=-1

Graphs of Power Functions , n=-2

Practice Question 3c – Graphs of Power Functions , n=-2

Graphs of Sums of Power Functions

Practice Question 4a – Graphs of Sums of Power Functions

Graphs of Exponential Functions

Practice Question 5a – Graphs of Exponential Functions

Practice Question 5b – Graphs of Exponential Functions

Gradient of Curves

Practice Question 6a – Gradient of Curves

4) Congruence and Similarity 25 Topics

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Introduction to Congruence and Similarity

Congruence – Side-Side-Side Test (SSS)

Practice Question 1a – Congruence – Side-Side-Side Test (SSS)

Practice Question 1b – Congruence – Side-Side-Side Test (SSS)

Congruence – Side-Angle-Side Test (SAS)

Practice Question 2a – Congruence – Side-Angle-Side Test (SAS)

Congruence – Angle-Side-Angle Test (ASA)

Practice Question 3a – Congruence – Angle-Side-Angle Test (ASA)

Congruence – Angle-Angle-Side Test (AAS)

Practice Question 4a – Congruence – Angle-Angle-Side Test (AAS)

Congruence – Right Angle-Hypotenuse-Side Test (RHS)

Practice Question 5a – Congruence – Right Angle-Hypotenuse-Side Test (RHS)

Practice Question 6a – Similarity – Angle-Angle-Angle Test (AAA)

Similarity – Side-Side-Side Test (SSS)

Practice Question 7a – Similarity – Side-Side-Side Test (SSS)

Similarity – Side-Angle-Side Test (SAS)

Practice Question 8a – Similarity – Side-Angle-Side Test (SAS)

Ratio of Areas of Similar Plane Figures

Practice Question 9a – Ratio of Areas of Similar Plane Figures

Practice Question 9b – Ratio of Areas of Similar Plane Figures

Practice Question 9c – Ratio of Areas of Similar Plane Figures

Ratio of Volumes of Similar Solids

Practice Question 10a – Ratio of Volumes of Similar Solids

Practice Question 10b – Ratio of Volumes of Similar Solids

5) Properties of Circles 25 Topics

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Introduction to Circles

Chord

Minor Arc and Major Arc

Minor Segment and Major Segment

Properties of Circles (POC)

POC 1 – Equal chords are equidistant from the centre

POC 2 – Perpendicular bisector of a chord passes through the centre

POC 3 – Sum of the angles in the opposite segments is 180°

POC 4 – Angle at centre is double the angle at the circumference

POC 5 – Angles in the same segment are equal

POC 6 – Angle in a semicircle is a right angle

POC 7 – A tangent to a circle is perpendicular to the radius of the circle

POC 8 – Tangents from an external point are equal in length

POC 9 – Line joining an external point to the centre of the circle bisects the angle between the tangents

Practice Question 1a – Properties of Circles

Practice Question 1b – Properties of Circles

Practice Question 1c – Properties of Circles

Practice Question 1d – Properties of Circles

Practice Question 1e – Properties of Circles

Practice Question 1f – Properties of Circles (Try it!)

Practice Question 2a – Properties of Circles

Practice Question 2b – Properties of Circles

Practice Question 2c – Properties of Circles

Practice Question 2d – Properties of Circles

Practice Question 2e – Properties of Circles

6) Pythagoras’ Theorem and trigonometry 47 Topics

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Pythagoras’s Theorem

Practice Question 1a – Pythagoras’s Theorem

Trigonometric Ratios of Acute Angles

Trigonometric Ratios of Acute Angles – How to key in

Practice Question 2a – Trigonometric Ratios of Acute Angles

Practice Question 2b – Trigonometric Ratios of Acute Angles

Practice Question 2c – Trigonometric Ratios of Acute Angles

Practice Question 2d – Trigonometric Ratios of Acute Angles

Practice Question 2e – Trigonometric Ratios of Acute Angles

Practice Question 2f – Trigonometric Ratios of Acute Angles

Practice Question 2g – Trigonometric Ratios of Acute Angles

Practice Question 2h – Trigonometric Ratios of Acute Angles

Practice Question 2i – Trigonometric Ratios of Acute Angles

Practice Question 2j – Trigonometric Ratios of Acute Angles

Trigonometric Ratios of Obtuse Angles

Practice Question 3a – Trigonometric Ratios of Obtuse Angles

Practice Question 3b – Trigonometric Ratios of Obtuse Angles

Practice Question 3c – Trigonometric Ratios of Obtuse Angles

Trigonometric Ratios of Obtuse Angles – 2nd Observation

Practice Question 4a – Trigonometric Ratios of Obtuse Angles

Practice Question 4b – Trigonometric Ratios of Obtuse Angles

Area of a Triangle

Area of a Triangle : Proof

Practice Question 5a – Area of a Triangle

Practice Question 5b – Area of a Triangle

Practice Question 5c – Area of a Triangle

Sine Rule

Sine Rule – Proof

Practice Question 6a – Sine Rule

Practice Question 6b – Sine Rule (First Case)

Practice Question 6b – Sine Rule (Second Case)

Practice Question 6c – Sine Rule

Cosine Rule

Cosine Rule – Proof

Practice Question 7a – Cosine Rule

Practice Question 7b – Cosine Rule

Bearings

Bearings – My Way of Teaching

Practice Question 8a – Bearings

Practice Question 8b – Bearings

Angle of Elevation and Depression

Practice Question 9a – Angle of Elevation and Depression

Practice Question 9b – Angle of Elevation and Depression

Practice Question 9c – Angle of Elevation and Depression

Three-Dimensional Problems

Practice Question 10a – Three-Dimensional Problem

Practice Question 10b – Three-Dimensional Problem

7) Arc Lengths and Sector Areas 23 Topics

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Minor Segment and Major Segment

Minor Sector and Major Sector

Arc Lengths (Using Degrees)

Practice Question 1a – Arc Lengths (Using Degrees)

Practice Question 1b – Arc Lengths (Using Degrees)

Sector Areas (Using Degrees)

Practice Question 2a – Sector Areas (Using Degrees)

Practice Question 2b – Sector Areas (Using Degrees)

Practice Question 2c – Sector Areas (Using Degrees)

Using Radians for measurement of angles

Conversion between Radians and Degrees

Practice Question 3a – Conversion between Radians and Degrees

Practice Question 3b – Conversion between Radians and Degrees

Practice Question 3c – Conversion between Radians and Degrees

Practice Question 3d – Conversion between Radians and Degrees

Practice Question 3e – Conversion between Radians and Degrees

Arc Lengths (Using Radians)

Practice Question 4a – Arc Lengths (Using Radians)

Practice Question 4b – Arc Lengths (Using Radians)

Sector Areas (Using Radians)

Practice Question 5a – Sector Areas (Using Radians)

Practice Question 5b – Sector Areas (Using Radians)

Practice Question 5c – Sector Areas (Using Radians)

8) Coordinate Geometry 25 Topics

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What is Coordinate Geometry

Length of a line segment

Practice Question 1a – Length of a line segment

Practice Question 1b – Length of a line segment

Practice Question 1c – Length of a line segment

Gradient of a straight line

Gradient of a horizontal line

Gradient of a vertical line

Practice Question 2a – Gradient of a straight line

Practice Question 2b – Gradient of a straight line

Practice Question 2c – Gradient of a straight line

Interpreting Equation Of A Straight Line

Practice Question 3a – Interpreting Equation Of A Straight Line

Practice Question 3b – Interpreting Equation Of A Straight Line

Practice Question 3c – Interpreting Equation Of A Straight Line

Practice Question 3d – Interpreting Equation Of A Straight Line

Finding Equation Of A Straight Line

Finding Equation Of A Straight Line (2 points on the line provided)

Finding Equation Of A Straight Line (1 point on the line and gradient provided)

Practice Question 4a – Finding Equation Of A Straight Line (2 points on the line provided)

Practice Question 4b – Finding Equation Of A Straight Line (1 point on the line and gradient provided)

Finding Equation Of A Horizontal Line

Finding Equation Of A Vertical Line

Practice Question 5a – Finding Equation Of A Horizontal Line (2 points on the line provided)

Practice Question 5b – Finding Equation Of A Vertical Line (2 points on the line provided)

1) Set language and notation 20 Topics

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What is a Set

What is a Universal Set – Represent Set with Venn Diagram

Let’s Draw a Venn Diagram

The Union of Sets

The Intersection of Sets

The Complement of a Set

Empty Set

The Number of Elements in a Set

The Number of Elements in a Set – More Examples

Is an element of …

Is not an element of …

Subset

Proper Subset

Important Sets of Numbers

Practice Question 1a – Set language and notation

Practice Question 1b – Set language and notation

Practice Question 1c – Set language and notation

Practice Question 1d – Set language and notation

Practice Question 1e – Set language and notation

Practice Question 1f – Set language and notation

2) Matrices 29 Topics

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Introduction to Matrices

Order of a Matrix

Equal Matrices

Practice Question 1a – Interpretation of Matrices

Practice Question 1b – Equal Matrices

Addition of Matrices

Commutative Property of Addition

Associative Property of Addition

Additive Identity Property

Practice Question 2a – Addition of Matrices

Practice Question 2b – Addition of Matrices

Practice Question 2c – Addition of Matrices

Subtraction of Matrices

Practice Question 3a – Subtraction of Matrices

Practice Question 3b – Subtraction of Matrices

Multiplication of a Matrix By a Scalar

Practice Question 4a – Multiplication of a Matrix By a Scalar

Practice Question 4b – Multiplication of a Matrix By a Scalar

Practice Question 4c – Multiplication of a Matrix By a Scalar

Multiplication of Matrices – Example

Multiplication of Matrices

Generally, Matrix AB is not equal to Matrix BA

Multiplication of Matrix A by an Identity Matrix I

Multiplication of Matrix A by a Zero Matrix O

Associative Property of Multiplication

Practice Question 5a – Multiplication of Matrices

Practice Question 5b – Multiplication of Matrices

Practice Question 5c – Multiplication of Matrices

Practice Question 5d – Multiplication of Matrices

3) Vectors in two dimensions 28 Topics

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Introduction To Vectors

Vector Representation and Notations

Equal Vectors

Practice Question 1a – Equal Vectors

Triangle Law of Vector Addition

Triangle Law of Vector Addition – My Way of Teaching

Parallelogram Law of Vector Addition

Parallelogram Law of Vector Addition – My Way of Teaching

Commutative Law and Associative Law For Vectors

My Tip for you to remember Vector Addition

Practice Question 2a – Vector Addition

Practice Question 2b – Vector Addition

Negative of the vector

Subtraction of Vector can be considered as Addition of Vector

Zero Vector

Scalar Multiplication of Vectors

Rules of Scalar Multiplication of Vectors

Practice Question 3a – Vector Practice

Practice Question 3b – Vector Practice

Position Vectors

Practice Question 4a – Position Vectors

Vectors On The Coordinate Plane

Practice Question 5a – Vector Practice 2

Addition and Subtraction of Column Vectors

Scalar Multiplication of a column vector

Parallel Vectors

Practice Question 6a – Vector Practice 3

Practice Question 6b – Vector Practice 3

4) Probability 13 Topics

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Introduction to Probability

Basic Properties of Probability

Possibility Diagram

Practice Question 1a – Possibility Diagram

Probability using Venn Diagram

Mutually Exclusive Events

Practice Question 2a – Mutually Exclusive Events

Independent Events

Practice Question 3a – Independent Events

Tree Diagram

Practice Question 4a – Tree Diagrams

Tree Diagram – Without Replacement

Practice Question 5a – Tree Diagrams – Without Replacement

5) Data handling and analysis 16 Topics

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Recap on Mean and Median

Range

Interquartile Range

Standard Deviation For Ungrouped Data

Summation Notation

Alternative Formula for Standard Deviation

Practice Question 1a – Standard Deviation

Standard Deviation For Grouped Data

Practice Question 2a – Standard Deviation

Practice Question 2b – Standard Deviation

Comparison of Two Data Sets

Practice Question 3a – Comparison of Two Data Sets

Cumulative Frequency Curve

Practice Question 4a – Cumulative Frequency Curve

Box-and-Whisker Plot

Practice Question 5a – Box-and-Whisker Plot