4) Secondary 4 Elementary Mathematics (yearly access)
1) Numbers and their operations
39 Topics
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
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
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
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)
Similarity – Angle-Angle-Angle Test (AAA)
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
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
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
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
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
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
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
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
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
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
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Practice Question 1m – Laws of Indices
4) Secondary 4 Elementary Mathematics (yearly access)
1) Numbers and their operations
Practice Question 1m – Laws of Indices
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