SPM Additional Mathematics

Download our free App.

SPM Add. Maths (Model Test Paper)

1. Paper 2 Section A (Question only)
2. Paper 2 Section B & C (Question only)
3. Paper 2 Section A (Question and Answer)
   • Question 1 & 2, Question 3 & 4, Question 5 & 6
4. Paper 2 Section B (Question and Answer)
   • Question 7, Question 8, Question 9
   • Question 10, Question 11
5. Paper 2 Section C (Question and Answer)
   • Question 12, Question 13

01 Functions

1. Relation
   1. Domain and Codomain
   2. Types of Relation
2. Functions
1. Notation of Function
2. Domain, Range, Objects, Images and Absolute Value Functions
3. Example 1, Example 2 & 3, Example 4 & 5
3. Composite Function
   • Example 1, Example 2 & Example 3
4. Composite Function (Comparison Method)
   • Example 1, Example 2 & Example 3
5. Finding new function given a composite function (Case A : First function is given)
   • Example 1, Example 2 & Example 3
6. Finding new function given a composite function (Case B : Second function is given) Harder. Make sure you try it ! (Substitution Method)
   • Example 1 , Example 2 , Example 3 
7. Inverse Function
   • Example 1, Example 2 & Example 3
   • Example 4, Example 5, Example 6 & Example 7
8. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 – 4, Question 5 – 8
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4, Question 5
9. Mind Map

Videos：

1. Relation – Domain, Codomain, Objects and Images of Relations | Types of Relation
2. Function – Function and Function Notation | Function and Function Notation (Examples) | Absolute Value Function
3. (i) Types of Relation and Function Notation | (ii) Finding Object and Image for Ordered Pair | (iii) Finding Domain, Codomain and Range from Arrow Diagram

 

02 Quadratic Equations

1. Introduction to Quadratic Equations
2. General Form of Quadratic Equations
3. Quadratic Equation and Its Roots
   • Example : Roots satisfy an equation
4. Solving Quadratic Equations
   1. Factorisation
   2. Completing the Square
      • Examples : Steps to solve quadratic equation using competing square
   3. Quadratic Formula
5. Forming Quadratic Equations from Given Roots
6. Finding the Sum of Roots and Product of Roots of a Quadratic Equation
   • More example : Finding the Sum of Roots and Product of Roots of a Quadratic Equation
7. Forming New Quadratic Equation given another Quadratic Equation
8. Discriminant of a Quadratic Equations
9. SPM Focus Practice, Paper 1 (with Solution)
   • Download PDF Copy-Without Answer Space
   • Download PDF Copy-With Answer Space
   • Step by Step Answer
   • Question 1 – 5, Question 6 – 10, Question 11 – 15
10. SPM Focus Practice, Paper 2 (with Solution)
    • Question 1, Question 2, Question 3 & 4, Question 5
11. Mind Map

Videos：

1. Introduction to the Quadratic Equation and It’s General Form
2. Using Casio fx-570ES Plus / Casio fx-991ES Plus Calculator for Quadratic Equations
3. Solving Quadratic Equation by – (Factorisation) | (Completing the Square) | Completing the Square (Examples) | (Quadratic Formula)
4. Relationship between the Roots and the Coefficients – (Part 1) | (Part 2) | (Part 3) | (Part 4)
5. Nature of Roots of Quadratic Equations – (Part 1) | (Part 2) | (Part 3)

03 Quadratic Functions

1. General Form of Quadratic Function
2. Graph of Quadratic Functions
   • Axis of Symmetry
3. Maximum and Minimum Value of Quadratic Functions
   • Example 1 : Finding maximum/minimum point and axis of symmetry of a quadratic function 
4. Finding the Maximum and Minimum points of Quadratic Function using completing the square
   • Example 1 : Finding Maximum and minimum point of quadratic function using completing the square
5. Sketching the Graph of Quadratic Functions
   • Example 1  
6. Quadratic Inequalities
   • Steps to solve a Quadratic Inequalities
   • Example 1 (Linear Inequality)
   • Example 2 (Quadratic Inequalities)
7. Nature of the Roots (Combination of Straight Line and the Curve)
   • Example 1 (Straight Line is Tangent to the Curve)
   • Example 2 (Straight Line intersect the curve at two distinct points)
   • Example 3 (Straight Line does not intersect the curve)
8. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 & 2, Question 3 & 4, Question 5 – 7
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4, Question 5 & 6
9. Mind Map

Videos:

1. Quadratic Function (Linear Inequality)
2. Quadratic Function (Quadratic Inequality)

04 Simultaneous Equation

1. Simultaneous Equations in Two Unknowns
   • Example 1 & 2
2. SPM Focus Practice, Paper 2 (with Solution)
   • Question 1 & 2, Question 3 & 4, Question 5 & 6, Question 7
3. Using Casio fx-570ES Plus / Casio fx-991ES Plus Calculator for Simultaneous Equations
4. Mind Map

05 Indices and Logarithms

1. Indices
   1. Indices Part 1
   2. Indices Part 2
2. Logarithms
   • Example 1 & Example 2
3. 1. Laws of Logarithms
      • Example 1, Example 2 & Example 3
   2. Change of Base of Logarithms
      • Example 1, Example 2, Example 3 & Example 4
4. Equations Involving Indices
   • Example 1 (Index Equation – Equal Base)
   • Example 2 (Index Equation – Equal Base)
   • Example 3 (Index Equation – Equal Base)
   • Example 4 (Index Equation – Substitution)
   • Example 5 (Unequal Base – Put log both side)
5. Equations Involving Logarithms
   • Example 1, Example 2, Example 3, Example 4 & Example 5
6. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 – 8, Question 9 – 14
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4
7. Mind Map

Videos:

1. Indices – Introduction | Zero Indices & Negative Integral Indices | Fractional Indices | Fractional Indices (Examples) | Express a Number in Index Form
2. Law of Indices – Product of Two Indices Number | Quotient of Two Indices Number | Index of An Index Number | Index of A Product/ Quotient | Summary | Examples
3. Logarithm – Introduction 1 | Introduction 2 | Laws of Logarithm | Laws of Logarithm (Examples)
4. Finding Exact Value of a Logarithm – Part 1 | Part 2 | Part 3 | Part 4
5. Change of Base of a Logarithm – Part 1 | Part 2 | Part 3
6. Solving Equation with Index Number – Part 1 | Part 2 | Part 3 (Simultaneous Equation) | Part 4 (Addition/ Subtraction) | Part 5 (Examples)
7. Using Casio fx-570ES Plus / Casio fx-991ES Plus Calculator for Indices & Logarithm
8. Solving Exponential Equation

06 Coordinate Geometry

1. Distance between 2 Points
2. Division of Line Segment
3. Areas of Polygons
4. Equations of Straight Lines (Part 1)
5. Equations of Straight Lines (Part 2)
6. Parallel and Perpendicular Lines
7. Equation of a Locus
8. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 & 2, Question 3 – 5, Question 6 & 7
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4, Question 5 & 6, Question 7
9. Mind Map

07 Statistics

1. Measures of Central Tendency
   1. Mean
   2. Mode
   3. Median
2. Measures of Dispersion
   1. Range
   2. Interquartile Range 1
   3. Interquartile Range 2
   4. Variance and Standard Deviation
3. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 & 2, Question 3 & 4, Question 5 & 6, Question 7
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4, Question 5 & 6
4. Mind Map

08 Circular Measure

1. Radian
2. Arc Length of a Circle
3. Area of Sector of a Circle
4. SPM Focus Practice (with Solution)
   1. Short Questions (Paper 1)
      • Question 1 – 3, Question 4 – 6
   2. Long Questions (Paper 2)
      • Question 1 & 2, Question 3 & 4, Question 5 & Question 6
5. Mind Map

09 Differentiation

1. Differentiation
2. First Derivatives for Polynomial Functions
3. First Derivatives of the Product of Two Polynomials
4. First Derivatives of the Quotient of Two Polynomials
5. First Derivatives of Composite Function
6. Gradients of Tangents, Equations of Tangents and Normals
7. Second Order Differentiation, Turning Points, Maximum and Minimum Points
8. Related Rates of Change
9. Small Changes and Approximations
10. SPM Focus Practice (with Solution)
    1. Short Questions (Paper 1)
       • Question 1 – 5, Question 6 – 10, Question 11 – 14, Question 15 – 18
       • Question 19 – 21, Question 22 – 25
    2. Long Questions (Paper 2)
       • Question 1, Question 2 & 3
11. Mind Map

Videos

1. Technique of Differentiation
2. Finding the Equation of Tangent
3. Finding the Equation of Normal
4. Finding the Maximum Value of a Quadratic Function
5. Finding Maximum and Minimum Point – Second Derivative Test
6. Differentiation – Rate of Change Example 1
7. Using Casio fx-570ES Plus / Casio fx-991ES Plus Calculator for Differentiation

10 Solution of Triangles

1. Sine Rule
2. Cosine Rule
3. Areas of Triangles
4. SPM Focus Practice, Paper 2 (with Solution)
   • Question 1 & 2, Question 3 & 4, Question 5 & 6
5. Mind Map

11 Index Number

1. Index Number
2. Composite Index
3. SPM Focus Practice, Paper 2 (with Solution)
   • Question 1, Question 2, Question 3 & Question 4
4. Mind Map