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Higher 2 Maths Topics

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1. Introduction to Relations and Functions

1.1 Relationship between two variables
1.2 Understand relations between x- and y-intercepts
1.3 Domain and range of a function
1.4 Identifying functions
1.5 Function notation

2. Functions

2.1 Function notation
2.2 Operations with functions
2.3 Adding functions
2.4 Subtracting functions
2.5 Multiplying functions
2.6 Dividing functions
2.7 Composite functions
2.8 Inequalities of combined functions
2.9 Inverse functions
2.10 One to one functions
2.11 Difference quotient: applications of functions

3. Transformations of Functions

3.1 Transformations of functions: Horizontal translations
3.2 Transformations of functions: Vertical translations
3.3 Reflection across the y-axis: y = f(-x)
3.4 Reflection across the x-axis: y = -f(x)
3.5 Transformations of functions: Horizontal stretches
3.6 Transformations of functions: Vertical stretches
3.7 Combining transformations of functions
3.8 Even and odd functions

4. Quadratic Functions

4.1 Characteristics of quadratic functions
4.2 Transformations of quadratic functions
4.3 Quadratic function in general form: y = ax^2 + bx + c
4.4 Quadratic function in vertex form: y = a(x-p)^2 + q
4.5 Completing the square
4.6 Converting from general to vertex form by completing the square
4.7 Shortcut: Vertex formula
4.8 Graphing parabolas for given quadratic functions
4.9 Finding the quadratic functions for given parabolas
4.10 Applications of quadratic functions

5. Quadratic Equations and Inequalities

5.1 Solving quadratic equations by factorising
5.2 Solving quadratic equations by completing the square
5.3 Using quadratic formula to solve quadratic equations
5.4 Nature of roots of quadratic equations: The discriminant
5.5 Applications of quadratic equations
5.6 Solving quadratic inequalities

6. Polynomial Functions

6.1 What is a polynomial function?
6.2 Polynomial long division
6.3 Polynomial synthetic division
6.4 Remainder theorem
6.5 Factor theorem
6.6 Rational zero theorem
6.7 Characteristics of polynomial graphs
6.8 Multiplicities of polynomials
6.9 Imaginary zeros of polynomials
6.10 Determining the equation of a polynomial function
6.11 Applications of polynomial functions
6.12 Solving polynomial inequalities
6.13 Fundamental theorem of algebra
6.14 Descartes' rule of signs

7. Rational Functions

7.1 What is a rational function?
7.2 Point of discontinuity
7.3 Vertical asymptote
7.4 Horizontal asymptote
7.5 Slant asymptote
7.6 Graphs of rational functions
7.7 Solving equations with algebraic fractions
7.8 Solving rational inequalities

8. Solving Simultaneous Equations

8.1 Determining number of solutions to linear equations
8.2 Solving simultaneous equations by graphing
8.3 Solving simultaneous equations by elimination
8.4 Solving simultaneous equations by substitution
8.5 Money related questions in linear equations
8.6 Unknown number related questions in linear equations
8.7 Distance and time related questions in linear equations
8.8 Rectangular shape related questions in linear equations

9. Inequalities in two variables

9.1 Graphing linear inequalities in two variables
9.2 Graphing simultaneous linear inequalities
9.3 Graphing quadratic inequalities in two variables
9.4 Graphing simultaneous quadratic inequalities
9.5 Applications of inequalities
9.6 What is linear programming?
9.7 Linear programming word problems

10. Introduction to Matrices

10.1 Notation of matrices
10.2 Adding and subtracting matrices
10.3 Scalar multiplication
10.4 Matrix multiplication
10.5 The three types of matrix row operations
10.6 Representing a linear system as a matrix
10.7 Solving a linear system with matrices using Gaussian elimination

11. Determinants and Inverses of Matrices

11.1 The determinant of a 2 x 2 matrix
11.2 The determinant of a 3 x 3 matrix (General & Shortcut Method)
11.3 The inverse of a 2 x 2 matrix
11.4 The inverse of 3 x 3 matrices with matrix row operations
11.5 The inverse of 3 x 3 matrix with determinants and adjugate
11.6 2 x 2 invertible matrix
11.7 Solving linear systems using Cramer's Rule
11.8 Solving linear systems using 2 x 2 inverse matrices

12. Conics

12.1 Conics - Parabola
12.2 Conics - Ellipse
12.3 Conics - Circle
12.4 Conics - Hyperbola

13. Imaginary and Complex Numbers

13.1 Introduction to imaginary numbers
13.2 Complex numbers and complex planes
13.3 Adding and subtracting complex numbers
13.4 Complex conjugates
13.5 Multiplying and dividing complex numbers
13.6 Distance and midpoint of complex numbers
13.7 Angle and absolute value of complex numbers
13.8 Polar form of complex numbers
13.9 Operations on complex numbers in polar form

14. Vectors

14.1 Introduction to vectors
14.2 Magnitude of a vector
14.3 Direction angle of a vector
14.4 Scalar multiplication
14.5 Equivalent vectors
14.6 Adding and subtracting vectors in component form
14.7 Operations on vectors in magnitude and direction form
14.8 Unit Vector
14.9 Word problems on vectors

15. Sequences and Series

15.1 Arithmetic sequences
15.2 Arithmetic series
15.3 Geometric sequences
15.4 Geometric series
15.5 Infinite geometric series
15.6 Sigma notation
15.7 Arithmetic mean vs. Geometric mean

16. Limits

16.1 Finding limits from graphs
16.2 Continuity
16.3 Finding limits algebraically - direct substitution
16.4 Finding limits algebraically - when direct substitution is not possible
16.5 Infinite limits - vertical asymptotes
16.6 Limits at infinity - horizontal asymptotes
16.7 Intermediate value theorem
16.8 Squeeze theorem

17. Derivatives

17.1 Definition of derivative
17.2 Power rule
17.3 Gradient and equation of tangent line
17.4 Chain rule
17.5 Derivative of trigonometric functions
17.6 Derivative of exponential functions
17.7 Product rule
17.8 Quotient rule
17.9 Implicit differentiation
17.10 Derivative of inverse trigonometric functions
17.11 Derivative of logarithmic functions
17.12 Higher order derivatives

18. Permutations and Combinations

18.1 Fundamental counting principle
18.2 Factorial notation
18.3 Path counting problems
18.4 Permutation vs. Combination
18.5 Permutations
18.6 Combinations
18.7 Problems involving both permutations and combinations
18.8 Pascal's triangle
18.9 Binomial theorem

19. Probability

19.1 Addition rule for "OR"
19.2 Multiplication rule for "AND"
19.3 Conditional probability
19.4 Probability with permutations and combinations
19.5 Law of total probability
19.6 Bayes' rule
19.7 Probability with Venn diagrams

20. Data Interpretation

20.1 Center of a data set: mean, median, mode
20.2 Spread of a data set - standard deviation & variance
20.3 Measures of relative standing - z-score, quartiles, percentiles
20.4 Bivariate, scatter plots and correlation
20.5 Regression analysis
20.6 Equation of the best fit line

21. Discrete Probabilities

21.1 Probability distribution - histogram, mean, variance & standard deviation
21.2 Binomial distribution
21.3 Mean and standard deviation of binomial distribution
21.4 Poisson distribution
21.5 Geometric distribution
21.6 Negative binomial distribution
21.7 Hypergeometric distribution
21.8 Properties of expectation

22. Normal Distribution and Z-score

22.1 Introduction to normal distribution
22.2 Normal distribution and continuous random variable
22.3 Z-scores and random continuous variables
22.4 Sampling distributions
22.5 Central limit theorem
22.6 Rare event rule

22 Chapters · 177 Topics · 1189 Videos

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Yes — our Higher 2 Maths content covers all major topics for Singapore A-Level exams, including calculus, vectors, statistics, and complex numbers.

Is this aligned to Singapore A-Level exams?

Yes — all content is designed for Singapore A-Level H2 Mathematics syllabus with real exam-style practice questions.

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