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GCE O-Level A Maths Topics

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1. Solving Linear Equations

1.1 Solving linear equations using multiplication and division
1.2 Solving two-step linear equations: ax + b = c, x/a + b = c
1.3 Solving linear equations using distributive property: a(x + b) = c
1.4 Solving linear equations with variables on both sides
1.5 Solving literal equations

2. Linear Inequalities

2.1 Express linear inequalities graphically and algebraically
2.2 Solving one-step linear inequalities
2.3 Solving multi-step linear inequalities

3. Measuring Systems

3.1 Metric systems
3.2 Imperial systems
3.3 Conversions between metric and imperial systems
3.4 Conversions involve squares and cubic

4. Number Systems

4.1 Understanding the number systems
4.2 Prime factorisation
4.3 Highest common factors (HCF)
4.4 Least Common Multiple (LCM)
4.5 Rational vs. Irrational numbers
4.6 Converting repeating decimals to fractions

5. Direct and Inverse Proportion

5.1 Direct variation

6. Algebraic Expressions

6.1 Equivalent algebraic expressions
6.2 Adding and subtracting algebraic expressions
6.3 Multiplying monomial by monomial
6.4 Multiplying monomial by binomial
6.5 Multiplying binomial by binomial
6.6 Multiplying polynomial by polynomial
6.7 Applications of polynomials

7. Surds

7.1 Square and square roots
7.2 Cubic and cube roots
7.3 Operations with surds
7.4 Conversion between entire radicals and mixed radicals
7.5 Adding and subtracting surds
7.6 Multiplying surds
7.7 Rationalize the denominator
7.8 Solving equations with surds

8. Linear Functions

8.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
8.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
8.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
8.4 Gradient intercept form: y = mx + b
8.5 General form: Ax + By + C = 0
8.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
8.7 Rate of change
8.8 Graphing linear functions using table of values
8.9 Graphing linear functions using x- and y-intercepts
8.10 Graphing from slope-intercept form y=mx+b
8.11 Graphing linear functions using a single point and gradient
8.12 Word problems of graphing linear functions
8.13 Applications of linear relations

9. Factorising Quadratic Functions

9.1 Factorise by taking out the greatest common factor
9.2 Factorise by grouping
9.3 Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
9.4 Factorising difference of squares: x^2 - y^2
9.5 Factorising trinomials
9.6 Solving polynomials with unknown coefficients
9.7 Solving polynomials with unknown constant terms

10. Quadratic Functions

10.1 Introduction to quadratic functions
10.2 Transformations of quadratic functions
10.3 Quadratic function in general form: y = ax^2 + bx + c
10.4 Quadratic function in vertex form: y = a(x-p)^2 + q
10.5 Completing the square
10.6 Converting from general to vertex form by completing the square
10.7 Shortcut: Vertex formula
10.8 Graphing quadratic functions: General form VS. Vertex form
10.9 Finding the quadratic functions for given parabolas
10.10 Applications of quadratic functions

11. Quadratic Equations and Inequalities

11.1 Solving quadratic equations by factoring
11.2 Solving quadratic equations by completing the square
11.3 Using quadratic formula to solve quadratic equations
11.4 Nature of roots of quadratic equations: The discriminant
11.5 Applications of quadratic equations
11.6 Solving quadratic inequalities

12. Algebraic Fractions

12.1 Simplifying algebraic fractions and restrictions
12.2 Adding and subtracting algebraic fractions
12.3 Multiplying algebraic fractions
12.4 Dividing algebraic fractions
12.5 Solving equations with algebraic fractions
12.6 Applications of equations with algebraic fractions
12.7 Simplifying complex fractions
12.8 Partial fraction decomposition

13. Simultaneous Equations

13.1 Determining number of solutions to linear equations
13.2 Solving simultaneous linear equations by graphing
13.3 Solving simultaneous linear equations by elimination
13.4 Solving simultaneous linear equations by substitution
13.5 Money related questions in linear equations
13.6 Unknown number related questions in linear equations
13.7 Distance and time related questions in linear equations
13.8 Rectangular shape related questions in linear equations
13.9 Simultaneous linear equations
13.10 Simultaneous linear-quadratic equations
13.11 Simultaneous quadratic-quadratic equations

14. Inequalities in Two Variables

14.1 Graphing linear inequalities in two variables
14.2 Graphing systems of linear inequalities
14.3 Graphing quadratic inequalities in two variables
14.4 Graphing systems of quadratic inequalities
14.5 Applications of inequalities
14.6 What is linear programming?
14.7 Linear programming word problems

15. Laws of Indices

15.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
15.2 Indices: Division rule (a^x / a^y) = a^(x-y)
15.3 Indices: Power rule (a^x)^y = a^(x * y)
15.4 Negative indices
15.5 Zero index: a^0 = 1
15.6 Rational indices
15.7 Standard form

16. Polynomial Functions

16.1 Polynomial long division
16.2 Polynomial synthetic division
16.3 Remainder theorem
16.4 Factor theorem

17. Binomial expansions

17.1 Factorial notation
17.2 Binomial theorem

18. Exponential Functions

18.1 Solving exponential equations using laws of indices
18.2 Graphing exponential functions
18.3 Graphing transformations of exponential functions
18.4 Finding an exponential function given its graph

19. Logarithms

19.1 What is a logarithm?
19.2 Converting from logarithmic form to exponential form
19.3 Evaluating logarithms without a calculator
19.4 Common logarithms
19.5 Natural log: ln
19.6 Evaluating logarithms using change-of-base formula
19.7 Converting from exponential form to logarithmic form
19.8 Solving exponential equations with logarithms
19.9 Product rule of logarithms
19.10 Quotient rule of logarithms
19.11 Combining product rule and quotient rule in logarithms
19.12 Evaluating logarithms using logarithm rules
19.13 Solving logarithmic equations
19.14 Graphing logarithmic functions
19.15 Finding a logarithmic function given its graph

20. Modulus Functions

20.1 Modulus functions
20.2 Solving modulus equations

21. Vectors

21.1 Introduction to vectors
21.2 Magnitude of a vector
21.3 Direction angle of a vector
21.4 Scalar multiplication
21.5 Adding and subtracting vectors in component form
21.6 Operations on vectors in magnitude and direction form
21.7 Word problems on vectors

22. Matrices

22.1 Notation of matrices
22.2 Adding and subtracting matrices
22.3 Multiplying a matrix by a scalar
22.4 Multiplying a matrix by another matrix

23. Trigonometric Ratios and Angle Measure

23.1 Angle in standard position
23.2 Coterminal angles
23.3 Reference angle
23.4 Find the exact value of trigonometric ratios
23.5 ASTC rule in trigonometry (All Students Take Calculus)
23.6 Unit circle
23.7 Converting between degrees and radians
23.8 Trigonometric ratios of angles in radians
23.9 Radian measure and arc length

24. Sine Rule and Cosine Rule

24.1 Sine rule
24.2 Cosine rule
24.3 Sine rule and cosine rule word problems

25. Bearings

25.1 Introduction to bearings
25.2 Bearings and direction word problems
25.3 Angle of elevation and depression

26. Graphing Trigonometric Functions

26.1 Sine graph: y = sin x
26.2 Cosine graph: y = cos x
26.3 Tangent graph: y = tan x
26.4 Cotangent graph: y = cot x
26.5 Secant graph: y = sec x
26.6 Cosecant graph: y = csc x
26.7 Graphing transformations of trigonometric functions
26.8 Determining trigonometric functions given their graphs

27. Applications of Trigonometric Functions

27.1 Ferris wheel trig problems
27.2 Tides and water depth trig problems
27.3 Spring (simple harmonic motion) trig problems

28. Trigonometric Identities

28.1 Quotient identities and reciprocal identities
28.2 Pythagorean identities
28.3 Sum and difference identities
28.4 Cofunction identities
28.5 Double-angle identities

29. Solving Trigonometric Equations

29.1 Solving first degree trigonometric equations
29.2 Determining non-permissible values for trig expressions
29.3 Solving second degree trigonometric equations
29.4 Solving trigonometric equations involving multiple angles
29.5 Solving trigonometric equations using pythagorean identities
29.6 Solving trigonometric equations using sum and difference identities
29.7 Solving trigonometric equations using double-angle identities

30. Inverse Trigonometric Functions

30.1 Finding inverse trigonometric function from its graph
30.2 Evaluating inverse trigonometric functions
30.3 Finding inverse reciprocal trigonometric function from its graph
30.4 Inverse reciprocal trigonometric function: finding the exact value

31. Angles, Lines, and Transversals

31.1 Pairs of lines and angles
31.2 Parallel lines and transversals
31.3 Parallel line proofs
31.4 Perpendicular line proofs

32. Scale Factors and Similarity

32.1 Enlargements and reductions with scale factors
32.2 Scale diagrams
32.3 Similar triangles
32.4 Similar polygons

33. Congruent Triangles

33.1 Congruence and congruent triangles
33.2 Triangles congruent by SSS proofs
33.3 Triangles congruent by SAS and HL proofs
33.4 Triangles congruent by ASA and AAS proofs

34. Circles

34.1 Angles in a circle
34.2 Chord properties
34.3 Tangent properties
34.4 Circle and circumference
34.5 Arcs of a circle
34.6 Areas and sectors of circles
34.7 Inscribed quadrilaterals in circles
34.8 Central and inscribed angles in circles

35. Surface Area and Volume

35.1 Surface area and volume of prisms
35.2 Surface area and volume of pyramids
35.3 Surface area and volume of cylinders
35.4 Surface area and volume of cones
35.5 Surface area and volume of spheres

36. Conics

36.1 Conics - Parabola
36.2 Conics - Circle

37. Set Theory

37.1 Set notation
37.2 Set builder notation
37.3 Intersection and union of 2 sets
37.4 Intersection and union of 3 sets

38. Data and Graphs

38.1 Reading and drawing bar graphs
38.2 Reading and drawing histograms
38.3 Reading and drawing line graphs
38.4 Box-and-whisker plots and scatter plots
38.5 Stem-and-leaf plots
38.6 Reading and drawing Venn diagrams
38.7 Frequency tables and dot diagrams
38.8 Pie charts

39. Statistics

39.1 Median and mode
39.2 Mean
39.3 Range and outliers
39.4 Application of averages
39.5 Standard deviation, and variance
39.6 Z-score, quartiles, and percentiles

40. Probability

40.1 Determining probabilities using tree diagrams and tables
40.2 Probability of independent events
40.3 Frequency distribution and histograms
40.4 Addition rule for "OR"
40.5 Multiplication rule for "AND"

41. Differentiation

41.1 Power rule
41.2 Slope and equation of tangent line
41.3 Chain rule
41.4 Derivative of trigonometric functions
41.5 Derivative of exponential functions
41.6 Product rule
41.7 Quotient rule
41.8 Derivative of logarithmic functions
41.9 Higher order derivatives
41.10 Rectilinear Motion: Derivative
41.11 Critical number & maximum and minimum values

42. Integration

42.1 Antiderivatives
42.2 Definite integral
42.3 Integration by parts
42.4 Trigonometric substitution
42.5 Integration of rational functions by partial fractions
42.6 Areas between curves

42 Chapters · 250 Topics · 1712 Videos

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Yes — our GCE O-Level A Maths content covers all major topics regardless of textbook, aligned to standard high school curriculum for your region.

What topics are covered in O-Level A Maths?

All core topics: trigonometry, calculus (differentiation and integration), logarithms, exponentials, binomial theorem, vectors, and coordinate geometry.

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