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GCE O-Level Maths Topics

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1. Numbers and Relations

1.1

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Number Theory

2.1

Divisibility Rules

2.2

Determining Common Factors

2.3

Determining Common Multiples

2.4

Introduction to exponents

3. Adding and Subtracting Integers

3.1

Introduction to integer addition

3.2

Adding integers

3.3

Introduction to integer subtraction

3.4

Subtracting integers

3.5

Application of integer operations

4. Multiplying and Dividing Integers

4.1

Understanding integer multiplication

4.2

Multiplying integers

4.3

Understanding integer division

4.4

Dividing integers

4.5

Applications of integer operations

5. Operations with decimals

5.1

Adding and subtracting decimals

5.2

Multiplying decimals

5.3

Dividing decimals

5.4

Order of operations (BEDMAS)

6. Adding and Subtracting Fractions

6.1

Using models to add and subtract fractions

6.2

Adding fractions with like denominators

6.3

Subtracting fractions with like denominators

6.4

Adding and subtracting fractions with unlike denominators

6.5

Adding and subtracting mixed numbers

7. Multiplying and Dividing Fractions

7.1

Multiplying fractions and whole numbers

7.2

Dividing fractions with whole numbers

7.3

Multiplying proper fractions

7.4

Multiplying improper fractions and mixed numbers

7.5

Dividing fractions and mixed numbers

7.6

Applications of fraction operations

8. Ratios, Rates, and Proportions

8.1

8.2

8.3

9. Percents

9.1

Representing percents

9.2

Percents, fractions, and decimals

9.3

Percent of a number

9.4

Adding and multiplying percents

9.5

Taxes, discounts, tips and more

9.6

Simple interest

10. Solving Linear Equations

10.1

Solving linear equations using multiplication and division

10.2

Solving two-step linear equations: ax + b = c, x/a + b = c

10.3

Solving linear equations using distributive property: a(x + b) = c

10.4

Solving linear equations with variables on both sides

10.5

Solving literal equations

11. Linear Inequalities

11.1

Express linear inequalities graphically and algebraically

11.2

Solving one-step linear inequalities

11.3

Solving multi-step linear inequalities

12. Measuring Systems

12.1

12.2

Imperial systems

12.3

Conversions between metric and imperial systems

12.4

Conversions involve squares and cubic

13. Number Systems

13.1

Understanding the number systems

13.2

Prime factorisation

13.3

Highest common factors (HCF)

13.4

Least Common Multiple (LCM)

13.5

Rational vs. Irrational numbers

13.6

Converting repeating decimals to fractions

14. Surds

14.1

Square and square roots

14.2

Cubic and cube roots

14.3

Evaluating and simplifying radicals

14.4

Converting radicals to mixed radicals

14.5

Converting radicals to entire radicals

14.6

Adding and subtracting surds

14.7

Multiplying and dividing surds

14.8

Rationalize the denominator

15. Direct and Inverse Proportion

15.1

Direct variation

16. Algebraic Expressions

16.1

Equivalent algebraic expressions

16.2

Adding and subtracting algebraic expressions

16.3

Multiplying monomial by monomial

16.4

Multiplying monomial by binomial

16.5

Multiplying binomial by binomial

16.6

Multiplying polynomial by polynomial

16.7

Applications of polynomials

17. Linear Functions

17.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

17.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

17.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

17.4

Gradient intercept form: y = mx + b

17.5

General form: Ax + By + C = 0

17.6

Gradient-point form:

y - y_1 = m (x - x_1)

17.7

17.8

Graphing linear functions using table of values

17.9

Graphing linear functions using x- and y-intercepts

17.10

Graphing from slope-intercept form y=mx+b

17.11

Graphing linear functions using a single point and gradient

17.12

Word problems of graphing linear functions

17.13

Applications of linear relations

18. Simultaneous Equations

18.1

Determining number of solutions to linear equations

18.2

Solving simultaneous linear equations by graphing

18.3

Solving simultaneous linear equations by elimination

18.4

Solving simultaneous linear equations by substitution

18.5

Money related questions in linear equations

18.6

Unknown number related questions in linear equations

18.7

Distance and time related questions in linear equations

18.8

Rectangular shape related questions in linear equations

19. Factorising Quadratic Functions

19.1

Factorise by taking out the greatest common factor

19.2

Factorise by grouping

19.3

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

19.4

Factorising difference of squares: (a - b)(a + b) = (a^2 - b^2)

19.5

Factorising trinomials

19.6

Solving polynomials with unknown coefficients

19.7

Solving polynomials with unknown constant terms

20. Quadratic Functions

20.1

Introduction to quadratic functions

20.2

Transformations of quadratic functions

20.3

Quadratic function in general form: y = ax^2 + bx + c

20.4

Quadratic function in vertex form: y = a(x-p)^2 + q

20.5

Completing the square

20.6

Converting from general to vertex form by completing the square

20.7

Shortcut: Vertex formula

20.8

Graphing quadratic functions: General form VS. Vertex form

20.9

Finding the quadratic functions for given parabolas

20.10

Applications of quadratic functions

21. Solving Quadratic Equations

21.1

Solving quadratic equations by factorising

21.2

Solving quadratic equations by completing the square

21.3

Using quadratic formula to solve quadratic equations

21.4

The discriminant: Nature of roots of quadratic equations

21.5

Applications of quadratic equations

22. Algeraic Fractions

22.1

Simplifying algebraic fractions and restrictions

22.2

Adding and subtracting algebraic fractions

22.3

Multiplying algebraic fractions

22.4

Dividing algebraic fractions

22.5

Solving equations with algebraic fractions

22.6

Applications of equations with algebraic fractions

22.7

Simplifying complex fractions

22.8

Partial fraction decomposition

23. Laws of Indices

23.1

Indices: Product rule (a^x)(a^y) = a^(x+y)

23.2

Indices: Division rule (a^x / a^y) = a^(x-y)

23.3

Indices: Power rule (a^x)^y = a^(x * y)

23.4

Negative indices

23.5

Zero index: a^0 = 1

23.6

Rational indices

24. Exponential Functions

24.1

Solving exponential equations using laws of indices

24.2

Graphing exponential functions

25. Vectors

25.1

Introduction to vectors

25.2

Magnitude of a vector

25.3

Direction angle of a vector

25.4

Scalar multiplication

25.5

Adding and subtracting vectors in component form

25.6

Operations on vectors in magnitude and direction form

25.7

Word problems on vectors

26. Matrices

26.1

Notation of matrices

26.2

Adding and subtracting matrices

26.3

Multiplying a matrix by a scalar

26.4

Multiplying a matrix by another matrix

27. Geometry and Measurement

27.1

Parallel and perpendicular line segments

27.2

Perpendicular bisectors

27.3

Angle bisectors

28. Scale Factors and Similarity

28.1

Enlargements and reductions with scale factors

28.2

28.3

Similar triangles

28.4

Similar polygons

29. Congruent Triangles

29.1

Classifying Triangles

29.2

Congruence and Congruent Triangles

29.3

Triangles Congruent by SSS Proofs

29.4

Triangles Congruent by SAS and HL Proofs

29.5

Triangles Congruent by ASA and AAS Proofs

29.6

Isosceles and Equilateral Triangles

30. Angles, Lines, and Transversals

30.1

Pairs of lines and angles

30.2

Parallel lines and transversals

30.3

Parallel line proofs

30.4

Perpendicular line proofs

31. Circles

31.1

Angles in a circle

31.2

Chord properties

31.3

Tangent properties

31.4

Circle and circumference

31.5

Arcs of a circle

31.6

Areas and sectors of circles

31.7

Inscribed quadrilaterals in circles

31.8

Central and inscribed angles in circles

32. Surface Area and Volume

32.1

Surface area and volume of prisms

32.2

Surface area and volume of pyramids

32.3

Surface area and volume of cylinders

32.4

Surface area and volume of cones

32.5

Surface area and volume of spheres

33. Trigonometry

33.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

33.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

33.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

33.4

Combination of SohCahToa questions

33.5

Solving expressions using 45-45-90 special right triangles

33.6

Solving expressions using 30-60-90 special right triangles

33.7

Word problems relating ladder in trigonometry

33.8

Word problems relating guy wire in trigonometry

33.9

Other word problems relating angles in trigonometry

34. Angle Measure in Radian

34.1

Converting between degrees and radians

34.2

Radian measure and arc length

35. Sine Rule and Cosine Rule

35.1

35.2

35.3

Sine rule and cosine rule word problems

36. Bearings

36.1

Introduction to bearings

36.2

Bearings and direction word problems

36.3

Angle of elevation and depression

37. Set Theory

37.1

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

Reading and drawing stem-and-leaf diagrams

38.6

Reading and drawing Venn diagrams

38.7

Frequency tables and dot diagrams

38.8

39. Representing Data

39.1

Advantages and disadvantages of different graphs

39.2

Misleading graphs

39.3

Critiquing data presentation

40. Statistics

40.1

Median and mode

40.2

40.3

Range and outliers

40.4

Application of averages

40.5

Standard deviation and variance

40.6

Z-score, quartiles, and percentiles

41. Probability

41.1

Determining probabilities using tree diagrams and tables

41.2

Probability of independent events

41.3

Frequency distribution and histograms

41.4

Addition rule for "OR"

41.5

Multiplication rule for "AND"

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