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GCE O-Level Maths Topics

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1Numbers and Relations

1.1Place value
1.2Comparing and ordering numbers
1.3Rounding numbers

2Number Theory

2.1Divisibility Rules
2.2Determining Common Factors
2.3Determining Common Multiples
2.4Introduction to exponents

3Adding and Subtracting Integers

3.1Introduction to integer addition
3.2Adding integers
3.3Introduction to integer subtraction
3.4Subtracting integers
3.5Application of integer operations

4Multiplying and Dividing Integers

4.1Understanding integer multiplication
4.2Multiplying integers
4.3Understanding integer division
4.4Dividing integers
4.5Applications of integer operations

5Operations with decimals

5.1Adding and subtracting decimals
5.2Multiplying decimals
5.3Dividing decimals
5.4Order of operations (BEDMAS)

6Adding and Subtracting Fractions

6.1Using models to add and subtract fractions
6.2Adding fractions with like denominators
6.3Subtracting fractions with like denominators
6.4Adding and subtracting fractions with unlike denominators
6.5Adding and subtracting mixed numbers

7Multiplying and Dividing Fractions

7.1Multiplying fractions and whole numbers (free lessons)
7.2Dividing fractions with whole numbers
7.3Multiplying proper fractions
7.4Multiplying improper fractions and mixed numbers
7.5Dividing fractions and mixed numbers
7.6Applications of fraction operations

8Ratios, Rates, and Proportions

8.1Ratios (free lessons)
8.2Rates
8.3Proportions

9Percents

9.1Representing percents (free lessons)
9.2Percents, fractions, and decimals
9.3Percent of a number
9.4Adding and multiplying percents
9.5Taxes, discounts, tips and more
9.6Simple interest

10Solving Linear Equations

10.1Solving linear equations using multiplication and division (free lessons)
10.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
10.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
10.4Solving linear equations with variables on both sides
10.5Solving literal equations

11Linear Inequalities

11.1Express linear inequalities graphically and algebraically (free lessons)
11.2Solving one-step linear inequalities (free lessons)
11.3Solving multi-step linear inequalities (free lessons)

12Measuring Systems

12.1Metric systems (free lessons)
12.2Imperial systems
12.3Conversions between metric and imperial systems
12.4Conversions involve squares and cubic

13Number Systems

13.1Understanding the number systems (free lessons)
13.2Prime factorisation
13.3Highest common factors (HCF)
13.4Least Common Multiple (LCM) (free lessons)
13.5Rational vs. Irrational numbers
13.6Converting repeating decimals to fractions

14Surds

14.1Square and square roots (free lessons)
14.2Cubic and cube roots
14.3Evaluating and simplifying radicals
14.4Converting radicals to mixed radicals
14.5Converting radicals to entire radicals (free lessons)
14.6Adding and subtracting surds
14.7Multiplying and dividing surds
14.8Rationalize the denominator

15Algebraic Expressions

15.1Equivalent algebraic expressions
15.2Adding and subtracting algebraic expressions
15.3Multiplying monomial by monomial
15.4Multiplying monomial by binomial
15.5Multiplying binomial by binomial (free lessons)
15.6Multiplying polynomial by polynomial
15.7Applications of polynomials

16Linear Functions

16.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
16.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
16.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
16.4Gradient intercept form: y = mx + b (free lessons)
16.5General form: Ax + By + C = 0 (free lessons)
16.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
16.7Rate of change
16.8Graphing linear functions using table of values
16.9Graphing linear functions using x- and y-intercepts (free lessons)
16.10Graphing from slope-intercept form y=mx+b
16.11Graphing linear functions using a single point and gradient
16.12Word problems of graphing linear functions
16.13Applications of linear relations

17Simultaneous Equations

17.1Determining number of solutions to linear equations (free lessons)
17.2Solving simultaneous linear equations by graphing
17.3Solving simultaneous linear equations by elimination
17.4Solving simultaneous linear equations by substitution
17.5Money related questions in linear equations (free lessons)
17.6Unknown number related questions in linear equations
17.7Distance and time related questions in linear equations
17.8Rectangular shape related questions in linear equations

18Factorising Quadratic Functions

18.1Factorise by taking out the greatest common factor (free lessons)
18.2Factorise by grouping
18.3Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
18.4Factorising difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
18.5Factorising trinomials
18.6Solving polynomials with unknown coefficients
18.7Solving polynomials with unknown constant terms

19Quadratic Functions

19.1Introduction to quadratic functions (free lessons)
19.2Transformations of quadratic functions
19.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
19.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
19.5Completing the square (free lessons)
19.6Converting from general to vertex form by completing the square
19.7Shortcut: Vertex formula (free lessons)
19.8Graphing quadratic functions: General form VS. Vertex form
19.9Finding the quadratic functions for given parabolas (free lessons)
19.10Applications of quadratic functions

20Solving Quadratic Equations

20.1Solving quadratic equations by factorising
20.2Solving quadratic equations by completing the square
20.3Using quadratic formula to solve quadratic equations
20.4The discriminant: Nature of roots of quadratic equations
20.5Applications of quadratic equations

21Algeraic Fractions

21.1Simplifying algebraic fractions and restrictions
21.2Adding and subtracting algebraic fractions (free lessons)
21.3Multiplying algebraic fractions
21.4Dividing algebraic fractions
21.5Solving equations with algebraic fractions
21.6Applications of equations with algebraic fractions
21.7Simplifying complex fractions
21.8Partial fraction decomposition

22Laws of Indices

22.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
22.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
22.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
22.4Negative indices
22.5Zero index: a0=1 a^0 = 1
22.6Rational indices

23Exponential Functions

23.1Solving exponential equations using laws of indices
23.2Graphing exponential functions

24Vectors

24.1Introduction to vectors
24.2Magnitude of a vector
24.3Direction angle of a vector
24.4Scalar multiplication
24.5Adding and subtracting vectors in component form
24.6Operations on vectors in magnitude and direction form

25Matrices

25.1Notation of matrices
25.2Adding and subtracting matrices
25.3Multiplying a matrix by a scalar
25.4Multiplying a matrix by another matrix

26Geometry and Measurement

26.1Parallel and perpendicular line segments
26.2Perpendicular bisectors
26.3Angle bisectors

27Scale Factors and Similarity

27.1Enlargements and reductions with scale factors (free lessons)
27.2Scale diagrams
27.3Similar triangles
27.4Similar polygons

28Congruent Triangles

28.1Classifying Triangles
28.2Congruence and Congruent Triangles
28.3Triangles Congruent by SSS Proofs
28.4Triangles Congruent by SAS and HL Proofs
28.5Triangles Congruent by ASA and AAS Proofs
28.6Isosceles and Equilateral Triangles

29Angles, Lines, and Transversals

29.1Pairs of lines and angles
29.2Parallel lines and transversals
29.3Parallel line proofs
29.4Perpendicular line proofs (free lessons)

30Circles

30.1Angles in a circle (free lessons)
30.2Chord properties
30.3Tangent properties
30.4Circle and circumference
30.5Arcs of a circle
30.6Areas and sectors of circles
30.7Inscribed quadrilaterals in circles
30.8Central and inscribed angles in circles

31Surface Area and Volume

31.1Surface area and volume of prisms (free lessons)
31.2Surface area and volume of pyramids
31.3Surface area and volume of cylinders
31.4Surface area and volume of cones (free lessons)
31.5Surface area and volume of spheres

32Trigonometry

32.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
32.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
32.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
32.4Combination of SohCahToa questions (free lessons)
32.5Solving expressions using 45-45-90 special right triangles (free lessons)
32.6Solving expressions using 30-60-90 special right triangles
32.7Word problems relating ladder in trigonometry
32.8Word problems relating guy wire in trigonometry
32.9Other word problems relating angles in trigonometry

33Angle Measure in Radian

33.1Converting between degrees and radians
33.2Radian measure and arc length

34Sine Rule and Cosine Rule

34.1Sine rule
34.2Cosine rule
34.3Sine rule and cosine rule word problems

35Set Theory

35.1Set notation
35.2Set builder notation

36Data and Graphs

36.1Reading and drawing histograms
36.2Reading and drawing line graphs
36.3Box-and-whisker plots and scatter plots
36.4Reading and drawing stem-and-leaf diagrams
36.5Reading and drawing Venn diagrams

37Representing Data

37.1Advantages and disadvantages of different graphs (free lessons)
37.2Misleading graphs
37.3Critiquing data presentation

38Statistics

38.1Median and mode
38.2Mean
38.3Range and outliers
38.4Application of averages
38.5Standard deviation and variance
38.6Z-score, quartiles, and percentiles

39Probability

39.1Determining probabilities using tree diagrams and tables (free lessons)
39.2Probability of independent events
39.3Frequency distribution and histograms
39.4Addition rule for "OR"
39.5Multiplication rule for "AND"
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