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GCE O-Level Maths Topics

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1. Numbers and Relations

1.1 Place value
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 Ratios
8.2 Rates
8.3 Proportions

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 Metric systems
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=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
17.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
17.3 Gradient equation: m=y2−y1x2−x1m = \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−y1=m(x−x1)y - y_1 = m (x - x_1)
17.7 Rate of change
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 Scale diagrams
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 = oh \frac{o}{h} )
33.2 Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
33.3 Use tangent ratio to calculate angles and sides (Tan = oa \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 Sine rule
35.2 Cosine rule
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 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 Reading and drawing stem-and-leaf diagrams
38.6 Reading and drawing Venn diagrams
38.7 Frequency tables and dot diagrams
38.8 Pie charts

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 Mean
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"

41 Chapters · 218 Topics · 1754 Videos

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