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GCE O-Level A Maths Topics

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1Solving Linear Equations

1.1Solving linear equations using multiplication and division (free lessons)
1.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
1.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
1.4Solving linear equations with variables on both sides
1.5Solving literal equations

2Linear Inequalities

2.1Express linear inequalities graphically and algebraically (free lessons)
2.2Solving one-step linear inequalities (free lessons)
2.3Solving multi-step linear inequalities (free lessons)

3Measuring Systems

3.1Metric systems (free lessons)
3.2Imperial systems
3.3Conversions between metric and imperial systems
3.4Conversions involve squares and cubic

4Number Systems

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

5Algebraic Expressions

5.1Equivalent algebraic expressions
5.2Adding and subtracting algebraic expressions
5.3Multiplying monomial by monomial
5.4Multiplying monomial by binomial
5.5Multiplying binomial by binomial (free lessons)
5.6Multiplying polynomial by polynomial
5.7Applications of polynomials

6Surds

6.1Square and square roots (free lessons)
6.2Cubic and cube roots
6.3Operations with surds (free lessons)
6.4Conversion between entire radicals and mixed radicals
6.5Adding and subtracting surds (free lessons)
6.6Multiplying surds
6.7Rationalize the denominator
6.8Solving equations with surds

7Linear Functions

7.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
7.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
7.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
7.4Gradient intercept form: y = mx + b (free lessons)
7.5General form: Ax + By + C = 0 (free lessons)
7.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
7.7Rate of change
7.8Graphing linear functions using table of values
7.9Graphing linear functions using x- and y-intercepts (free lessons)
7.10Graphing from slope-intercept form y=mx+b
7.11Graphing linear functions using a single point and gradient
7.12Word problems of graphing linear functions
7.13Applications of linear relations

8Factorising Quadratic Functions

8.1Factorise by taking out the greatest common factor (free lessons)
8.2Factorise by grouping
8.3Factorising 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)
8.4Factorising difference of squares: x2−y2x^2 - y^2
8.5Factorising trinomials
8.6Solving polynomials with unknown coefficients
8.7Solving polynomials with unknown constant terms

9Quadratic Functions

9.1Introduction to quadratic functions (free lessons)
9.2Transformations of quadratic functions
9.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
9.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
9.5Completing the square (free lessons)
9.6Converting from general to vertex form by completing the square
9.7Shortcut: Vertex formula (free lessons)
9.8Graphing quadratic functions: General form VS. Vertex form
9.9Finding the quadratic functions for given parabolas (free lessons)
9.10Applications of quadratic functions

10Quadratic Equations and Inequalities

10.1Solving quadratic equations by factoring
10.2Solving quadratic equations by completing the square
10.3Using quadratic formula to solve quadratic equations
10.4Nature of roots of quadratic equations: The discriminant
10.5Applications of quadratic equations
10.6Solving quadratic inequalities

11Algebraic Fractions

11.1Simplifying algebraic fractions and restrictions
11.2Adding and subtracting algebraic fractions (free lessons)
11.3Multiplying algebraic fractions
11.4Dividing algebraic fractions
11.5Solving equations with algebraic fractions
11.6Applications of equations with algebraic fractions
11.7Simplifying complex fractions
11.8Partial fraction decomposition

12Simultaneous Equations

12.1Determining number of solutions to linear equations (free lessons)
12.2Solving simultaneous linear equations by graphing
12.3Solving simultaneous linear equations by elimination
12.4Solving simultaneous linear equations by substitution
12.5Money related questions in linear equations (free lessons)
12.6Unknown number related questions in linear equations
12.7Distance and time related questions in linear equations
12.8Rectangular shape related questions in linear equations
12.9Simultaneous linear equations
12.10Simultaneous linear-quadratic equations (free lessons)
12.11Simultaneous quadratic-quadratic equations

13Inequalities in Two Variables

13.1Graphing linear inequalities in two variables (free lessons)
13.2Graphing systems of linear inequalities (free lessons)
13.3Graphing quadratic inequalities in two variables
13.4Graphing systems of quadratic inequalities
13.5Applications of inequalities
13.6What is linear programming?
13.7Linear programming word problems

14Laws of Indices

14.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
14.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
14.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
14.4Negative indices
14.5Zero index: a0=1 a^0 = 1
14.6Rational indices
14.7Standard form

15Polynomial Functions

15.1Polynomial long division (free lessons)
15.2Polynomial synthetic division
15.3Remainder theorem
15.4Factor theorem

16Binomial expansions

16.1Factorial notation
16.2Binomial theorem

17Exponential Functions

17.1Solving exponential equations using laws of indices
17.2Graphing exponential functions
17.3Graphing transformations of exponential functions
17.4Finding an exponential function given its graph

18Logarithms

18.1What is a logarithm?
18.2Converting from logarithmic form to exponential form (free lessons)
18.3Evaluating logarithms without a calculator
18.4Common logarithms
18.5Natural log: ln
18.6Evaluating logarithms using change-of-base formula
18.7Converting from exponential form to logarithmic form (free lessons)
18.8Solving exponential equations with logarithms
18.9Product rule of logarithms (free lessons)
18.10Quotient rule of logarithms
18.11Combining product rule and quotient rule in logarithms
18.12Evaluating logarithms using logarithm rules
18.13Solving logarithmic equations (free lessons)
18.14Graphing logarithmic functions
18.15Finding a logarithmic function given its graph

19Modulus Functions

19.1Modulus functions (free lessons)
19.2Solving modulus equations

20Vectors

20.1Introduction to vectors
20.2Magnitude of a vector
20.3Direction angle of a vector
20.4Scalar multiplication
20.5Adding and subtracting vectors in component form
20.6Operations on vectors in magnitude and direction form

21Matrices

21.1Notation of matrices
21.2Adding and subtracting matrices
21.3Multiplying a matrix by a scalar
21.4Multiplying a matrix by another matrix

22Trigonometric Ratios and Angle Measure

22.1Angle in standard position
22.2Coterminal angles (free lessons)
22.3Reference angle
22.4Find the exact value of trigonometric ratios
22.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
22.6Unit circle (free lessons)
22.7Converting between degrees and radians
22.8Trigonometric ratios of angles in radians
22.9Radian measure and arc length

23Sine Rule and Cosine Rule

23.1Sine rule
23.2Cosine rule
23.3Sine rule and cosine rule word problems

24Graphing Trigonometric Functions

24.1Sine graph: y = sin x
24.2Cosine graph: y = cos x
24.3Tangent graph: y = tan x
24.4Cotangent graph: y = cot x
24.5Secant graph: y = sec x
24.6Cosecant graph: y = csc x
24.7Graphing transformations of trigonometric functions
24.8Determining trigonometric functions given their graphs

25Applications of Trigonometric Functions

25.1Ferris wheel trig problems
25.2Tides and water depth trig problems
25.3Spring (simple harmonic motion) trig problems

26Trigonometric Identities

26.1Quotient identities and reciprocal identities (free lessons)
26.2Pythagorean identities
26.3Sum and difference identities
26.4Cofunction identities
26.5Double-angle identities (free lessons)

27Solving Trigonometric Equations

27.1Solving first degree trigonometric equations (free lessons)
27.2Determining non-permissible values for trig expressions
27.3Solving second degree trigonometric equations
27.4Solving trigonometric equations involving multiple angles (free lessons)
27.5Solving trigonometric equations using pythagorean identities
27.6Solving trigonometric equations using sum and difference identities
27.7Solving trigonometric equations using double-angle identities

28Inverse Trigonometric Functions

28.1Finding inverse trigonometric function from its graph
28.2Evaluating inverse trigonometric functions
28.3Finding inverse reciprocal trigonometric function from its graph
28.4Inverse reciprocal trigonometric function: finding the exact value

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)

30Scale Factors and Similarity

30.1Enlargements and reductions with scale factors (free lessons)
30.2Scale diagrams
30.3Similar triangles
30.4Similar polygons

31Congruent Triangles

31.1Congruence and congruent triangles
31.2Triangles congruent by SSS proofs
31.3Triangles congruent by SAS and HL proofs
31.4Triangles congruent by ASA and AAS proofs

32Circles

32.1Angles in a circle (free lessons)
32.2Chord properties
32.3Tangent properties
32.4Circle and circumference
32.5Arcs of a circle
32.6Areas and sectors of circles
32.7Inscribed quadrilaterals in circles
32.8Central and inscribed angles in circles

33Surface Area and Volume

33.1Surface area and volume of prisms (free lessons)
33.2Surface area and volume of pyramids
33.3Surface area and volume of cylinders
33.4Surface area and volume of cones (free lessons)
33.5Surface area and volume of spheres

34Conics

34.1Conics - Parabola
34.2Conics - Circle

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
36.4Stem-and-leaf plots
36.5Reading and drawing Venn diagrams

37Statistics

37.1Median and mode
37.2Mean
37.3Range and outliers
37.4Application of averages
37.5Standard deviation, and variance
37.6Z-score, quartiles, and percentiles

38Probability

38.1Determining probabilities using tree diagrams and tables (free lessons)
38.2Probability of independent events
38.3Frequency distribution and histograms
38.4Addition rule for "OR"
38.5Multiplication rule for "AND"

39Differentiation

39.1Power rule
39.2Slope and equation of tangent line
39.3Chain rule
39.4Derivative of trigonometric functions
39.5Derivative of exponential functions
39.6Product rule
39.7Quotient rule
39.8Derivative of logarithmic functions
39.9Higher order derivatives
39.10Rectilinear Motion: Derivative
39.11Critical number & maximum and minimum values

40Integration

40.1Antiderivatives
40.2Definite integral
40.3Integration by parts
40.4Trigonometric substitution
40.5Integration of rational functions by partial fractions
40.6Areas between curves
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