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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

5Direct and Inverse Proportion

5.1Direct variation

6Algebraic Expressions

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

7Surds

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

8Linear Functions

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

9Factorising Quadratic Functions

9.1Factorise by taking out the greatest common factor (free lessons)
9.2Factorise by grouping
9.3Factorising 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)
9.4Factorising difference of squares: x2−y2x^2 - y^2
9.5Factorising trinomials
9.6Solving polynomials with unknown coefficients
9.7Solving polynomials with unknown constant terms

10Quadratic Functions

10.1Introduction to quadratic functions (free lessons)
10.2Transformations of quadratic functions
10.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
10.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
10.5Completing the square (free lessons)
10.6Converting from general to vertex form by completing the square
10.7Shortcut: Vertex formula (free lessons)
10.8Graphing quadratic functions: General form VS. Vertex form
10.9Finding the quadratic functions for given parabolas (free lessons)
10.10Applications of quadratic functions

11Quadratic Equations and Inequalities

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

12Algebraic Fractions

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

13Simultaneous Equations

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

14Inequalities in Two Variables

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

15Laws of Indices

15.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
15.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
15.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
15.4Negative indices
15.5Zero index: a0=1 a^0 = 1
15.6Rational indices
15.7Standard form

16Polynomial Functions

16.1Polynomial long division (free lessons)
16.2Polynomial synthetic division
16.3Remainder theorem
16.4Factor theorem

17Binomial expansions

17.1Factorial notation
17.2Binomial theorem

18Exponential Functions

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

19Logarithms

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

20Modulus Functions

20.1Modulus functions (free lessons)
20.2Solving modulus equations

21Vectors

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

22Matrices

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

23Trigonometric Ratios and Angle Measure

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

24Sine Rule and Cosine Rule

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

25Bearings

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

26Graphing Trigonometric Functions

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

27Applications of Trigonometric Functions

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

28Trigonometric Identities

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

29Solving Trigonometric Equations

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

30Inverse Trigonometric Functions

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

31Angles, Lines, and Transversals

31.1Pairs of lines and angles
31.2Parallel lines and transversals
31.3Parallel line proofs
31.4Perpendicular line proofs (free lessons)

32Scale Factors and Similarity

32.1Enlargements and reductions with scale factors (free lessons)
32.2Scale diagrams
32.3Similar triangles
32.4Similar polygons

33Congruent Triangles

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

34Circles

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

35Surface Area and Volume

35.1Surface area and volume of prisms (free lessons)
35.2Surface area and volume of pyramids
35.3Surface area and volume of cylinders
35.4Surface area and volume of cones (free lessons)
35.5Surface area and volume of spheres

36Conics

36.1Conics - Parabola
36.2Conics - Circle

37Set Theory

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

38Data and Graphs

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

39Statistics

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

40Probability

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

41Differentiation

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

42Integration

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