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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

15Direct and Inverse Proportion

15.1Direct variation

16Algebraic Expressions

16.1Equivalent algebraic expressions
16.2Adding and subtracting algebraic expressions
16.3Multiplying monomial by monomial
16.4Multiplying monomial by binomial
16.5Multiplying binomial by binomial (free lessons)
16.6Multiplying polynomial by polynomial
16.7Applications of polynomials

17Linear Functions

17.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
17.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
17.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
17.4Gradient intercept form: y = mx + b (free lessons)
17.5General form: Ax + By + C = 0 (free lessons)
17.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
17.7Rate of change
17.8Graphing linear functions using table of values
17.9Graphing linear functions using x- and y-intercepts (free lessons)
17.10Graphing from slope-intercept form y=mx+b
17.11Graphing linear functions using a single point and gradient
17.12Word problems of graphing linear functions
17.13Applications of linear relations

18Simultaneous Equations

18.1Determining number of solutions to linear equations (free lessons)
18.2Solving simultaneous linear equations by graphing
18.3Solving simultaneous linear equations by elimination
18.4Solving simultaneous linear equations by substitution
18.5Money related questions in linear equations (free lessons)
18.6Unknown number related questions in linear equations
18.7Distance and time related questions in linear equations
18.8Rectangular shape related questions in linear equations

19Factorising Quadratic Functions

19.1Factorise by taking out the greatest common factor (free lessons)
19.2Factorise by grouping
19.3Factorising 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)
19.4Factorising difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
19.5Factorising trinomials
19.6Solving polynomials with unknown coefficients
19.7Solving polynomials with unknown constant terms

20Quadratic Functions

20.1Introduction to quadratic functions (free lessons)
20.2Transformations of quadratic functions
20.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
20.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
20.5Completing the square (free lessons)
20.6Converting from general to vertex form by completing the square
20.7Shortcut: Vertex formula (free lessons)
20.8Graphing quadratic functions: General form VS. Vertex form
20.9Finding the quadratic functions for given parabolas (free lessons)
20.10Applications of quadratic functions

21Solving Quadratic Equations

21.1Solving quadratic equations by factorising
21.2Solving quadratic equations by completing the square
21.3Using quadratic formula to solve quadratic equations
21.4The discriminant: Nature of roots of quadratic equations
21.5Applications of quadratic equations

22Algeraic Fractions

22.1Simplifying algebraic fractions and restrictions
22.2Adding and subtracting algebraic fractions (free lessons)
22.3Multiplying algebraic fractions
22.4Dividing algebraic fractions
22.5Solving equations with algebraic fractions
22.6Applications of equations with algebraic fractions
22.7Simplifying complex fractions
22.8Partial fraction decomposition

23Laws of Indices

23.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
23.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
23.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
23.4Negative indices
23.5Zero index: a0=1 a^0 = 1
23.6Rational indices

24Exponential Functions

24.1Solving exponential equations using laws of indices
24.2Graphing exponential functions

25Vectors

25.1Introduction to vectors
25.2Magnitude of a vector
25.3Direction angle of a vector
25.4Scalar multiplication
25.5Adding and subtracting vectors in component form
25.6Operations on vectors in magnitude and direction form
25.7Word problems on vectors

26Matrices

26.1Notation of matrices
26.2Adding and subtracting matrices
26.3Multiplying a matrix by a scalar
26.4Multiplying a matrix by another matrix

27Geometry and Measurement

27.1Parallel and perpendicular line segments
27.2Perpendicular bisectors
27.3Angle bisectors

28Scale Factors and Similarity

28.1Enlargements and reductions with scale factors (free lessons)
28.2Scale diagrams
28.3Similar triangles
28.4Similar polygons

29Congruent Triangles

29.1Classifying Triangles
29.2Congruence and Congruent Triangles
29.3Triangles Congruent by SSS Proofs
29.4Triangles Congruent by SAS and HL Proofs
29.5Triangles Congruent by ASA and AAS Proofs
29.6Isosceles and Equilateral Triangles

30Angles, Lines, and Transversals

30.1Pairs of lines and angles
30.2Parallel lines and transversals
30.3Parallel line proofs
30.4Perpendicular line proofs (free lessons)

31Circles

31.1Angles in a circle (free lessons)
31.2Chord properties
31.3Tangent properties
31.4Circle and circumference
31.5Arcs of a circle
31.6Areas and sectors of circles
31.7Inscribed quadrilaterals in circles
31.8Central and inscribed angles in circles

32Surface Area and Volume

32.1Surface area and volume of prisms (free lessons)
32.2Surface area and volume of pyramids
32.3Surface area and volume of cylinders
32.4Surface area and volume of cones (free lessons)
32.5Surface area and volume of spheres

33Trigonometry

33.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
33.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
33.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
33.4Combination of SohCahToa questions (free lessons)
33.5Solving expressions using 45-45-90 special right triangles (free lessons)
33.6Solving expressions using 30-60-90 special right triangles
33.7Word problems relating ladder in trigonometry
33.8Word problems relating guy wire in trigonometry
33.9Other word problems relating angles in trigonometry

34Angle Measure in Radian

34.1Converting between degrees and radians
34.2Radian measure and arc length

35Sine Rule and Cosine Rule

35.1Sine rule
35.2Cosine rule
35.3Sine rule and cosine rule word problems

36Bearings

36.1Introduction to bearings
36.2Bearings and direction word problems
36.3Angle of elevation and depression

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
38.5Reading and drawing stem-and-leaf diagrams
38.6Reading and drawing Venn diagrams
38.7Frequency tables and dot diagrams
38.8Pie charts

39Representing Data

39.1Advantages and disadvantages of different graphs (free lessons)
39.2Misleading graphs
39.3Critiquing data presentation

40Statistics

40.1Median and mode
40.2Mean
40.3Range and outliers
40.4Application of averages
40.5Standard deviation and variance
40.6Z-score, quartiles, and percentiles

41Probability

41.1Determining probabilities using tree diagrams and tables (free lessons)
41.2Probability of independent events
41.3Frequency distribution and histograms
41.4Addition rule for "OR"
41.5Multiplication rule for "AND"
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