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GCE N(A)-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)
8.2Converting among ratios, fractions, and decimals
8.3Rates
8.4Proportions

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

10Scale Factors and Similarity

10.1Enlargements and reductions with scale factors (free lessons)
10.2Scale diagrams
10.3Similar triangles
10.4Similar polygons

11Measuring Systems

11.1Metric systems (free lessons)
11.2Imperial systems
11.3Conversions between metric and imperial systems
11.4Conversions involve squares and cubic

12Number Systems

12.1Understanding the number systems (free lessons)
12.2Prime factorisation
12.3Highest common factors (HCF)
12.4Least Common Multiple (LCM) (free lessons)
12.5Rational vs. Irrational numbers
12.6Converting repeating decimals to fractions

13Solving Linear Equations

13.1Solving linear equations using multiplication and division (free lessons)
13.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
13.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c (free lessons)
13.4Solving linear equations with variables on both sides
13.5Solving literal equations

14Linear Inequalities

14.1Express linear inequalities graphically and algebraically (free lessons)
14.2Solving one-step linear inequalities (free lessons)
14.3Solving multi-step linear inequalities (free lessons)

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 algebraic expressions

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

18Laws of Indices

18.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
18.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
18.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
18.4Negative indices
18.5Zero index: a0=1 a^0 = 1
18.6Rational indices
18.7Standard form

19Quadratic 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: x2−y2x^2 - y^2
19.5Factorising trinomials
19.6Solving polynomials with unknown coefficients
19.7Solving polynomials with unknown constant terms
19.8Properties and graphs of quadratic functions (free lessons)

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

21Algebraic 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

22Exponential Functions

22.1Solving exponential equations using exponent rules
22.2Graphing exponential functions

23Geometry and Measurement

23.1Parallel and perpendicular line segments
23.2Perpendicular bisectors
23.3Angle bisectors

24Congruent Triangles

24.1Classifying Triangles
24.2Congruence and Congruent Triangles
24.3Triangles Congruent by SSS Proofs
24.4Triangles Congruent by SAS and HL Proofs
24.5Triangles Congruent by ASA and AAS Proofs
24.6Isosceles and Equilateral Triangles

25Angles, Lines, and Transversals

25.1Pairs of lines and angles
25.2Parallel lines and transversals
25.3Parallel line proofs
25.4Perpendicular line proofs (free lessons)

26Circles

26.1Angles in a circle (free lessons)
26.2Chord properties
26.3Tangent properties
26.4Circle and circumference
26.5Arcs of a circle
26.6Areas and sectors of circles
26.7Inscribed Angles and Proofs
26.8Central and inscribed angles in circles

27Surface Area and Volume

27.1Surface area and volume of prisms (free lessons)
27.2Surface area and volume of pyramids
27.3Surface area and volume of cylinders
27.4Surface area and volume of cones (free lessons)
27.5Surface area and volume of spheres

28Trigonometry

28.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} ) (free lessons)
28.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
28.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
28.4Combination of SohCahToa questions (free lessons)
28.5Solving expressions using 45-45-90 special right triangles (free lessons)
28.6Solving expressions using 30-60-90 special right triangles
28.7Word problems relating ladder in trigonometry
28.8Word problems relating guy wire in trigonometry
28.9Other word problems relating angles in trigonometry

29Angle Measure in Radian

29.1Converting between degrees and radians
29.2Radian measure and arc length

30Sine Rule and Cosine Rule

30.1Sine rule
30.2Cosine rule
30.3Sine rule and cosine rule word problems

31Bearings

31.1Introduction to bearings
31.2Bearings and direction word problems
31.3Angle of elevation and depression

32Data and Graphs

32.1Reading and drawing bar graphs
32.2Reading and drawing histograms
32.3Reading and drawing line graphs
32.4Box-and-whisker plots and scatter plots
32.5Reading and drawing stem-and-leaf diagrams
32.6Reading and drawing Venn diagrams
32.7Frequency tables and dot diagrams
32.8Pie charts

33Representing Data

33.1Advantages and disadvantages of different graphs (free lessons)
33.2Misleading graphs
33.3Critiquing data presentation

34Statistics

34.1Median and mode
34.2Mean
34.3Range and outliers
34.4Application of averages
34.5Standard deviation, and variance
34.6Z-score, quartiles, and percentiles

35Probability

35.1Determining probabilities using tree diagrams and tables (free lessons)
35.2Probability of independent events
35.3Frequency distribution and histograms
35.4Addition rule for "OR"
35.5Multiplication rule for "AND"
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