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GCE N(A)-Level A Maths Topics

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1. Linear Inequalities

1.1

Express linear inequalities graphically and algebraically

1.2

Solving one-step linear inequalities

1.3

Solving multi-step linear inequalities

2. Algebraic Expressions

2.1

Equivalent algebraic expressions

2.2

Adding and subtracting algebraic expressions

2.3

Multiplying monomial by monomial

2.4

Multiplying monomial by binomial

2.5

Multiplying binomial by binomial

2.6

Multiplying polynomial by polynomial

2.7

Applications of algebraic expressions

3. Linear Functions

3.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

3.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

3.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

3.4

Gradient intercept form: y = mx + b

3.5

General form: Ax + By + C = 0

3.6

Gradient-point form:

y - y_1 = m (x - x_1)

3.7

3.8

Graphing linear functions using table of values

3.9

Graphing linear functions using x- and y-intercepts

3.10

Graphing from slope-intercept form y=mx+b

3.11

Graphing linear functions using a single point and gradient

3.12

Word problems of graphing linear functions

3.13

Applications of linear relations

4. Simultaneous Equations

4.1

Determining number of solutions to linear equations

4.2

Solving simultaneous linear equations by graphing

4.3

Solving simultaneous linear equations by elimination

4.4

Solving simultaneous linear equations by substitution

4.5

Money related questions in linear equations

4.6

Unknown number related questions in linear equations

4.7

Distance and time related questions in linear equations

4.8

Rectangular shape related questions in linear equations

5. Factorisation

5.1

Factorise by taking out the greatest common factor

5.2

Factorise by grouping

5.3

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

5.4

Factorising difference of squares: x^2 - y^2

5.5

Factorise trinomials

5.6

Solving polynomials with unknown coefficients

5.7

Solving polynomials with unknown constant terms

5.8

Factorising difference of cubes:

a^3-b^3

5.9

Factorising sum of cubes:

a^3+b^3

6. Quadratic Functions

6.1

Introduction to quadratic functions

6.2

Transformations of quadratic functions

6.3

Quadratic function in general form: y = ax^2 + bx + c

6.4

Quadratic function in vertex form: y = a(x-p)^2 + q

6.5

Completing the square

6.6

Converting from general to vertex form by completing the square

6.7

Shortcut: Vertex formula

6.8

Graphing quadratic functions: General form VS. Vertex form

6.9

Finding the quadratic functions for given parabolas

6.10

Applications of quadratic functions

7. Quadratic Equations and Inequalities

7.1

Solving quadratic equations by factoring

7.2

Solving quadratic equations by completing the square

7.3

Using quadratic formula to solve quadratic equations

7.4

Nature of roots of quadratic equations: The discriminant

7.5

Applications of quadratic equations

7.6

Solving quadratic inequalities

8. Surds

8.1

Square and square roots

8.2

Cubic and cube roots

8.3

Operations with surds

8.4

Conversion between entire radicals and mixed radicals

8.5

Adding and subtracting surds

8.6

Multiplying surds

8.7

Rationalize the denominator

8.8

Solving equations with surds

9. Solving Simultaneous Equations

9.1

System of linear equations

9.2

System of linear-quadratic equations

9.3

System of quadratic-quadratic equations

9.4

Solving 3 variable systems of equations by substitution

9.5

Solving 3 variable systems of equations by elimination

9.6

Solving 3 variable systems of equations with no solution, infinite solutions

9.7

Word problems relating 3 variable systems of equations

10. Laws of Indices

10.1

Indices: Product rule (a^x)(a^y) = a^(x+y)

10.2

Indices: Division rule (a^x / a^y) = a^(x-y)

10.3

Indices: Power rule (a^x)^y = a^(x * y)

10.4

Negative indices

10.5

Zero index: a^0 = 1

10.6

Rational indices

10.7

11. Algebraic Fractions

11.1

Simplifying algebraic fractions and restrictions

11.2

Adding and subtracting algebraic fractions

11.3

Multiplying algebraic fractions

11.4

Dividing algebraic fractions

11.5

Solving equations with algebraic fractions

11.6

Applications of equations with algebraic fractions

11.7

Simplifying complex fractions

12. Exponential Functions

12.1

Solving exponential equations using laws of indices

12.2

Graphing exponential functions

12.3

Graphing transformations of exponential functions

12.4

Finding an exponential function given its graph

13. Binomial expansions

13.1

Factorial notation

13.2

Binomial theorem

14. Geometry and Measurement

14.1

Parallel and perpendicular line segments

14.2

Perpendicular bisectors

14.3

Angle bisectors

15. Congruent Triangles

15.1

Classifying Triangles

15.2

Congruence and Congruent Triangles

15.3

Triangles Congruent by SSS Proofs

15.4

Triangles Congruent by SAS and HL Proofs

15.5

Triangles Congruent by ASA and AAS Proofs

15.6

Isosceles and Equilateral Triangles

16. Angles, Lines, and Transversals

16.1

Pairs of lines and angles

16.2

Parallel lines and transversals

16.3

Parallel line proofs

16.4

Perpendicular line proofs

17. Circles

17.1

Angles in a circle

17.2

Chord properties

17.3

Tangent properties

17.4

Circle and circumference

17.5

Arcs of a circle

17.6

Areas and sectors of circles

17.7

Inscribed quadrilaterals in circles

17.8

Central and inscribed angles in circles

18. Surface Area and Volume

18.1

Surface area and volume of prisms

18.2

Surface area and volume of pyramids

18.3

Surface area and volume of cylinders

18.4

Surface area and volume of cones

18.5

Surface area and volume of spheres

19. Conics

19.1

Conics - Parabola

19.2

Conics - Circle

20. Trigonometric Ratios and Angle Measure

20.1

Angle in standard position

20.2

Coterminal angles

20.3

Reference angle

20.4

Find the exact value of trigonometric ratios

20.5

ASTC rule in trigonometry (All Students Take Calculus)

20.6

20.7

Converting between degrees and radians

20.8

Trigonometric ratios of angles in radians

20.9

Radian measure and arc length

21. Sine Rule and Cosine Rule

21.1

21.2

21.3

Sine rule and cosine rule word problems

22. Bearings

22.1

Introduction to bearings

22.2

Bearings and direction word problems

22.3

Angle of elevation and depression

23. Graphing Trigonometric Functions

23.1

Sine graph: y = sin x

23.2

Cosine graph: y = cos x

23.3

Tangent graph: y = tan x

23.4

Cotangent graph: y = cot x

23.5

Secant graph: y = sec x

23.6

Cosecant graph: y = csc x

23.7

Graphing transformations of trigonometric functions

23.8

Determining trigonometric functions given their graphs

24. Applications of Trigonometric Functions

24.1

Ferris wheel trig problems

24.2

Tides and water depth trig problems

24.3

Spring (simple harmonic motion) trig problems

25. Trigonometric Identities

25.1

Quotient identities and reciprocal identities

25.2

Pythagorean identities

25.3

Sum and difference identities

25.4

Cofunction identities

25.5

Double-angle identities

26. Solving Trigonometric Equations

26.1

Solving first degree trigonometric equations

26.2

Determining non-permissible values for trig expressions

26.3

Solving second degree trigonometric equations

26.4

Solving trigonometric equations involving multiple angles

26.5

Solving trigonometric equations using pythagorean identities

26.6

Solving trigonometric equations using sum and difference identities

26.7

Solving trigonometric equations using double-angle identities

27. Inverse Trigonometric Functions

27.1

Finding inverse trigonometric function from its graph

27.2

Evaluating inverse trigonometric functions

27.3

Finding inverse reciprocal trigonometric function from its graph

27.4

Inverse reciprocal trigonometric function: finding the exact value

28. Data and Graphs

28.1

Reading and drawing bar graphs

28.2

Reading and drawing histograms

28.3

Reading and drawing line graphs

28.4

Box-and-whisker plots and scatter plots

28.5

Reading and drawing stem-and-leaf diagrams

28.6

Reading and drawing Venn diagrams

28.7

Frequency tables and dot diagrams

28.8

29. Representing Data

29.1

Advantages and disadvantages of different graphs

29.2

Misleading graphs

29.3

Critiquing data presentation

30. Statistics

30.1

Median and mode

30.2

30.3

Range and outliers

30.4

Application of averages

30.5

Standard deviation, and variance

30.6

Z-score, quartiles, and percentiles

31. Probability

31.1

Determining probabilities using tree diagrams and tables

31.2

Probability of independent events

31.3

Frequency distribution and histograms

31.4

Addition rule for "OR"

31.5

Multiplication rule for "AND"

32. Differentiation

32.1

32.2

Slope and equation of tangent line

32.3

32.4

32.5

32.6

Higher order derivatives

32.7

Critical number & maximum and minimum values

33. Integration

33.1

Antiderivatives

33.2

Definite integral

33.3

Integration by parts

33.4

Integration of rational functions by partial fractions

33.5

Areas between curves

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