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GCE N(A)-Level Maths Topics

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1. Numbers and Relations

1.1

Place value

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Number Theory

2.1

Divisibility rules

2.2

Determining common factors

2.3

Determining common multiples

2.4

Introduction to exponents

3. Adding and Subtracting Integers

3.1

Introduction to integer addition

3.2

Adding integers

3.3

Introduction to integer subtraction

3.4

Subtracting integers

3.5

Application of integer operations

4. Multiplying and Dividing Integers

4.1

Understanding integer multiplication

4.2

Multiplying integers

4.3

Understanding integer division

4.4

Dividing integers

4.5

Applications of integer operations

5. Operations with decimals

5.1

Adding and subtracting decimals

5.2

Multiplying decimals

5.3

Dividing decimals

5.4

Order of operations (BEDMAS)

6. Adding and Subtracting Fractions

6.1

Using models to add and subtract fractions

6.2

Adding fractions with like denominators

6.3

Subtracting fractions with like denominators

6.4

Adding and subtracting fractions with unlike denominators

6.5

Adding and subtracting mixed numbers

7. Multiplying and Dividing Fractions

7.1

Multiplying fractions and whole numbers

7.2

Dividing fractions with whole numbers

7.3

Multiplying proper fractions

7.4

Multiplying improper fractions and mixed numbers

7.5

Dividing fractions and mixed numbers

7.6

Applications of fraction operations

8. Ratios, Rates, and Proportions

8.1

Ratios

8.2

Converting among ratios, fractions, and decimals

8.3

Rates

8.4

Proportions

9. Percents

9.1

Representing percents

9.2

Percents, fractions, and decimals

9.3

Percent of a number

9.4

Adding and multiplying percents

9.5

Taxes, discounts, tips and more

9.6

Simple interest

10. Scale Factors and Similarity

10.1

Enlargements and reductions with scale factors

10.2

Scale diagrams

10.3

Similar triangles

10.4

Similar polygons

11. Measuring Systems

11.1

Metric systems

11.2

Imperial systems

11.3

Conversions between metric and imperial systems

11.4

Conversions involve squares and cubic

12. Number Systems

12.1

Understanding the number systems

12.2

Prime factorisation

12.3

Highest common factors (HCF)

12.4

Least Common Multiple (LCM)

12.5

Rational vs. Irrational numbers

12.6

Converting repeating decimals to fractions

13. Solving Linear Equations

13.1

Solving linear equations using multiplication and division

13.2

Solving two-step linear equations: ax + b = c, x/a + b = c

13.3

Solving linear equations using distributive property: a(x + b) = c

13.4

Solving linear equations with variables on both sides

13.5

Solving literal equations

14. Linear Inequalities

14.1

Express linear inequalities graphically and algebraically

14.2

Solving one-step linear inequalities

14.3

Solving multi-step linear inequalities

15. Algebraic Expressions

15.1

Equivalent algebraic expressions

15.2

Adding and subtracting algebraic expressions

15.3

Multiplying monomial by monomial

15.4

Multiplying monomial by binomial

15.5

Multiplying binomial by binomial

15.6

Multiplying polynomial by polynomial

15.7

Applications of algebraic expressions

16. Linear Functions

16.1

Distance formula:

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

16.2

Midpoint formula:

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

16.3

Gradient equation:

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

16.4

Gradient intercept form: y = mx + b

16.5

General form: Ax + By + C = 0

16.6

Gradient-point form:

y - y_1 = m (x - x_1)

16.7

Rate of change

16.8

Graphing linear functions using table of values

16.9

Graphing linear functions using x- and y-intercepts

16.10

Graphing from slope-intercept form y=mx+b

16.11

Graphing linear functions using a single point and gradient

16.12

Word problems of graphing linear functions

16.13

Applications of linear relations

17. Simultaneous Equations

17.1

Determining number of solutions to linear equations

17.2

Solving simultaneous linear equations by graphing

17.3

Solving simultaneous linear equations by elimination

17.4

Solving simultaneous linear equations by substitution

17.5

17.6

Unknown number related questions in linear equations

17.7

Distance and time related questions in linear equations

17.8

Rectangular shape related questions in linear equations

18. Laws of Indices

18.1

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

18.2

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

18.3

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

18.4

Negative indices

18.5

Zero index: a^0 = 1

18.6

Rational indices

18.7

Standard form

19. Quadratic Functions

19.1

Factorise by taking out the greatest common factor

19.2

Factorise by grouping

19.3

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

19.4

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

19.5

Factorising trinomials

19.6

Solving polynomials with unknown coefficients

19.7

Solving polynomials with unknown constant terms

19.8

Properties and graphs of quadratic functions

20. Solving Quadratic Equations

20.1

Solving quadratic equations by factorising

20.2

Solving quadratic equations by completing the square

20.3

Using quadratic formula to solve quadratic equations

20.4

The discriminant: Nature of roots of quadratic equations

20.5

Applications of quadratic equations

21. Algebraic Fractions

21.1

Simplifying algebraic fractions and restrictions

21.2

Adding and subtracting algebraic fractions

21.3

Multiplying algebraic fractions

21.4

Dividing algebraic fractions

21.5

Solving equations with algebraic fractions

21.6

Applications of equations with algebraic fractions

21.7

Simplifying complex fractions

22. Exponential Functions

22.1

Solving exponential equations using exponent rules

22.2

Graphing exponential functions

23. Geometry and Measurement

23.1

Parallel and perpendicular line segments

23.2

Perpendicular bisectors

23.3

Angle bisectors

24. Congruent Triangles

24.1

Classifying Triangles

24.2

Congruence and Congruent Triangles

24.3

Triangles Congruent by SSS Proofs

24.4

Triangles Congruent by SAS and HL Proofs

24.5

Triangles Congruent by ASA and AAS Proofs

24.6

Isosceles and Equilateral Triangles

25. Angles, Lines, and Transversals

25.1

Pairs of lines and angles

25.2

Parallel lines and transversals

25.3

Parallel line proofs

25.4

Perpendicular line proofs

26. Circles

26.1

Angles in a circle

26.2

Chord properties

26.3

Tangent properties

26.4

Circle and circumference

26.5

Arcs of a circle

26.6

Areas and sectors of circles

26.7

Inscribed Angles and Proofs

26.8

Central and inscribed angles in circles

27. Surface Area and Volume

27.1

Surface area and volume of prisms

27.2

Surface area and volume of pyramids

27.3

Surface area and volume of cylinders

27.4

Surface area and volume of cones

27.5

Surface area and volume of spheres

28. Trigonometry

28.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

)

28.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

)

28.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

)

28.4

Combination of SohCahToa questions

28.5

Solving expressions using 45-45-90 special right triangles

28.6

Solving expressions using 30-60-90 special right triangles

28.7

Word problems relating ladder in trigonometry

28.8

Word problems relating guy wire in trigonometry

28.9

Other word problems relating angles in trigonometry

29. Angle Measure in Radian

29.1

Converting between degrees and radians

29.2

Radian measure and arc length

30. Sine Rule and Cosine Rule

30.1

Sine rule

30.2

Cosine rule

30.3

Sine rule and cosine rule word problems

31. Bearings

31.1

Introduction to bearings

31.2

Bearings and direction word problems

31.3

Angle of elevation and depression

32. Data and Graphs

32.1

Reading and drawing bar graphs

32.2

Reading and drawing histograms

32.3

Reading and drawing line graphs

32.4

Box-and-whisker plots and scatter plots

32.5

Reading and drawing stem-and-leaf diagrams

32.6

Reading and drawing Venn diagrams

32.7

Frequency tables and dot diagrams

32.8

Pie charts

33. Representing Data

33.1

Advantages and disadvantages of different graphs

33.2

Misleading graphs

33.3

Critiquing data presentation

34. Statistics

34.1

Median and mode

34.2

Mean

34.3

Range and outliers

34.4

Application of averages

34.5

Standard deviation, and variance

34.6

Z-score, quartiles, and percentiles

35. Probability

35.1

Determining probabilities using tree diagrams and tables

35.2

Probability of independent events

35.3

Frequency distribution and histograms

35.4

Addition rule for "OR"

35.5

Multiplication rule for "AND"

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