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Secondary 4 Maths Topics

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1. Number System and Radicals

1.1

Understanding the number systems

1.2

Prime factorization

1.3

Greatest Common Factors (GCF)

1.4

Least Common Multiple (LCM)

1.5

Rational vs. Irrational numbers

1.6

Converting repeating decimals to fractions

2. Rational Numbers

2.1

Comparing and ordering rational numbers

2.2

Solving problems with rational numbers in decimal form

2.3

Solving problems with rational numbers in fraction form

2.4

Determine square roots of rational numbers

3. Solving Linear Equations

3.1

Solving linear equations using multiplication and division

3.2

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

3.3

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

3.4

Solving linear equations with variables on both sides

3.5

Solving literal equations

4. Linear Inequalities

4.1

Express linear inequalities graphically and algebraically

4.2

Solving one-step linear inequalities

4.3

Solving multi-step linear inequalities

4.4

Compound inequalities

5. Introduction to Relations and Functions

5.1

Relationship between two variables

5.2

Understand relations between x- and y-intercepts

5.3

Domain and range of a function

5.4

Identifying functions

5.5

Function notation

6. Linear Functions

6.1

Distance formula:

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

6.2

Midpoint formula:

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

6.3

Gradient equation:

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

6.4

Gradient intercept form: y = mx + b

6.5

General form: Ax + By + C = 0

6.6

Gradient-point form:

y - y_1 = m (x - x_1)

6.7

6.8

Graphing linear functions using table of values

6.9

Graphing linear functions using x- and y-intercepts

6.10

Graphing from gradient-intercept form y=mx+b

6.11

Graphing linear functions using a single point and gradient

6.12

Word problems of graphing linear functions

6.13

Parallel and perpendicular lines in linear functions

6.14

Applications of linear relations

7. Linear Equations (Advanced)

7.1

Introduction to linear equations

7.2

Introduction to nonlinear equations

7.3

Special case of linear equations: Horizontal lines

7.4

Special case of linear equations: Vertical lines

7.5

Parallel line equation

7.6

Perpendicular line equation

7.7

Combination of both parallel and perpendicular line equations

7.8

Applications of linear equations

8. Solving Simultaneous Equations

8.1

Determining number of solutions to linear equations

8.2

Solving simultaneous equations by graphing

8.3

Solving simultaneous equations by elimination

8.4

Solving simultaneous equations by substitution

8.5

Money related questions in linear equations

8.6

Unknown number related questions in linear equations

8.7

Distance and time related questions in linear equations

8.8

Rectangular shape related questions in linear equations

9. Exponents

9.1

Product rule of exponents

9.2

Quotient rule of exponents

9.3

Power of a product rule

9.4

Power of a quotient rule

9.5

Power of a power rule

9.6

Negative exponent rule

9.7

Combining the exponent rules

9.8

Scientific notation

9.9

Convert between radicals and rational exponents

9.10

Solving for exponents

10. Exponential Functions

10.1

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

10.2

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

10.3

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

10.4

Exponents: Negative exponents

10.5

Exponents: Zero exponent: a^0 = 1

10.6

Exponents: Rational exponents

10.7

Graphing exponential functions

10.8

Graphing transformations of exponential functions

10.9

Finding an exponential function given its graph

11. Exponential Growth and Decay

11.1

Exponential growth and decay by a factor

11.2

Exponential decay: Half-life

11.3

Exponential growth and decay by percentage

11.4

Continuous growth and decay

12. Operations of Polynomials

12.1

What is a polynomial?

12.2

Polynomial components

12.3

Multiplying monomial by monomial

12.4

Multiplying monomial by binomial

12.5

Multiplying binomial by binomial

12.6

Multiplying polynomial by polynomial

12.7

Applications of polynomials

12.8

Pascal's triangle

12.9

Binomial theorem

13. Factorising Quadratic Equations

13.1

Factorise by taking out the greatest common factor

13.2

Factorise by grouping

13.3

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

13.4

Factorising trinomials

13.5

Factoring difference of cubes

13.6

Factoring sum of cubes

14. Quadratic Functions

14.1

Characteristics of quadratic functions

14.2

Transformations of quadratic functions

14.3

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

14.4

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

14.5

Completing the square

14.6

Converting from general to vertex form by completing the square

14.7

Shortcut: Vertex formula

14.8

Graphing parabolas for given quadratic functions

14.9

Finding the quadratic functions for given parabolas

14.10

Applications of quadratic functions

15. Quadratic Equations and Inequalities

15.1

Solving quadratic equations by factorising

15.2

Solving quadratic equations by completing the square

15.3

Using quadratic formula to solve quadratic equations

15.4

Nature of roots of quadratic equations: The discriminant

15.5

Applications of quadratic equations

15.6

Solving quadratic inequalities

16. Pythagorean Theorem

16.1

Squares and square roots

16.2

Pythagorean theorem

16.3

Estimating square roots

16.4

Using the pythagorean relationship

16.5

Applications of pythagorean theorem

17. Angles, Lines and Transversals

17.1

Pairs of lines and angles

17.2

Parallel lines and transversals

17.3

Parallel line proofs

17.4

Perpendicular line proofs

17.5

Parallel and perpendicular line segments

17.6

Perpendicular bisectors

17.7

Angle Bisectors

18. Properties of Triangles

18.1

Classifying Triangles

18.2

Isosceles and Equilateral Triangles

19. Congruent Triangles

19.1

Congruence and Congruent Triangles

19.2

Triangles Congruent by SSS Proofs

19.3

Triangles Congruent by SAS and HL Proofs

19.4

Triangles Congruent by ASA and AAS Proofs

20. Symmetry and Surface Area

20.1

20.2

Rotational symmetry and transformations

20.3

Surface area of 3-dimensional shapes

21. Circle Geometry

21.1

Angles in a circle

21.2

Chord properties

21.3

Tangent properties

21.4

Circles and circumference

21.5

Arcs of a circle

21.6

Areas and sectors of circles

21.7

Inscribed Angles and Proofs

21.8

Central and inscribed angles in circles

22. Scale Factors and Similarity

22.1

Enlargements and reductions with scale factors

22.2

22.3

Similar triangles

22.4

Similar polygons

23. Surface Area and Volume

23.1

Surface area and volume of prisms

23.2

Surface area and volume of pyramids

23.3

Surface area and volume of cylinders

23.4

Surface area and volume of cones

23.5

Surface area and volume of spheres

24. Algebraic Fractions

24.1

Simplifying algebraic fractions and restrictions

24.2

Adding and subtracting algebraic fractions

24.3

Multiplying algebraic fractions

24.4

Dividing algebraic fractions

24.5

Solving equations with algebraic fractions

24.6

Applications of equations with algebraic fractions

24.7

Simplifying complex fractions

24.8

Partial fraction decomposition

25. Reciprocal Functions

25.1

Graphing reciprocals of linear functions

25.2

Graphing reciprocals of quadratic functions

26. Introduction to Trigonometry

26.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

26.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

26.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

26.4

Combination of SohCahToa questions

26.5

Solving expressions using 45-45-90 special right triangles

26.6

Solving expressions using 30-60-90 special right triangles

26.7

Word problems relating ladder in trigonometry

26.8

Word problems relating guy wire in trigonometry

26.9

Other word problems relating angles in trigonometry

27. Trigonometry

27.1

Angle in standard position

27.2

Coterminal angles

27.3

Reference angle

27.4

Find the exact value of trigonometric ratios

27.5

ASTC rule in trigonometry (All Students Take Calculus)

27.6

27.7

Converting between degrees and radians

27.8

Trigonometric ratios of angles in radians

27.9

Radian measure and arc length

27.10

27.11

27.12

Applications of the sine law and cosine law

28. Bearings

28.1

Introduction to bearings

28.2

Bearings and direction word problems

28.3

Angle of elevation and depression

29. Vectors

29.1

Introduction to vectors

29.2

Magnitude of a vector

29.3

Direction angle of a vector

29.4

Scalar multiplication

29.5

Equivalent vectors

29.6

Adding and subtracting vectors in component form

29.7

Operations on vectors in magnitude and direction form

29.8

29.9

Word problems on vectors

30. Probability

30.1

Determining probabilities using tree diagrams and tables

30.2

Probability of independent events

30.3

Probability with Venn diagrams

31. Statistics

31.1

Median and mode

31.2

31.3

Range and outliers

31.4

Application of averages

32. Data and Graphs

32.1

Reading and drawing histograms

32.2

Box-and-whisker plots and scatter plots

33. Derivatives

33.1

Definition of derivative

33.2

33.3

33.4

Derivative of exponential functions

33.5

33.6

34. Introduction to Matrices

34.1

Notation of matrices

34.2

Adding and subtracting matrices

34.3

Scalar multiplication

34.4

Matrix multiplication

34.5

The three types of matrix row operations

34.6

Representing a linear system as a matrix

34.7

Solving a linear system with matrices using Gaussian elimination

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