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Year 9 Maths Topics

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1. Number System and Radicals

1.1

Understanding the number systems

1.2

Prime factorisation

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. Adding and Subtracting Integers

2.1

Introduction to integer addition

2.2

Adding integers

2.3

Introduction to integer subtraction

2.4

Subtracting integers

2.5

Application of integer operations

3. Multiplying and Dividing Integers

3.1

Understanding integer multiplication

3.2

Multiplying integers

3.3

Understanding integer division

3.4

Dividing integers

3.5

Applications of integer operations

4. Ratios, Rates, and Proportions

4.1

4.2

4.3

5. Percents

5.1

Representing percents

5.2

Percents, fractions, and decimals

5.3

Percent of a number

5.4

Adding and multiplying percents

5.5

Taxes, discounts, tips and more

5.6

Simple interest

6. Lines, Angles and Transversals

6.1

Pairs of lines and angles

6.2

Parallel lines and transversals

6.3

Perpendicular bisectors

6.4

Angle bisectors

7. Pythagorean Theorem

7.1

Squares and square roots

7.2

Pythagorean theorem

7.3

Estimating square roots

7.4

Using the pythagorean relationship

7.5

Applications of pythagorean theorem

8. Introduction to Surface Area of 3D Shapes

8.1

Introduction to surface area of 3-dimensional shapes

8.2

Nets of 3-dimensional shapes

8.3

Surface area of prisms

8.4

Surface area of cylinders

9. Introduction to Volume

9.1

Introduction to volume

9.2

Volume of prisms

9.3

Volume of cylinders

9.4

Word problems relating volume of prisms and cylinders

10. Scale Factors and Similarity

10.1

Enlargements and reductions with scale factors

10.2

10.3

Similar triangles

10.4

Similar polygons

11. Introduction to Trigonometry

11.1

Use sine ratio to calculate angles and side (Sin =

\frac{o}{h}

11.2

Use cosine ratio to calculate angles and side (Cos =

\frac{a}{h}

11.3

Use tangent ratio to calculate angles and side (Tan =

\frac{o}{a}

11.4

Combination of SohCahToa questions

11.5

Solving expressions using 45-45-90 special right triangles

11.6

Solving expressions using 30-60-90 special right triangles

11.7

Word problems relating ladder in trigonometry

11.8

Word problems relating guy wire in trigonometry

11.9

Other word problems relating angles in trigonometry

12. Patterns and Solving Equations

12.1

12.2

Evaluating algebraic expressions

12.3

Solving one-step equations: x + a = b

12.4

Graphing Linear relations

13. Linear Equations (Basic)

13.1

Model and solve one-step linear equations: ax = b, x/a = b

13.2

Solving two-step linear equations using addition and subtraction: ax + b = c

13.3

Solving two-step linear equations using multiplication and division: x/a + b = c

13.4

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

14. Solving Linear Equations

14.1

Solving linear equations using multiplication and division

14.2

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

14.3

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

14.4

Solving linear equations with variables on both sides

14.5

Solving literal equations

15. Solving Linear Inequalities

15.1

Express linear inequalities graphically and algebraically

15.2

Solving one-step linear inequalities

15.3

Solving multi-step linear inequalities

15.4

Compound inequalities

16. Introduction to Relations and Functions

16.1

Relationship between two variables

16.2

Understand relations between x- and y-intercepts

16.3

Domain and range of a function

16.4

Identifying functions

16.5

Function notation

17. Linear Relations

17.1

Representing patterns in linear relations

17.2

Reading linear relation graphs

17.3

Solving linear equations by graphing

18. Linear Functions

18.1

Distance formula:

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

18.2

Midpoint formula:

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

18.3

Gradient equation:

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

18.4

Gradient intercept form: y = mx + b

18.5

General form: Ax + By + C = 0

18.6

Gradient-point form:

y - y_1 = m (x - x_1)

18.7

18.8

Graphing linear functions using table of values

18.9

Graphing linear functions using x- and y-intercepts

18.10

Graphing from gradient-intercept form y=mx+b

18.11

Graphing linear functions using a single point and gradient

18.12

Word problems of graphing linear functions

18.13

Parallel and perpendicular lines in linear functions

18.14

Applications of linear relations

19. Solving Simultaneous Equations

19.1

Determining number of solutions to linear equations

19.2

Solving simultaneous equations by graphing

19.3

Solving simultaneous equations by elimination

19.4

Solving simultaneous equations by substitution

19.5

Money related questions in linear equations

19.6

Unknown number related questions in linear equations

19.7

Distance and time related questions in linear equations

19.8

Rectangular shape related questions in linear equations

20. Introduction to Powers and Exponents

20.1

Using exponents to describe numbers

20.2

20.3

Order of operations with exponents

20.4

Using exponents to solve problems

21. Exponents

21.1

Product rule of exponents

21.2

Quotient rule of exponents

21.3

Power of a product rule

21.4

Power of a quotient rule

21.5

Power of a power rule

21.6

Negative exponent rule

21.7

Combining the exponent rules

21.8

Scientific notation

21.9

Convert between radicals and rational exponents

21.10

Solving for exponents

22. Introduction to Polynomials

22.1

Characteristics of polynomials

22.2

Equivalent expressions of polynomials

22.3

Adding and subtracting polynomials

23. Multiplying and Dividing Polynomials

23.1

Multiplying and dividing monomials

23.2

Multiplying polynomials by monomials

23.3

Dividing polynomials by monomials

24. Factorising Polynomial Expressions

24.1

Common factors of polynomials

24.2

Factorising polynomials by grouping

24.3

Solving polynomials with the unknown "b" from x^2 + bx + c

24.4

Solving polynomials with the unknown "c" from x^2 + bx + c

24.5

Factorising polynomials: x^2 + bx + c

24.6

Applications of polynomials: x^2 + bx + c

24.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

24.8

Factorising polynomials:

ax^2 + bx + c

24.9

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

24.10

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

24.11

Evaluating polynomials

24.12

Using algebra tiles to factorise polynomials

24.13

Solving polynomial equations

24.14

Word problems of polynomials

25. Radicals

25.1

Square and square roots

25.2

Cubic and cube roots

25.3

Evaluating and simplifying radicals

25.4

Converting radicals to mixed radicals

25.5

Converting radicals to entire radicals

25.6

Adding and subtracting radicals

25.7

Multiplying and dividing radicals

25.8

Rationalize the denominator

26. Algebraic Fractions

26.1

Simplifying algebraic fractions and restrictions

26.2

Adding and subtracting algebraic fractions

26.3

Multiplying algebraic fractions

26.4

Dividing algebraic fractions

26.5

Solving equations with algebraic fractions

26.6

Applications of equations with algebraic fractions

26.7

Simplifying complex fractions

26.8

Partial fraction decomposition

27. Reciprocal Functions

27.1

Graphing reciprocals of linear functions

27.2

Graphing reciprocals of quadratic functions

28. Introduction to Probability

28.1

Introduction to probability

28.2

Organizing outcomes

28.3

Probability of independent events

28.4

Comparing experimental and theoretical probability

29. Statistics

29.1

Median and mode

29.2

29.3

Range and outliers

29.4

Application of averages

30. Data and Graphs

30.1

Reading and drawing bar graphs

30.2

Reading and drawing histograms

30.3

Reading and drawing line graphs

30.4

Box-and-whisker plots and scatter plots

30.5

30.6

Reading and drawing Venn diagrams

30.7

Stem-and-leaf plots

30.8

Frequency tables and dot plots

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