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Year 10 Maths Topics

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1. Number System

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. Ratios, Rates, and Proportions

2.1

2.2

2.3

3. Percents

3.1

Representing percents

3.2

Percents, fractions, and decimals

3.3

Percent of a number

3.4

Adding and multiplying percents

3.5

Taxes, discounts, tips and more

3.6

Simple interest

4. Measuring Systems

4.1

4.2

Imperial systems

4.3

Conversions between metric and imperial systems

4.4

Conversions involve squares and cubic

4.5

Upper and lower bound

5. Pythagorean Theorem

5.1

Understanding of squares and square roots

5.2

Pythagorean theorem

5.3

Estimating square roots

5.4

Using the pythagorean relationship

5.5

Applications of pythagorean theorem

6. Coordinates, Quadrants, and Transformations

6.1

Cartesian plane

6.2

Draw on coordinate planes

6.3

Introduction to transformations

6.4

Horizontal and vertical distances

7. Surface area of 3D Objects

7.1

Introduction to surface area of 3-dimensional shapes

7.2

Nets of 3-dimensional shapes

7.3

Surface area of prisms

7.4

Surface area of cylinders

8. Volume of 3-dimensional figures

8.1

Introduction to volume

8.2

Volume of prisms

8.3

Volume of cylinders

8.4

Word problems relating volume of prisms and cylinders

9. Symmetry and Surface Area

9.1

9.2

Rotational symmetry and transformations

9.3

Surface area of 3-dimensional shapes

10. Scale Factors and Similarity

10.1

Enlargements and reductions with scale factors

10.2

10.3

Similar triangles

10.4

Similar polygons

11. Solving Linear Equations

11.1

Solving linear equations using multiplication and division

11.2

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

11.3

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

11.4

Solving linear equations with variables on both sides

11.5

Solving literal equations

12. Linear Inequalities

12.1

Express linear inequalities graphically and algebraically

12.2

Solving one-step linear inequalities

12.3

Solving multi-step linear inequalities

12.4

Compound inequalities

13. Introduction to Relations and Functions

13.1

Relationship between two variables

13.2

Understand relations between x- and y-intercepts

13.3

Domain and range of a function

13.4

Identifying functions

13.5

Function notation

14. Functions

14.1

Function notation (Advanced)

14.2

Operations with functions

14.3

Adding functions

14.4

Subtracting functions

14.5

Multiplying functions

14.6

Dividing functions

14.7

Composite functions

14.8

Inequalities of combined functions

14.9

Inverse functions

14.10

One to one functions

14.11

Difference quotient: applications of functions

15. Linear Functions

15.1

Distance formula:

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

15.2

Midpoint formula:

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

15.3

Gradient equation:

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

15.4

Gradient intercept form: y = mx + b

15.5

General form: Ax + By + C = 0

15.6

Gradient-point form:

y - y_1 = m (x - x_1)

15.7

15.8

Graphing linear functions using table of values

15.9

Graphing linear functions using x- and y-intercepts

15.10

Graphing from gradient-intercept form y=mx+b

15.11

Graphing linear functions using a single point and gradient

15.12

Word problems of graphing linear functions

15.13

Parallel and perpendicular lines in linear functions

15.14

Parallel and perpendicular lines in linear functions

16. Solving Simultaneous Equations

16.1

Determining number of solutions to linear equations

16.2

Solving simultaneous equations by graphing

16.3

Solving simultaneous equations by elimination

16.4

Solving simultaneous equations by substitution

16.5

Money related questions in linear equations

16.6

Unknown number related questions in linear equations

16.7

Distance and time related questions in linear equations

16.8

Rectangular shape related questions in linear equations

17. Laws of Indices

17.1

Product rule of exponents

17.2

Quotient rule of exponents

17.3

Power of a product rule

17.4

Power of a quotient rule

17.5

Power of a power rule

17.6

Negative exponent rule

17.7

Combining the exponent rules

17.8

17.9

Convert between radicals and rational exponents

17.10

Solving for indices

18. Sequences and Series

18.1

Arithmetic sequences

18.2

Arithmetic series

18.3

Geometric sequences

18.4

Geometric series

18.5

Infinite geometric series

18.6

18.7

Arithmetic mean vs. Geometric mean

19. Exponential Functions

19.1

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

19.2

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

19.3

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

19.4

Exponents: Negative exponents

19.5

Exponents: Zero exponent: a^0 = 1

19.6

Exponents: Rational exponents

19.7

Solving exponential equations using exponent rules

19.8

Graphing exponential functions

19.9

Graphing transformations of exponential functions

19.10

Finding an exponential function given its graph

20. Polynomials

20.1

Characteristics of polynomials

20.2

Equivalent expressions of polynomials

20.3

Adding and subtracting polynomials

21. Multiplication and Division of Polynomials

21.1

Multiplying and dividing monomials

21.2

Multiplying polynomials by monomials

21.3

Dividing polynomials by monomials

22. Factorising Polynomial Expressions

22.1

Common factors of polynomials

22.2

Factorising polynomials by grouping

22.3

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

22.4

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

22.5

Factorising polynomials: x^2 + bx + c

22.6

Applications of polynomials: x^2 + bx + c

22.7

Solving polynomials with the unknown "b" from

ax^2 + bx + c

22.8

Factorising polynomials:

ax^2 + bx + c

22.9

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

22.10

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

22.11

Evaluating polynomials

22.12

Using algebra tiles to factorise polynomials

22.13

Solving polynomial equations

22.14

Word problems of polynomials

23. Surds

23.1

Square and square roots

23.2

Cubic and cube roots

23.3

Evaluating and simplifying surds

23.4

Operations with surds

23.5

Conversion between entire surds and mixed surds

23.6

Adding and subtracting surds

23.7

Multiplying surds

23.8

Solving surd equations

23.9

Rationalize the denominator

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. Direct and Inverse Variation

26.1

Direct variation

27. Set Theory

27.1

27.2

Set builder notation

27.3

Intersection and union of 2 sets

27.4

Intersection and union of 3 sets

28. Probability

28.1

Determining probabilities using tree diagrams and tables

28.2

Probability of independent events

28.3

Probability with Venn diagrams

29. Statistics

29.1

Median and mode

29.2

29.3

Range and outliers

29.4

Application of averages

29.5

Influencing factors in data collection

29.6

Data collection

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

Stem-and-leaf plots

30.6

Reading and drawing Venn diagrams

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