Mathematics · Year 8

Lesson 1

Discover why multiplying powers with the same base means adding the indices, and use the law to simplify numerical expressions.

⏱ 18 min · 10 questions

Lesson 2

Use cancelling to see why dividing powers with the same base means subtracting the indices, then simplify expressions with the law.

⏱ 18 min · 10 questions

Lesson 3

Raise a power to a power by multiplying the indices, explain why any non-zero number to the power of 0 is 1, and combine all three index laws.

⏱ 20 min · 11 questions

Lesson 4

Convert fractions to decimals, predict whether they terminate or recur, and write recurring decimals with dot notation.

⏱ 18 min · 10 questions

Lesson 5

Distinguish rational numbers from irrational numbers such as √2 and π, and estimate irrational values.

⏱ 18 min · 10 questions

Lesson 6

Use patterns to explain the sign rules, then multiply and divide positive and negative integers confidently.

⏱ 17 min · 12 questions

Lesson 7

Evaluate multi-step integer expressions with brackets and powers, taking care when squaring negative numbers.

⏱ 18 min · 11 questions

Lesson 8

Add, subtract, multiply and divide positive and negative fractions and decimals, choosing efficient strategies.

⏱ 20 min · 11 questions

Lesson 9

Calculate a change as a percentage of the original amount and use multipliers for percentage increases and decreases.

⏱ 18 min · 11 questions

Lesson 10

Work backwards from a price after a percentage increase or decrease to find the original amount.

⏱ 18 min · 11 questions

Lesson 11

Calculate profit and loss in dollars and as a percentage of the cost price in small-business scenarios.

⏱ 19 min · 11 questions

Lesson 12

Compare unit prices, discounts and GST-inclusive prices to make smart spending decisions.

⏱ 19 min · 10 questions

Lesson 13

Spot like terms, including ones with negative coefficients and powers, and combine them to write expressions in their simplest form.

⏱ 18 min · 9 questions

Lesson 14

Multiply and divide algebraic terms by dealing with the coefficients and using index laws on the variables.

⏱ 18 min · 9 questions

Lesson 15

Use the distributive law to remove brackets — including negative multipliers — and simplify the result.

⏱ 18 min · 9 questions

Lesson 16

Reverse expanding by taking out the highest common factor — numbers, letters and negatives — and check by expanding.

⏱ 18 min · 9 questions

Lesson 17

Solve linear equations whose answers are negative numbers, fractions or decimals, and check them by substitution.

⏱ 18 min · 10 questions

Lesson 18

Solve equations with the variable on both sides by collecting like terms first, then verify the answer by substitution.

⏱ 18 min · 9 questions

Lesson 19

Solve linear equations containing brackets by expanding first, including problems that start out in words.

⏱ 20 min · 9 questions

Lesson 20

Solve one-variable inequalities, show the solutions on a number line, and know when to reverse the inequality sign.

⏱ 20 min · 9 questions

Lesson 21

Build tables of values from rules like y = 2x − 3, plot the points and see that they fall on a straight line.

⏱ 18 min · 10 questions

Lesson 22

Find where a straight line crosses each axis and test whether a given point lies on the line.

⏱ 18 min · 10 questions

Lesson 23

Use straight-line graphs and their intersections to solve equations and inequalities, then confirm the answers algebraically.

⏱ 20 min · 10 questions

Lesson 24

Model phone plans, hire charges and other real situations with linear rules, then use them to compare options and make decisions.

⏱ 20 min · 10 questions

Lesson 25

Derive the area formulas for trapeziums, rhombuses and kites from parallelograms and rectangles, then use them forwards and backwards.

⏱ 18 min · 9 questions

Lesson 26

Break irregular shapes into familiar pieces to find area and perimeter, working out missing lengths and converting between units of area.

⏱ 20 min · 9 questions

Lesson 27

Find the perimeter of semicircles and quadrants, give exact answers in terms of π, and work backwards from a circumference to the radius.

⏱ 18 min · 9 questions

Lesson 28

Understand why the area of a circle is πr² and use it for circles, semicircles and quadrants, giving exact or rounded answers.

⏱ 18 min · 9 questions

Lesson 29

Find the area and perimeter of running tracks, rings, garden beds and other shapes built from rectangles and parts of circles.

⏱ 20 min · 10 questions

Lesson 30

Use V = Ah to find the volume of any right prism, including prisms with trapezium and composite cross-sections.

⏱ 18 min · 9 questions

Lesson 31

Link volume to capacity to solve practical problems about tanks, pools and troughs, converting between cm³, m³, litres and kilolitres.

⏱ 20 min · 9 questions

Lesson 32

Calculate durations and convert times across Australian and international time zones, using 24-hour time and allowing for daylight saving.

⏱ 20 min · 10 questions

Lesson 33

Recognise rates as comparisons of different kinds of quantities, simplify them to unit rates and use them to compare and convert.

⏱ 18 min · 10 questions

Lesson 34

Use speed as a rate to find distance, time or average speed in travel problems, keeping the units consistent.

⏱ 18 min · 10 questions

Lesson 35

Identify the hypotenuse of a right-angled triangle and use Pythagoras’ theorem to find its length, exactly or rounded.

⏱ 18 min · 10 questions

Lesson 36

Rearrange Pythagoras’ theorem to find a shorter side, test whether a triangle is right-angled and solve ladder and ramp problems.

⏱ 20 min · 11 questions

Lesson 37

Recognise congruent figures, match their corresponding sides and angles, and read and write congruence statements using ≅.

⏱ 18 min · 9 questions

Lesson 38

Use the SSS, SAS, AAS and RHS tests to decide whether two triangles are congruent, and spot information that is not enough.

⏱ 20 min · 9 questions

Lesson 39

Use congruent triangles and parallel-line angle facts to prove properties of parallelograms, rectangles and rhombuses, then use those properties to solve problems.

⏱ 20 min · 10 questions

Lesson 40

Identify line and rotational symmetry, and use coordinate rules to rotate and reflect points and shapes on the Cartesian plane.

⏱ 20 min · 10 questions

Lesson 41

Compare census, sample, experiment and observation as ways of collecting data, weighing up accuracy, cost and practicality.

⏱ 18 min · 9 questions

Lesson 42

Compare simple random, systematic, stratified, convenience and self-selected samples, and identify the ways a sample can become biased.

⏱ 20 min · 9 questions

Lesson 43

Compare statistics from several random samples and see why larger samples vary less and give more reliable estimates of the population.

⏱ 18 min · 10 questions

Lesson 44

Plan and carry out a statistical investigation using a fair sample, analyse the results and write cautious conclusions about the population.

⏱ 20 min · 10 questions

Lesson 45

Recognise that an event and its complement have probabilities adding to 1, and use this to find probabilities quickly, including ‘at least one’ problems.

⏱ 18 min · 9 questions

Lesson 46

Organise outcomes for two events in two-way tables and Venn diagrams, fill in missing values, and use them to calculate probabilities with ‘and’, ‘or’ and ‘only’.

⏱ 20 min · 9 questions

Lesson 47

Draw tree diagrams for two-step chance experiments, with and without replacement, and multiply along branches to find probabilities.

⏱ 20 min · 9 questions

Lesson 48

Use digital tools to run large simulations of chance events, compare observed relative frequencies with predictions, and explain the differences.

⏱ 18 min · 10 questions