Linear expressions and equations
Year 8 · 6 questions
Expand, factorise and solve linear equations and inequalities.
For parents: By the end of Year 8, your child should be able to expand, factorise and simplify linear expressions, and solve linear equations and inequalities.
AC9M8A01create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse propertiesAC9M8A02graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution
Sample question and its hints
Expand 3(2x − 5).
- Expanding means removing the brackets by multiplying each term inside by the number outside.
- Multiply 3 by 2x, then 3 by −5. Keep the sign with each term.
- 4(3a − 2) = 12a − 8. Now try yours.
Rates, circles and composite areas
Year 8 · 6 questions
Road trips, best buys, bike wheels and L-shaped lawns.
For parents: By the end of Year 8, your child should be able to work with rates such as speed and best buys, and find the circumference and area of circles and composite shapes.
AC9M8M01solve problems involving the area and perimeter of irregular and composite shapes using appropriate unitsAC9M8M03solve problems involving the circumference and area of a circle using formulas and appropriate unitsAC9M8M05recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure
Sample question and its hints
A car travels 240 km in 3 hours. What is its average speed in km/h?
- Speed is a rate: kilometres per hour, which means how far the car goes in one hour.
- Divide the distance by the number of hours.
- 150 km in 2 hours: 150 ÷ 2 = 75 km/h. Now try yours.
Index laws and rational numbers
Year 8 · 6 questions
Multiply and divide powers, meet the zero index and sort rational from irrational.
For parents: By the end of Year 8, your child should be able to use the index laws, including the zero index, and tell rational and irrational numbers apart.
AC9M8N01recognise irrational numbers in applied contexts, including square roots andAC9M8N02establish and apply the exponent laws with positive integer exponents and the zero-exponent, using exponent notation with numbersAC9M8N03recognise terminating and recurring decimals, using digital tools as appropriate
Sample question and its hints
Write 3⁴ × 3⁵ as a single power of 3.
- 3⁴ means 3 × 3 × 3 × 3. How many 3s are multiplied altogether?
- When you multiply powers of the same base, keep the base and add the indices.
- 5² × 5⁶ = 5^(2 + 6) = 5^8. Now try yours.
Two-way tables, Venn diagrams and sampling
Year 8 · 6 questions
Rain in Hobart, cricket and soccer, and fair surveys: combine events and sample well.
For parents: By the end of Year 8, your child should be able to use two-way tables and Venn diagrams to work out probabilities, and explain what makes a fair sample.
AC9M8P01recognise that complementary events have a combined probability of one; use this relationship to calculate probabilities in applied contextsAC9M8P02determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situationsAC9M8ST01investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniquesAC9M8ST02analyse and report on the distribution of data from primary and secondary sources using random and non-random sampling techniques to select and study samples
Sample question and its hints
The probability that it rains in Hobart tomorrow is 0.35. What is the probability that it does not rain?
- It either rains or it doesn’t. Those two probabilities must add to 1.
- P(not rain) = 1 − P(rain).
- If P(win) = 0.2, then P(not win) = 1 − 0.2 = 0.8. Now try yours.
Integers and negative numbers
For Years 6–8 · 6 questions
Temperatures below zero, number lines, and adding, subtracting and multiplying integers.
For parents: Across Years 6 to 8, your child learns to place negative numbers on a number line, and add, subtract and multiply positive and negative numbers.
AC9M6N01recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian planeAC9M7N07compare, order and solve problems involving addition and subtraction of integersAC9M8N04use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
Sample question and its hints
Which number is the smallest?
Choices: −2 · 0 · −8 · 3
- Smallest means furthest to the left on a number line.
- Draw a number line from −10 to 5 and mark each number. Which one is furthest left?
- Between −5 and −1, −5 is smaller because it is further below zero. Now try yours.
Algebra basics
For Years 7–9 · 6 questions
Pronumerals, writing and substituting into expressions, and solving simple equations.
For parents: Across Years 7 to 9, your child learns to use letters for unknown numbers, substitute into expressions, and solve simple equations.
AC9M7A01recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknownAC9M7A03solve one-variable linear equations with natural number solutions; verify the solution by substitutionAC9M8A01create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties
Sample question and its hints
Which expression means “5 more than a number n”?
Choices: 5n · n + 5 · n − 5 · 5 − n
- A pronumeral like n stands for a number we don’t know yet.
- Try a real number. If n were 10, what is 5 more than it? Which expression gives that?
- “3 less than x” means start with x and take away 3, written x − 3. Now try yours.
Percentages
For Years 7–10 · 6 questions
Discounts, class surveys and percentage increase, in dollars and cents.
For parents: Across Years 7 to 10, your child learns to work out discounts, percentage increases and decreases, and compare amounts as percentages.
AC9M7N06use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategiesAC9M7N09use mathematical modelling to solve practical problems, involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representationAC9M8N05use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model
Sample question and its hints
What is 25% of $80?
- 25% means 25 out of every 100, which is the same as a quarter.
- Change the percentage into a fraction or a decimal, then multiply it by 80.
- 25% of $40: a quarter of 40 is 10, so it’s $10. Now try yours.