Formulas and linear equations
Year 7 · 6 questions
Substitute into formulas, write expressions and solve two-step equations.
For parents: By the end of Year 7, your child should be able to substitute numbers into formulas, write algebraic expressions, and solve simple equations and check the answer.
AC9M7A01recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknownAC9M7A02formulate algebraic expressions using constants, variables, operations and bracketsAC9M7A03solve one-variable linear equations with natural number solutions; verify the solution by substitution
Sample question and its hints
The perimeter of a rectangle is P = 2(l + w). Find P when l = 9 cm and w = 4 cm.
- Swap the letters for the numbers: l is 9 and w is 4. Then follow the formula.
- Work out the brackets first, then multiply the result by 2.
- If l = 5 and w = 3, P = 2(5 + 3) = 2 × 8 = 16 cm. Now try yours.
Area, volume and triangle angles
Year 7 · 6 questions
Sails, fish tanks and cheese wedges: area, volume and the 180° rule.
For parents: By the end of Year 7, your child should be able to find the area of triangles and parallelograms, the volume of prisms, and use the fact that a triangle’s angles add to 180°.
AC9M7M01solve problems involving the area of triangles and parallelograms using established formulas and appropriate unitsAC9M7M02solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate unitsAC9M7M05demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles
Sample question and its hints
A triangular sail has a base of 10 m and a perpendicular height of 7 m. What is its area?
- The area of a triangle uses its base and its perpendicular height.
- Use A = ½ × base × height: multiply the base by the height, then halve it.
- Base 8 m, height 5 m: ½ × 8 × 5 = 20 m². Now try yours.
Square roots, prime factors and ratios
Year 7 · 6 questions
Estimate square roots, break numbers into primes and share things fairly by ratio.
For parents: By the end of Year 7, your child should be able to work with square roots and prime factors, find equivalent fractions and decimals, and solve ratio problems.
AC9M7N01describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problemsAC9M7N02represent natural numbers as products of powers of prime numbers using exponent notationAC9M7N04find equivalent representations of rational numbers and represent rational numbers on a number lineAC9M7N08recognise, represent and solve problems involving ratios
Sample question and its hints
Without a calculator, estimate √50 to the nearest whole number.
- √50 is the number that, multiplied by itself, gives 50.
- Which two square numbers is 50 between? Which one is it closer to?
- √30: 30 is between 25 and 36, and closer to 25, so √30 is about 5. Now try yours.
Mean, median, range and chance
Year 7 · 6 questions
Netball scores, Darwin temperatures and spinners: summarise data and predict chance.
For parents: By the end of Year 7, your child should be able to find the mean, median, mode and range of data, and work out simple probabilities.
AC9M7ST01acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of dataAC9M7ST02create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and modeAC9M7P01identify the sample space for single-stage events; assign probabilities to the outcomes of these events and predict relative frequencies for related eventsAC9M7P02conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences
Sample question and its hints
A netball team’s scores in six games were 14, 9, 21, 17, 9 and 20. What is the mean score?
- The mean is the total shared equally across all the games.
- Add the six scores, then divide by 6.
- The mean of 4, 7 and 10 is (4 + 7 + 10) ÷ 3 = 21 ÷ 3 = 7. 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.