ICAS Maths Sample Questions with Worked Solutions

ICAS Maths is curriculum-aligned but pitched harder — it wraps familiar ideas (money, fractions, percentages, averages, measurement) in situations that make students apply what they know. Below are five original, ICAS-style questions with full worked solutions. Encourage your child to try each before reading the answer.

1. Money — change

Q. A book costs $12. Priya buys 3 of them and pays with a $50 note. How much change does she get?

Idea: find the total cost first, then subtract from what she paid.
Method: 3 × $12 = $36, then $50 − $36 = $14.
Check: $36 + $14 = $50. ✓

2. Fractions of a group

Q. In a class of 32 students, three-quarters walked to school. How many students did not walk?

Idea: the question asks for the ones who did not walk — so find the walkers, then subtract (or just take the remaining quarter).
Method: ¾ of 32 = 24 walked, so 32 − 24 = 8 did not (that's the remaining ¼).
Check: ¼ of 32 = 8. ✓

3. Percentages — a discount

Q. A shirt costs $40 and is reduced by 25% in a sale. What is the sale price?

Idea: 25% is a quarter, so work out the discount, then take it off.
Method: 25% of $40 = $10, so $40 − $10 = $30.
Check: $30 is three-quarters of $40. ✓

4. Data — the average

Q. The midday temperature over five days was 20, 22, 19, 24 and 20 °C. What was the average temperature?

Idea: the average (mean) is the total divided by how many values there are.
Method: 20 + 22 + 19 + 24 + 20 = 105, then 105 ÷ 5 = 21 °C.
Check: 21 sits in the middle of the readings, which range from 19 to 24. ✓

5. Measurement — unit conversion

Q. A row of square tiles, each 20 cm wide, runs the full length of a 3-metre wall. How many tiles are in the row?

Idea: the units don't match — convert the wall to centimetres first.
Method: 3 m = 300 cm, then 300 ÷ 20 = 15 tiles.
Check: 15 × 20 cm = 300 cm = 3 m. ✓

The common thread

Each question was a curriculum skill (money, fractions, percentages, averages, unit conversion) applied in a slightly unfamiliar way — and the first move was usually to set the problem up correctly (find the total, convert the units, read what's actually being asked). That set-up step is what ICAS Maths tests.

Practise more like these

PrepPath offers ICAS-style Maths practice for Years 3, 5, 7 and 9 — a timed, curriculum-aligned mock paper with an estimated award level and a worked explanation for every question. For the bigger picture, read What Is ICAS? and How to Prepare for ICAS.

PrepPath is an independent educational platform and is not affiliated with, endorsed by, or associated with ICAS Assessments. "ICAS" is used here for description only. These are original, ICAS-style practice questions written by PrepPath — not real ICAS papers.