ACER Scholarship mathematics: eight word problems with worked solutions

Quick Answer

These eight original word problems are labelled Level 1 or Level 2 to match ACER's scholarship levels, and each has a complete worked solution. They are practice written by Braintree Coaching Australia. They are not official ACER questions and not released ACER items.

Where are ACER's own sample questions?

Start with ACER. Its parent guide for the Scholarship Tests explains the levels and the practice materials, which parents buy through the Practice Materials tab of the ACER parent account at scholarships.acer.org. ACER says it does not sell past papers.

Use ACER's material to see what the real tests look like. Use the problems below as extra practice in turning an everyday situation into a calculation.

Which ACER level is my child sitting?

ACER's parent guide sets the levels by the year your child is entering:

Level	Entry year	Mathematics test
Level 1	Year 7 or 8	Yes
Level 2	Year 9 or 10	Yes

The school you apply to tells you which level it uses. Our practice hub has a level table and one sample at each level, and the test preparation page covers what to do once the level is locked. If you are still comparing providers, see ACER or EduTest.

Level 1 problems (entry to Years 7–8)

Try each on paper first. Choose A, B, C or D.

Level 1, Question 1 (timetable). Aroha catches a bus at 7:48 am. The bus ride takes 35 minutes, then she walks 12 minutes to school. Classes start at 8:45 am. How many minutes before classes start does she arrive?

• A. 10 minutes
• B. 22 minutes
• C. 33 minutes
• D. 57 minutes

Level 1, Question 2 (scaled recipe). A pancake recipe for 6 people uses 450 g of flour, 3 eggs and 240 mL of milk. Dev scales it up for 10 people, keeping the same proportions. How much milk does he need?

• A. 280 mL
• B. 400 mL
• C. 144 mL
• D. 640 mL

Level 1, Question 3 (rate). A tank holds 90 L and already contains 30 L. A hose adds 15 L every 4 minutes. How many minutes until the tank is full?

• A. 4 minutes
• B. 16 minutes
• C. 24 minutes
• D. 15 minutes

Level 1, Question 4 (area and cost). A rectangular classroom floor is 6 m by 4.5 m. Floor tiles cost $18 per square metre, and delivery is a flat $50. What is the total cost?

• A. $428
• B. $486
• C. $536
• D. $95

Level 2 problems (entry to Years 9–10)

Try each on paper first. Choose A, B, C or D.

Level 2, Question 5 (percentage change). A concert ticket costs $80. The price rises by 25%. Later it is reduced by 20% of the new price. What is the final price?

• A. $64
• B. $80
• C. $84
• D. $100

Level 2, Question 6 (average speed). Imani cycles 24 km to a lake at 18 km/h and rides back the same way at 12 km/h. What is her average speed for the whole trip?

• A. 14.4 km/h
• B. 15 km/h
• C. 16 km/h
• D. 30 km/h

Level 2, Question 7 (ratio). A painter mixes 24 L of green paint from blue and yellow in the ratio 3 : 5. How many litres of blue must she add so that blue and yellow are in equal amounts?

• A. 3 L
• B. 6 L
• C. 9 L
• D. 15 L

Level 2, Question 8 (area and cost). A wall is 8 m wide and 3 m high, with a triangular section on top that is also 8 m wide at its base and 2 m high. It has one window 2 m by 1 m that will not be painted. Paint costs $12 for each square metre of wall painted. What does it cost to paint the wall, including the triangular section?

• A. $264
• B. $360
• C. $384
• D. $456

Worked solutions

Answer key: Level 1: Q1 A, Q2 B, Q3 B, Q4 C. Level 2: Q5 B, Q6 A, Q7 B, Q8 B.

Level 1, Question 1: A, 10 minutes.

• Working: 7:48 + 35 minutes = 8:23. Then 8:23 + 12 minutes = 8:35. From 8:35 to 8:45 is 10 minutes.
• Answer: 10 minutes.
• Likeliest wrong path: stopping at the bus arrival time. 8:45 − 8:23 = 22 minutes forgets the walk (option B).

Level 1, Question 2: B, 400 mL.

• Working: 240 mL for 6 people is 240 ÷ 6 = 40 mL per person. For 10 people, 40 × 10 = 400 mL.
• Answer: 400 mL.
• Likeliest wrong path: adding one person's worth to the original (240 + 40 = 280 mL, option A) because the change is "4 more people", not "10 people in total".

Level 1, Question 3: B, 16 minutes.

• Working: the tank needs 90 − 30 = 60 L more. The hose adds 15 L per 4 minutes, so 60 ÷ 15 = 4 lots of 15 L. Four lots take 4 × 4 = 16 minutes.
• Answer: 16 minutes.
• Likeliest wrong path: stopping at 4 (the number of lots, option A), or using the full 90 L (90 ÷ 15 × 4 = 24 minutes, option C).

Level 1, Question 4: C, $536.

• Working: area = 6 × 4.5 = 27 m². Tiles cost 27 × $18 = $486. Add delivery: $486 + $50 = $536.
• Answer: $536.
• Likeliest wrong path: leaving out delivery ($486, option B), or using the perimeter instead of the area (2 × (6 + 4.5) = 21; 21 × 18 + 50 = $428, option A).

Level 2, Question 5: B, $80.

• Working: a 25% rise is × 1.25, so $80 × 1.25 = $100. A 20% cut of that is × 0.8, so $100 × 0.8 = $80.
• Answer: $80.
• Likeliest wrong path: cancelling the percentages (25 − 20 = 5% rise, $84, option C). The 20% is taken from the larger, new price, so it removes more than the 25% added.

Level 2, Question 6: A, 14.4 km/h.

• Working: the way there takes 24 ÷ 18 = 4/3 hours (1 h 20 min). The way back takes 24 ÷ 12 = 2 hours. Total distance is 48 km and total time is 4/3 + 2 = 10/3 hours. Average speed = 48 ÷ (10/3) = 14.4 km/h.
• Answer: 14.4 km/h.
• Likeliest wrong path: averaging the two speeds ((18 + 12) ÷ 2 = 15 km/h, option B). She spends longer at the slower speed, so the average is below 15.

Level 2, Question 7: B, 6 L.

• Working: 3 + 5 = 8 parts, so one part is 24 ÷ 8 = 3 L. Blue is 9 L and yellow is 15 L. To make blue equal yellow, blue must reach 15 L, so add 15 − 9 = 6 L.
• Answer: 6 L.
• Likeliest wrong path: stopping at one part (3 L, option A), or giving the amount of blue (9 L, option C) or the target (15 L, option D) instead of the amount to add.

Level 2, Question 8: B, $360.

• Working: rectangle = 8 × 3 = 24 m². Triangle = ½ × 8 × 2 = 8 m². Total = 32 m². Take away the window, 2 × 1 = 2 m², to get 30 m². Cost = 30 × $12 = $360.
• Answer: $360.
• Likeliest wrong path: forgetting the window (32 × 12 = $384, option C), forgetting the triangle (22 × 12 = $264, option A), or using the full 8 × 2 for the triangle without halving (24 + 16 − 2 = 38; 38 × 12 = $456, option D).

What mistakes should we look for?

Most wrong answers in this set come from four slips:

• Stopping one step early. Level 1 Questions 1 and 3 and Level 2 Question 7 all give a tempting number part-way through the working.
• Adding when the situation scales. The recipe in Level 1 Question 2 needs a rate per person, not "add the extra people's share once".
• Averaging speeds, or cancelling percentages. Both look neat and both are wrong. Ask your child which quantity is being averaged, or which amount each percentage is taken from.
• Forgetting a part. A flat delivery fee or a window is easy to leave out. Ask your child to tick off every number in the question once the answer is written.

If your child gets one wrong, ask them to say in words what each line of their working stands for.

Can my child tell which level a problem belongs to?

Try this one without a label first:

A shop sells 3 pens for $4.20. How much do 8 pens cost at the same price per pen?

Ask your child two things before solving it. How many separate steps does it need? Is any step a percentage, a ratio or an average? Then solve it and compare.

It is a Level 1 style problem by our rough guide: one rate step ($4.20 ÷ 3 = $1.40 per pen), then one multiplication (8 × $1.40 = $11.20). The Level 2 problems above each add a second idea on top, such as a percentage of a changed price or an average over two journeys. This is our own guide to difficulty, not an ACER rule, and your child may disagree with it for good reasons.

For general timed practice that is not specific to ACER, try our free mock tests.

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Answers were checked on 15 October 2026 by an automated second solve. A named teacher review has not yet been recorded for this set.