ACER says Quantitative Reasoning tests thinking and reasoning with numbers, patterns and shapes. These 8 worked questions show what that looks like, before the exam in June 2027 Expected.
It asks your child to spot rules and relationships, sometimes in a puzzle they haven't seen before. ACER says it uses numbers, patterns and shapes in both abstract and real-world settings.
Quantitative Reasoning shares the first sitting with Mathematics: 60 minutes for both parts. The questions are multiple choice, with answers shaded in a supplied answer booklet. As in Maths, calculators are among the banned items: no phones, smart watches, calculators, translation devices or dictionaries, headphones, recording devices of any kind, notebooks or extra paper.
In our questions it leans less on school content than Maths does. A question might ask for the rule in a growing pattern, the number a shape stands for, a fact from a table, or what an experiment really shows.
Worked questions: patterns, symbols, tables and experiments
Each one shows the answer and the working, so read them with your child and talk through why the right option is right. We wrote these in the style of ACER's published samples, and none appears in our Practice tests.
Worked explanation 1
Square tiles are laid to make hollow square frames: a single ring of tiles around an empty middle. Step 1 is a frame 3 tiles long on each side and uses 8 tiles. Step 2 is 4 tiles long on each side and uses 12 tiles. Step 3 is 5 tiles long on each side and uses 16 tiles. The pattern continues in the same way. How many tiles are in step 10?
AA.
36
BB.
40
CC.
44
DD.
48
Answer: C
Answer: C
Each frame's side is 2 tiles longer than its step number, so step 10 is 12 tiles on each side. Four sides of 12 count each corner tile twice, so the frame uses 4 × 12 − 4 = 44 tiles (check step 1: 4 × 3 − 4 = 8). Choosing 48 counts the corners twice; 36 forgets that the side is 2 longer than the step number.
Worked explanation 2
Each shape stands for a number, and the same shape always stands for the same number.
triangle + circle = 14
circle + circle + triangle = 20
square + triangle = circle + circle + circle
What number does the square stand for?
AA.
2
BB.
6
CC.
8
DD.
10
Answer: D
Answer: D
Compare the first two lines: the second has one extra circle and is 6 more, so a circle is 6 and a triangle is 14 − 6 = 8. Three circles make 18, so square + 8 = 18 and the square is 10. Choosing 8 gives the triangle and 6 gives the circle, so both stop before the last step.
Worked explanation 3
A beekeeper weighed the honey taken from each of her four hives in spring and again in autumn. Which hive gave a total for the two seasons closest to 50 kg?
Hive
Spring honey (kg)
Autumn honey (kg)
Hive 1
24
19
Hive 2
31
18
Hive 3
22
30
Hive 4
35
21
AA.
Hive 1
BB.
Hive 2
CC.
Hive 3
DD.
Hive 4
Answer: B
Answer: B
Add the two seasons for each hive: Hive 1 43 kg, Hive 2 49 kg, Hive 3 52 kg, Hive 4 56 kg. Hive 2 is 1 kg away from 50, the closest. Hive 3 is tempting because it gave the most autumn honey and is also near 50, but it is 2 kg away.
Worked explanation 4
Zara filled three cans, one black, one white and one silver, with the same amount of water at 18 °C. She placed them side by side in the sun and measured the water temperature in each can after 30 minutes. Which conclusion is best supported by her results?
Can
Water temperature after 30 minutes
Black
34 °C
White
27 °C
Silver
25 °C
AA.
In Zara's test, the water in the black can warmed up the most.
BB.
Silver cans keep drinks colder than other cans in a fridge.
CC.
Black objects always become hotter than objects of any other colour.
DD.
The colour of the can made no difference, because all three cans warmed up.
Answer: A
Answer: A
A good conclusion says only what the results show. All three cans started at 18 °C in the same sun, and the black can ended hottest, so A is supported. C goes too far: only three colours were tried, once each. D is wrong because the water warmed by different amounts (16, 9 and 7 degrees).
Worked questions: made-up rules, sequences, ticket data and ratios
The second set takes longer. Each question has a step that is easy to skip, so checking the answer against the question matters more.
Worked explanation 5
In a puzzle, ■ means 'multiply the two numbers, then subtract the larger one', and ▲ means 'add the two numbers, then halve the result'. For example, 5 ■ 3 = 15 − 5 = 10, and 4 ▲ 8 = 6.
What is (6 ■ 4) ▲ 10?
AA.
14
BB.
15
CC.
18
DD.
35
Answer: A
Answer: A
Work out the brackets first. 6 ■ 4 = 24 − 6 = 18, because 6 is the larger number. Then 18 ▲ 10 = 28 ÷ 2 = 14. Choosing 15 comes from subtracting the smaller number (24 − 4 = 20, then 20 ▲ 10 = 15); choosing 35 comes from doing the ▲ step first.
Worked explanation 6
In this sequence, each number after the first two is the sum of the two numbers just before it. Four numbers are missing.
?, 5, ?, ?, ?, 37
What is the first number?
AA.
3
BB.
4
CC.
5
DD.
6
Answer: B
Answer: B
Try a first number and build the sequence. Starting with 3 gives 3, 5, 8, 13, 21, 34, which is 3 short of 37. Each extra 1 at the start adds 3 to the sixth number, so start with 4: 4, 5, 9, 14, 23, 37. Choosing 3 or 5 lands close (34 or 40), which is why checking all the way to the end matters.
Worked explanation 7
A school play sold three kinds of ticket: adult $12, child $6, and family $30 (one family ticket lets in 2 adults and 2 children). The table shows how many of each kind were sold. On which day did ticket sales bring in the most money?
Day
Adult tickets
Child tickets
Family tickets
Monday
20
45
10
Tuesday
25
55
2
Wednesday
30
20
12
Thursday
45
12
6
Friday
20
30
8
AA.
Monday
BB.
Tuesday
CC.
Wednesday
DD.
Thursday
Answer: C
Answer: C
Count in $6 units: adult 2, child 1, family 5. Monday 40 + 45 + 50 = 135, Tuesday 115, Wednesday 60 + 20 + 60 = 140, Thursday 132, Friday 110. Wednesday earns the most, 140 × $6 = $840. Monday ($810) had the most people through the door and Tuesday sold the most tickets, but neither earned the most.
Worked explanation 8
A jar holds red and blue marbles in the ratio 3 : 5. Ana adds 12 red marbles, and the ratio of red to blue becomes 3 : 4. She then adds just enough blue marbles to make the ratio 3 : 5 again. How many marbles are in the jar now?
AA.
128
BB.
140
CC.
152
DD.
160
Answer: D
Answer: D
The blue marbles do not change at first. Red goes from 3/5 of blue to 3/4 of blue, a rise of 3/20 of blue, and that rise is the 12 marbles, so there are 80 blue. Red goes from 48 to 60. For 3 : 5 again, 60 red needs 100 blue, so the jar holds 160. Choosing 140 stops before the blue marbles are added.
What are the common traps?
Each wrong option here comes from a common slip. Go through the list together after reading the questions, and name the slip that looked most tempting.
×
Counting something twice: In a square frame of tiles, each corner tile belongs to two sides.
×
Stopping before the last step: If the question asks about the square, the triangle and circle are only steps.
×
Trusting numbers that look close: Big numbers can look close and still be far apart. Work out every option.
×
Saying more than the results show: A few cans, tried once each, can't prove a rule about every colour.
×
Bending a made-up rule: If the rule says 'subtract the larger one', subtracting the smaller one gives a wrong option. Do the brackets first.
×
Answering a different question: The day with the most people or tickets is not always the day with the most money.
The fix each time: your child says the rule in their own words, then checks the answer fits the whole question.
Which skills do these questions cover?
Each question belongs to one kind of Quantitative Reasoning question and links to its skill page. If one was hard to follow, start there: each page has more worked questions, from easier to harder.
No, they are ours, written in ACER's published style. On its Prepare page, ACER offers a set of sample questions to download, for the style and format of the exam questions. Which year they come from is not published.
Is Quantitative Reasoning the same as Maths?
No. ACER says Maths tests year-level maths knowledge and reasoning, and using maths in real-world contexts, while Quantitative Reasoning tests thinking and reasoning with numbers, patterns and shapes.
Yes, slowly. ACER says the skills the exam measures grow over time, through a culture of learning, varied engaging material and talking freely about ideas. So a few questions a week, talked through, help more than a long cram.
Our selective entry practice tests give the full sitting under the real time. Afterwards you'll see results by skill, so you know which kinds of question to practise next.
