ACER Level 1 Mathematics has 32–36 multiple-choice questions in 40 minutes, and it aims to measure mathematical ability rather than school achievement. These eight worked questions show what that means: school maths in situations your child hasn't seen.
Whether your child can work out which maths a new situation needs. Level 1 is ACER's scholarship test for students entering Year 7 or 8, and Mathematics sits beside Written Expression and Humanities. ACER says it aims to measure mathematical ability rather than school achievement.
These are the groups our lessons and results use: our way of organising the maths, not ACER's own headings.
Each question shows the answer and the working. Read them with your child and talk through why the right option is right. Every one starts in a setting your child probably hasn't seen, which is the point.
We wrote these to match the style and level of ACER's Level 1 Mathematics test. They are not ACER questions.
Worked explanation 1
A school club makes a booklet by stacking 9 sheets of paper, folding the whole stack in half and stapling along the fold. Each sheet becomes 4 pages, and the pages are numbered 1 to 36 in order. When the booklet is pulled apart, one sheet has page 7 printed on it. What is the largest page number printed on that same sheet?
AA.
28
BB.
29
CC.
30
DD.
31
Answer: C
Answer: C (30)
The outside sheet carries pages 1, 2, 35 and 36. Each sheet further in carries the next two pages from the front and the next two from the back: 3, 4, 33, 34, then 5, 6, 31, 32, then 7, 8, 29, 30. Notice that on each sheet a front page and its partner at the back add to 37, so page 7 sits with 37 − 7 = 30 (and page 8 with 29). The largest number on the sheet is 30.
The trap: 29 tempts children who work out 36 − 7. Page 29 is on the sheet, but the pairs add to 37, not 36, so 30 is there too and is larger.
Why the other options are wrong
A (28): 28 comes from pairing page 8 so the total is 36; 28 is actually on the next sheet in.
B (29): 29 is on the sheet, but 30 is also there and is larger.
D (31): 31 pairs page 7 with page 6 because they face each other when the booklet lies open; but each sheet starts with an odd page, so 7 shares its sheet with 8, not 6.
Worked explanation 2
A nature guide uses this rule for one kind of cricket: count the chirps in 25 seconds, divide by 3, then add 4 to estimate the air temperature in °C. One evening the temperature is 22 °C. About how many chirps would the guide expect to count in 25 seconds?
AA.
54
BB.
62
CC.
70
DD.
78
Answer: A
Answer: A (54)
Undo the rule, working backwards. Before 4 was added, the number was 22 − 4 = 18. Before it was divided by 3, it was 18 × 3 = 54. Check: 54 ÷ 3 = 18 and 18 + 4 = 22. The answer is 54 chirps.
The trap: 78 tempts children who reverse the dividing but forget to reverse the adding, so they work out (22 + 4) × 3 instead of (22 − 4) × 3.
Why the other options are wrong
B (62): 62 is 22 × 3 − 4: the steps are undone in the wrong order.
C (70): 70 is 22 × 3 + 4: the rule is half applied forwards instead of undone.
D (78): 78 is (22 + 4) × 3: the 4 is added instead of taken away.
Worked explanation 3
Three gear wheels sit in a row, each touching the next. Gear A on the left has 12 teeth, gear B in the middle has 18 teeth and gear C on the right has 8 teeth. Gear A is turned clockwise through exactly 2 full turns. What does gear C do?
AA.
It makes 3 full turns clockwise.
BB.
It makes 3 full turns anticlockwise.
CC.
It makes 2 full turns clockwise.
DD.
It makes 1⅓ turns anticlockwise.
Answer: A
Answer: A (It makes 3 full turns clockwise.)
Touching gears turn in opposite directions, so A clockwise makes B anticlockwise, which makes C clockwise. Two turns of A pushes 2 × 12 = 24 teeth past each meeting point. C has 8 teeth, so 24 teeth means 24 ÷ 8 = 3 full turns. Gear C makes 3 full turns clockwise.
The trap: 3 turns anticlockwise tempts children who get the number right but assume every other gear turns the opposite way to A. Only the middle gear is reversed; C is reversed twice, so it matches A.
Why the other options are wrong
B (It makes 3 full turns anticlockwise.): Right number of turns, but C is reversed twice, so it turns the same way as A.
C (It makes 2 full turns clockwise.): Assumes every gear turns the same number of times, ignoring the different numbers of teeth.
D (It makes 1⅓ turns anticlockwise.): 1⅓ turns anticlockwise is what the middle gear B does, not gear C.
Worked explanation 4
A cook counts that 40 grains of rice weigh 1 gram. A school canteen is open only on school days, 5 days a week, and it uses one 10 kg sack of rice every 2 days that it is open. About how many grains of rice does the canteen use in 4 weeks?
AA.
400 000
BB.
4 000 000
CC.
5 600 000
DD.
8 000 000
Answer: B
Answer: B (4 000 000)
In 4 weeks the canteen is open 4 × 5 = 20 days. One sack lasts 2 of those days, so it uses 20 ÷ 2 = 10 sacks, which is 10 × 10 = 100 kg of rice. 100 kg = 100 000 g, and each gram is about 40 grains, so 100 000 × 40 = 4 000 000 grains.
The trap: 5 600 000 tempts children who count all 28 days in 4 weeks. The canteen only uses rice on the 20 days it is open.
Why the other options are wrong
A (400 000): 400 000 changes kilograms to grams by multiplying by 100 instead of 1000.
C (5 600 000): 5 600 000 counts all 28 days in 4 weeks, not just the 20 school days.
D (8 000 000): 8 000 000 uses one sack every day instead of one every 2 days.
Worked explanation 5
A class tied a weight to strings of different lengths to make pendulums. For each length they timed 10 complete swings. Their results were: 25 cm took 10 seconds, 50 cm took 14 seconds, 100 cm took 20 seconds and 200 cm took 28 seconds. Following the pattern in the results, about how long would 10 swings take for a pendulum 400 cm long?
Length of string (cm)
Time for 10 swings (s)
25
10
50
14
100
20
200
28
AA.
36 seconds
BB.
40 seconds
CC.
56 seconds
DD.
80 seconds
Answer: B
Answer: B (40 seconds)
Doubling the length does not double the time: 100 cm to 200 cm only goes from 20 s to 28 s. Instead look at lengths that are four times as long: 25 cm to 100 cm doubles the time (10 s to 20 s), and 50 cm to 200 cm also doubles it (14 s to 28 s). 400 cm is four times 100 cm, so the time doubles from 20 s to 40 s.
The trap: 56 seconds tempts children who assume doubling the length doubles the time (28 × 2). The table itself shows that is false: 100 cm to 200 cm does not double 20 s.
Why the other options are wrong
A (36 seconds): 36 seconds just adds the last jump of 8 seconds again.
C (56 seconds): 56 seconds doubles the 200 cm time, but the table shows doubling the length does not double the time.
D (80 seconds): 80 seconds treats the time as growing in step with the length from 100 cm (20 × 4).
Worked explanation 6
A packet of seeds says that, on average, 3 out of every 4 seeds sprout. Ana wants at least 36 seedlings for the school garden. What is the smallest number of seeds she should plant so that she can expect at least 36 seedlings?
AA.
27
BB.
39
CC.
45
DD.
48
Answer: D
Answer: D (48)
The seedlings are 3 out of every 4 seeds planted. 36 seedlings is 36 ÷ 3 = 12 groups of 3, and each group of 3 seedlings comes from 4 seeds. 12 × 4 = 48 seeds. Check: three-quarters of 48 is 36.
The trap: 45 tempts children who add a quarter of 36 (9) to 36. The quarter that fail is a quarter of the seeds planted, not of the seedlings, and three-quarters of 45 is only 33.75.
Why the other options are wrong
A (27): 27 is three-quarters of 36, which works the fraction the wrong way round.
B (39): 39 adds 3 to 36 without using the fraction properly.
C (45): 45 adds a quarter of 36; three-quarters of 45 is under 36.
Worked explanation 7
In a science lab, a dish holds 300 bacteria at 9:00 am. The number of bacteria doubles every 20 minutes. At what time will the dish first hold more than 10 000 bacteria?
AA.
10:40 am
BB.
11:00 am
CC.
11:20 am
DD.
1:00 pm
Answer: B
Answer: B (11:00 am)
Double every 20 minutes: 9:20 am 600, 9:40 am 1200, 10:00 am 2400, 10:20 am 4800, 10:40 am 9600, 11:00 am 19 200. At 10:40 am there are 9600, still under 10 000. The first time there are more than 10 000 is 11:00 am.
The trap: 10:40 am tempts children because 9600 is very close to 10 000, but it is not more than 10 000.
Why the other options are wrong
A (10:40 am): At 10:40 am there are 9600, which is close to but still under 10 000.
C (11:20 am): 11:20 am is one doubling too many: by 11:00 am there are already 19 200.
D (1:00 pm): 1:00 pm treats doubling every 20 minutes as tripling every hour; three doublings in an hour multiply by 8, not 3.
Worked explanation 8
A garden designer marks out a garden bed in the shape of a regular hexagon. Straight paths join every second corner of the hexagon, so the three paths form a triangle inside it. The triangle is planted with lawn, and the three pieces outside the triangle are planted with flowers. What fraction of the whole bed is lawn?
AA.
1/2
BB.
3/5
CC.
2/3
DD.
3/4
Answer: A
Answer: A (1/2)
Join the centre of the hexagon to all six corners: the hexagon splits into 6 equal triangles. Each flower piece sits on one corner of the hexagon and is exactly half of the diamond made by two of those triangles, so each flower piece is worth 1 triangle. The three flower pieces make 3 of the 6 triangles, so the lawn is the other 3 out of 6, which is one half.
The trap: 2/3 or 3/4 tempt children because the lawn triangle looks much bigger than the thin corner pieces. Together, though, the three corner pieces match the lawn exactly.
Why the other options are wrong
B (3/5): 3/5 does not come from splitting the hexagon into equal parts.
C (2/3): 2/3 guesses from how big the lawn looks; the three corner pieces add up to as much as the lawn.
D (3/4): 3/4 overestimates the lawn; the corner pieces are each one-sixth of the bed.
How should your child tackle an unfamiliar question?
In the same order every time: read the situation, find the maths, check. A fixed routine stops a strange setting from turning into panic.
Read the situation to the end
Find what is being asked before touching the numbers. Underline the word that decides it: largest, first, at least, more than.
Find the maths underneath
Name what the story really is: a rate, a pattern, a multiple, a fraction of a whole. A quick sketch or list often shows it.
Work it on paper
Write each step, so a slip can be found and fixed rather than repeated.
Check against the story
Put the answer back into the situation. Does three-quarters of the seeds give enough seedlings? Is the page really on that sheet?
In our questions most wrong options come from a real slip, so an answer that appears among the options can still be wrong.
Is ACER Maths harder than school maths?
Different more than harder. A school test may check only the method just taught; ACER aims at mathematical ability rather than school achievement, so a question rarely says which method to use.
In our questions, the maths underneath is usually maths your child has met in class. What's new is the situation around it: a booklet being folded, a cricket chirping, gears turning.
That's why a child who is strong in class can still find the first few questions unsettling.
In these questions, the traps are mostly in the reading, not the arithmetic. As you read the working, ask your child which option looked right at first, and which slip it shows.
The slips, one by one
Answering a nearby question. The bacteria dish must hold more than the target. A time just under the target is wrong, however close.
Assuming a pattern instead of reading it. In the pendulum table, doubling the length does not double the time. The table shows it, if your child looks before calculating.
Counting what the story leaves out. The canteen uses rice only on the days it is open, not every day.
Trusting how a shape looks. The lawn triangle in the hexagon looks far bigger than the corner pieces. Splitting the shape into equal parts shows the three corner pieces together match it.
Undoing a rule in the wrong order. To reverse "divide, then add", take away first, then multiply.
Stopping at the first likely answer. In the booklet question, one page on the sheet is easy to find; the largest needs the pairing rule.
How should your child pace the Maths test?
At a little over a minute a question on average, since there are 32–36 multiple-choice questions in 40 minutes. Some take seconds; others need a list or a sketch.
Staying too long on a hard question costs time for easier ones later. A good habit: if a question hasn't started to make sense after a careful read and a first try, mark it, move on and come back if time allows.
ACER says its scholarship tests are designed to be challenging, and they are used across Australia to rank scholarship applicants. Meeting questions your child can't finish is expected, not a warning sign.
No. ACER says not to bring rulers, books or papers, calculators, watches or mobile phones to the test.
Quick mental arithmetic, times tables and neat setting out all save time on the day. Without a ruler, a diagram is something to reason about from the lengths and angles given, not something to measure.
Talk through a problem before solving it: ask your child to say what the situation is and what it asks. That habit is close to the ability the test measures.
Look for maths in ordinary moments, such as how fast a tap fills a bottle. ACER's practice tests are there to get familiar with the question types, not to drill, so a few varied questions, talked through, do more than a pile of drills.
When your child is ready for the clock, Practice test 1 has a full Mathematics section on ACER's time. Afterwards you'll see results by skill, so you know which kinds of question cost the most marks. The other tests have sample pages too: ACER Humanities questions and ACER writing topics.
