Read them with your child to see how each one is solved and which slip it catches.
Practice test 1 is free. No card needed.
ACER says the Mathematics part tests year-level maths knowledge and reasoning, and using maths in real-world contexts. These 8 worked questions show what that looks like, before the exam in June 2027 Expected.
Checked by the SelectiveReady team on 12 October 2026 · Updated 3 November 2026 · How we check facts
Independent. Not affiliated with the Victorian Department of Education or ACER.
It asks your child to use the maths they already know, including in everyday problems, and to work every step by hand. ACER says the knowledge needed is no more than the Year 8 curriculum. 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.
Mathematics shares the first sitting with Quantitative Reasoning: 60 minutes for both parts. The questions are multiple choice, with answers shaded in a supplied answer booklet.
In our questions below, the arithmetic is rarely the hard part. Turning the words into the right steps is, and each worked answer shows those steps in order.
Each question 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.
In this set, watch the units and the last line of each question. Both are easy to skim past.
A jacket normally costs $80. In a sale it is marked 25% off. At the counter, Ruby is given a further 10% off the sale price. How much does Ruby pay for the jacket?
Answer: B
Answer: B
Apply each discount in turn. 25% off $80 leaves $60, and 10% of $60 is $6, so Ruby pays $54. The tempting $52 comes from adding the discounts to make 35% off $80, but the second 10% is taken from the lower sale price, not the original price.
A scooter travels along a path at a steady 18 km/h. Each of its wheels has a circumference (the distance around the wheel) of 50 cm. How many full turns does each wheel make every second?
Answer: A
Answer: A
Change the speed to metres per second: 18 km/h is 18 000 m in 3600 seconds, which is 5 m every second. Each turn of a wheel moves the scooter 50 cm, or 0.5 m, so each wheel turns 5 ÷ 0.5 = 10 times a second. 36 comes from 18 ÷ 0.5 without changing the units; 600 and 36 000 are turns per minute and per hour.
A bag holds 4 red, 5 blue and 3 green counters. Oscar takes out one counter without looking. What is the probability that the counter is not blue?
Answer: C
Answer: C
Count the counters that are not blue and compare with the total. There are 4 + 3 = 7 red or green counters out of 12, so the probability is 7/12. 5/12 is the chance of blue, the opposite of what was asked. 2/3 comes from counting colours (two of the three) instead of counters.
The table shows the rainfall at a weather station over five days. Friday's figure is missing. The mean (average) daily rainfall for the five days was 6 mm. What was the median daily rainfall for the five days?
| Day | Mon | Tue | Wed | Thu | Fri |
|---|---|---|---|---|---|
| Rainfall (mm) | 4 | 0 | 9 | 3 | ? |
Answer: A
Answer: A
First find Friday: a mean of 6 mm over 5 days is 30 mm in total, and the other days add to 16 mm, so Friday had 14 mm. In order the values are 0, 3, 4, 9, 14, and the middle one (the median) is 4 mm. 9 mm is Wednesday, the middle day of the week, not the middle value.
The second set is harder. Each question needs several steps, and the usual mistake is stopping one step early. A quick sketch of the garden bed or the angles around a point saves time.
A carpenter cuts a 3 m plank, with no waste, into five pieces for a bookcase: two equal side pieces and three equal shelves. Each side piece is 30 cm longer than each shelf. How long is each side piece?
Answer: C
Answer: C
Let each shelf be s cm, so each side piece is s + 30 cm. Then 3s + 2(s + 30) = 300, which gives 5s + 60 = 300, so s = 48 and each side piece is 78 cm. 48 cm is the shelf, not the side piece, and 60 cm splits the plank into five equal pieces, ignoring the extra 30 cm.
A rectangular garden bed is 6 m long and 4 m wide. A path 1 m wide runs around the outside of the bed, along all four sides. What is the area of the path?
Answer: B
Answer: B
Find the area of the bed and path together, then subtract the bed. Together they make a rectangle 8 m by 6 m, which is 48 m², and the bed is 24 m², so the path is 24 m². 20 m² comes from adding strips along the bed's sides (6 + 6 + 4 + 4) and forgetting the four 1 m corner squares.
Around a single point, a tiler fits one equilateral triangle and two identical regular polygons, with no gaps and no overlaps. How many sides does each of the two identical polygons have?
Answer: C
Answer: C
The angles around a point add to 360°. The triangle uses 60°, leaving 300° for the two polygons, so each has an interior angle of 150°. Its exterior angle is 180° − 150° = 30°, and exterior angles add to 360°, so it has 360 ÷ 30 = 12 sides. 30 is the exterior angle in degrees, not the number of sides.
The ratio of Mele's money to Declan's money is 5 : 3. Mele gives Declan $12. The ratio of Mele's money to Declan's money is now 7 : 9. How much money do Mele and Declan have altogether?
Answer: D
Answer: D
The gift doesn't change the total, so write both ratios with the same number of parts: 5 : 3 is 8 parts, so write it as 10 : 6 to match the 16 parts of 7 : 9. Mele drops from 10 parts to 7, so 3 parts are $12 and one part is $4. The total is 16 × $4 = $64. $40 is Mele's money at the start.
Each wrong option is an answer a child reaches by a common slip. After reading the questions, go through this list and ask your child which slip looked most tempting.
Adding discounts together: A second discount comes off the sale price, not the original price.
Mixing units: A speed in kilometres an hour and a wheel in centimetres need the same units before you divide.
Answering the opposite question: 'Not blue' means counting every other counter, and counting counters, not colours.
Picking the middle day: The median is the middle value once the numbers are in order, not midweek.
Forgetting the corners: A path around a garden bed has corner squares that strips along the sides leave out.
Giving a number from the working: An angle is not the number of sides, and one person's money is not the total.
One habit catches most of these: before choosing, your child rereads the question's last line and checks the answer is what it asks for.
Each question belongs to one skill and links to its page. If a question was hard to follow, start there: each skill page has more worked questions on that one skill, from easier to harder.
| Skill | What it covers |
|---|---|
| Number | Negatives, factors and patterns in digits |
| Fractions, decimals and percentages | Discounts and parts of a whole |
| Ratio | Sharing, scale and maps |
| Algebra | Substituting, solving and word problems |
| Measurement | Time, area and volume |
| Geometry and angles | Triangles, polygons and coordinates |
| Nets and 3D shapes | Cubes, views and folding |
| Tables and charts | Reading tables and finding averages |
| Probability | Chance with bags, dice and names |
| Rounding and estimation | Closest answers without a calculator |
| Rates and speed | Value for money, speed and time |
| Graphs | Travel graphs and comparing lines |
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.
ACER doesn't publish how many questions each part has. Our selective entry practice tests run the whole sitting under the real time, with counts of our own design. Afterwards you'll see results by skill, so you know which kinds of question cost the most marks.
ACER suggests a child who is stuck should make an informed guess and come back to it at the end if there is time. It also says half the questions correct is not unusual, so a hard question is no reason to panic. For the part as a whole, see VIC selective entry mathematics.
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.