Edutest Mathematics checks the maths of your child's own year, in 30 minutes and without a calculator. These eight worked questions show the kinds of question it asks, and the slip behind each wrong option.
The maths your child learns at school, asked in a harder way. Mathematics is one of Edutest's Achievement tests, which measure actual achievement in Reading Comprehension, Mathematics and Written Expression. Edutest describes it as year-level maths: numbers, measurement, algebra, space and data.
Children are tested at their current year level, so the content is your child's own year. The questions are still written to stretch strong students: Edutest says most students get only half the questions right.
The area names are Edutest's own. The split into skills is ours, so each question points to one skill page with more worked examples.
Primes, factors, multiples and mental multiplication
Numbers
Fractions, decimals and percentages
A fraction or percentage of an amount
Numbers
Algebra and patterns
A rule for a pattern, or an expression from words
Algebra
Measurement and time
Mass, area, volume and time
Measurement
Geometry
Angles, shapes and solids
Space
Data and chance
Graphs, averages and probability
Data
Eight sample questions with answers
Each question shows the answer and the working. Read them with your child and talk through why the right option is right.
We wrote these in the style of Edutest Mathematics, for a strong student in Year 6 or 7. None of them comes from an Edutest paper, and they run roughly from easier to harder.
Worked explanation 1
At a concert, 240 singers stand on risers in rows of 12. Just before the start, 5 of the rows are taken away, and the singers from those rows spread out equally across the rows that are left. How many singers are now in each row?
AA.
16
BB.
17
CC.
20
DD.
60
Answer: A
Answer: A (16)
At the start there are 240 ÷ 12 = 20 rows. Taking away 5 rows leaves 15 rows. All 240 singers still need a place, so 240 ÷ 15 = 16 singers in each row. Check: the 60 singers who moved add 60 ÷ 15 = 4 to each row of 12, and 12 + 4 = 16.
The trap: 17 is the quick guess of 12 + 5, as if each removed row added one singer to every other row. Only 60 singers move, and they are shared among 15 rows, so each row gains 4.
Why the other options are wrong
B (17): Adds the 5 removed rows to 12 instead of sharing out the singers who moved.
C (20): 20 is the number of rows at the start, not the number of singers in a row.
D (60): 60 is how many singers had to move, not how many are in each row.
Worked explanation 2
In a pottery class of 25 students, 40% are making bowls, one-fifth are making cups, and the rest are making vases. How many students are making vases?
AA.
5
BB.
10
CC.
15
DD.
16
Answer: B
Answer: B (10)
40% of 25 is 0.4 × 25 = 10 students making bowls. One-fifth of 25 is 5 students making cups. That accounts for 10 + 5 = 15 students, so 25 − 15 = 10 are making vases.
The trap: 15 tempts children who take away the bowl-makers (25 − 10 = 15) and forget to take away the cup-makers as well.
Why the other options are wrong
A (5): 5 is the number making cups, not vases.
C (15): Only the 10 bowl-makers have been taken away from 25.
D (16): Treats 40% of 25 as 4, then works out 25 − 4 − 5 = 16.
Worked explanation 3
Ella makes a pattern of figures from square tiles. The table shows how many tiles each of the first four figures uses: Figure 1 uses 6, Figure 2 uses 10, Figure 3 uses 14 and Figure 4 uses 18. If the pattern keeps going in the same way, which figure uses exactly 162 tiles?
Figure
Tiles used
1
6
2
10
3
14
4
18
AA.
Figure 27
BB.
Figure 38
CC.
Figure 40
DD.
Figure 41
Answer: C
Answer: C (Figure 40)
Each figure uses 4 more tiles than the one before, and Figure 1 uses 6 = 4 × 1 + 2. So Figure n uses 4 × n + 2 tiles. For 162 tiles: 4 × n = 162 − 2 = 160, so n = 40. Check: 4 × 40 + 2 = 162. The answer is Figure 40.
The trap: Figure 41 comes from dividing 162 by 4 (40.5) and rounding up, forgetting that every figure has 2 extra tiles on top of the fours.
Why the other options are wrong
A (Figure 27): Divides 162 by 6, as if every figure used 6 tiles.
B (Figure 38): Works out (162 − 10) ÷ 4 = 38 jumps of 4 after Figure 2, then forgets to add them on to Figure 2 (2 + 38 = 40).
D (Figure 41): Divides 162 by 4 and rounds up, ignoring the + 2.
Worked explanation 4
A rectangular garden bed is 9 m long and 5 m wide. Omar uses exactly the same length of edging to make a square garden bed instead. How many more square metres of garden does the square bed have than the rectangular bed?
AA.
0 m²
BB.
4 m²
CC.
14 m²
DD.
49 m²
Answer: B
Answer: B (4 m²)
The edging is the perimeter: 9 + 5 + 9 + 5 = 28 m. A square with a 28 m perimeter has sides of 28 ÷ 4 = 7 m, so its area is 7 × 7 = 49 m². The rectangle's area is 9 × 5 = 45 m². The square has 49 − 45 = 4 m² more.
The trap: 0 m² tempts children who think the same perimeter must give the same area. Shapes with equal perimeters can have different areas.
Why the other options are wrong
A (0 m²): Assumes equal edging means equal area.
C (14 m²): 14 m is half the perimeter (9 + 5), not a difference in area.
D (49 m²): 49 m² is the square's whole area, not how much more it has.
Worked explanation 5
A pentagon (a five-sided shape) has three right angles. Its other two angles are different sizes: one is 30° larger than the other. What is the size of the smaller of these two angles?
AA.
30°
BB.
120°
CC.
135°
DD.
150°
Answer: B
Answer: B (120°)
The angles of any pentagon add to 540°, because lines from one corner split it into three triangles (3 × 180° = 540°). The three right angles use 3 × 90° = 270°, leaving 540° − 270° = 270° for the other two. If they were equal, each would be 135°; one is 30° larger, so take the 30° off and halve what is left: (270° − 30°) ÷ 2 = 120°. Check: 120° + 150° = 270°.
The trap: 30° tempts children who use 360° as the angle total, as for a four-sided shape. That leaves only 90° to split into 30° and 60°. A pentagon's angles add to 540°.
Why the other options are wrong
A (30°): Uses 360° (the total for a four-sided shape) instead of 540°, leaving 90° to split into 30° and 60°.
C (135°): Shares the 270° equally and ignores the 30° difference.
D (150°): 150° is the larger of the two angles, not the smaller.
Worked explanation 6
The column graph shows how many kilograms of food scraps six classes collected for the school compost bins in one week: 3K 12 kg, 4K 8 kg, 4P 15 kg, 5A 9 kg, 5B 14 kg and 6R 8 kg. What is the difference between the mean and the median amount collected?
Food scraps collected in one week (kg)
3K
12
4K
8
4P
15
5A
9
5B
14
6R
8
·
AA.
0.5 kg
BB.
1 kg
CC.
2 kg
DD.
3 kg
Answer: A
Answer: A (0.5 kg)
Total = 12 + 8 + 15 + 9 + 14 + 8 = 66 kg, so the mean is 66 ÷ 6 = 11 kg. In order the amounts are 8, 8, 9, 12, 14, 15. With six values the median is halfway between the 3rd and 4th: (9 + 12) ÷ 2 = 10.5 kg. The difference is 11 − 10.5 = 0.5 kg.
The trap: 2 kg comes from taking 9 kg (the 3rd value) as the median. With an even number of values, the median is halfway between the two middle values.
Why the other options are wrong
B (1 kg): Takes 12 kg, the 4th value, as the median.
C (2 kg): Takes 9 kg, the 3rd value, as the median.
D (3 kg): Compares the mean with the mode (8 kg), not the median.
Worked explanation 7
The lockers in a school corridor are numbered 1 to 100. A sticker goes on every locker whose number is a multiple of 3, except lockers whose number is also a multiple of 5. How many lockers get a sticker?
AA.
6
BB.
13
CC.
26
DD.
27
Answer: D
Answer: D (27)
Multiples of 3 up to 100: 100 ÷ 3 = 33 remainder 1, so there are 33. The ones left out are multiples of both 3 and 5, which are the multiples of 15: 15, 30, 45, 60, 75 and 90, so 6 of them. 33 − 6 = 27 lockers get a sticker.
The trap: 13 tempts children who take away all 20 multiples of 5, instead of only the multiples of 5 that are also multiples of 3.
Why the other options are wrong
A (6): 6 is the number of lockers left out (the multiples of 15).
B (13): Takes away all 20 multiples of 5, most of which never had a sticker.
C (26): Counts 7 multiples of 15 by rounding 100 ÷ 15 up, but 105 is past 100.
Worked explanation 8
Six cards spell the word PEPPER, one letter on each card. Zara takes two of the cards at random at the same time. What is the probability that both cards show the same letter?
AA.
1/15
BB.
2/15
CC.
1/5
DD.
4/15
Answer: D
Answer: D (4/15)
Count pairs of cards. Six cards make 6 × 5 ÷ 2 = 15 different pairs, all equally likely. Matching pairs: the three P cards make 3 pairs, the two E cards make 1 pair, and the single R cannot match. That is 3 + 1 = 4 matching pairs out of 15, so the probability is 4/15.
The trap: 1/5 tempts children who count only the P pairs (3 out of 15) and forget that the two E cards can also match.
Why the other options are wrong
A (1/15): Counts only the E pair.
B (2/15): Finds the 4 matching pairs but divides by 30, counting every pair twice in the total.
C (1/5): Counts only the 3 pairs of P cards.
Each answer shows the working, names the trap behind the most tempting wrong option, and says why every other option is wrong.
How is the Mathematics test run?
On paper, multiple choice, with nothing to help with the arithmetic. Children shade bubbles on a paper answer sheet, and Edutest doesn't allow calculators, rulers, dictionaries, working-out paper, mobile phones, smart watches and fitness trackers.
So every multiplication, division and fraction step happens in your child's head or in pencil. That's why mental methods matter as much as knowing the topic.
Edutest doesn't publish a question count for each year level. Its practice page gives a range: 20 practice questions per test; real tests have 40 to 60.
One habit per kind of question saves the most marks. Teach one at a time, using the matching question above as the example.
Number: look for structure before you calculate
Factor pairs, divisibility rules and known squares turn a long sum into a short one.
Fractions and percentages: find the whole first
If a part is given, work back to the whole, then take the new part of it.
Algebra: find the rule, then test it
In a pattern, find the step between terms and check the rule on the first term.
Measurement: put everything in the same unit
Grams with grams, centimetres with centimetres. Convert before you add or compare.
Geometry: write the angle total down
Triangle, four-sided shape, pentagon: start from the correct total, then subtract what you know.
Data: decide which group the question means
Everyone, or just some? Count that group before you work out an average or a chance.
What mistakes cost the most marks?
Look for the slip behind a wrong answer, not only the topic. The wrong options in a good maths question are the answers children reach by a common slip, and these four come up most often above.
Stopping one step early. In the pottery question, taking away the bowl-makers gives an option on the list. The cup-makers still have to come off.
Assuming a rule that isn't true. A square and a rectangle with the same perimeter don't have the same area, and a pentagon's angles don't add to the same total as a four-sided shape's.
Counting the wrong things. In the lockers question, only the multiples of five that are also multiples of three are left out. In the cards question, the E cards can match too.
The middle of an even list. With an even number of values, the median sits halfway between the two middle values.
Talking through a wrong option
Ask your child which option looked right at first, and which slip would produce it. That conversation teaches more than the right answer does.
How should your child pace the test?
Keep moving, and leave no bubble blank. Edutest says many students will not finish every question, and there are no marks lost for wrong or blank answers.
A question that stalls after a fair try gets a quick estimate and a guess from the options left; your child can come back if time allows. After a skip, check that the next answer goes on the right line of the answer sheet.
Results are compared with thousands of students in the same year level across Australia. So a practice score that looks low may be normal for this test: look at which skills lost the marks, not the total.
Put the calculator away at home. A few mixed questions most days, done in pencil and then talked through, build the mental habits the test needs. Times tables to twelve and the common fraction, decimal and percentage pairs are worth knowing cold.
When your child is ready for the clock, Practice test 1 has a full Mathematics section on Edutest's time. Afterwards you'll see results by skill, so you know which topics cost the most marks. The reasoning tests use number differently, so the Numerical Reasoning sample questions are worth a look too.
See where your child stands
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.
Sample
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.
