Number questions test whole numbers without a calculator, and a factor pair or known square beats a long written sum. Your child is tested at their current year level, and each school selects its own test date.
Whole numbers themselves: how they are built and how they behave. Numbers is the first area in Edutest's description of Mathematics: year-level maths: numbers, measurement, algebra, space and data.
Our questions are written for children in Years 6–7 applying for Year 7 or 8. At that level, it means school knowledge put to work: place value, the four operations with large numbers, primes, factors, multiples and square numbers. Square roots and negative numbers come in around Year 6 or 7.
In our questions, a plain sum is the exception: expect a fact to use, or a count of the numbers that fit a rule. The facts in the table below are worth knowing cold.
Try primes until the prime squared is bigger than the number
Deciding quickly whether a number is prime
Squares up to 225
Every square from 1 to 225
Factor pairs, areas and square roots
Factor pairs
Factors come in pairs that multiply to the number
Counting every factor without missing any
How should your child work a number question?
Pause before calculating, and look for what the question hands over. A given fact or a pairing turns a long sum into a short one, which matters when every minute counts.
Read exactly what is asked
A number, how many numbers, or which one? Answering a different question is an easy slip to make.
Use the fact you are given
A product like 45 squared, or a total up to 40, is there to be used. Ask how the new sum relates to it.
Work in pairs or groups
Factors pair up. A run of numbers can be paired from both ends, or shifted by a fixed amount.
Check with a second method
A rough estimate or a different split catches slips. Some of the worked answers below show one.
Four worked examples
These are in the style of Edutest Mathematics and go from easier to harder. Each one shows the answer and the working. Read them with your child and spot the shortcut each one uses.
Compare shortcuts, not just answers. Ask how your child would have started, then find the step where the working uses the given fact.
Worked explanation 1
Which of these numbers is a prime number?
AA.
51
BB.
69
CC.
71
DD.
119
Answer: C
Answer: C (71)
A prime number has exactly two factors, 1 and itself. 51 = 3 × 17 and 69 = 3 × 23 (their digits add to 6 and 15, both in the 3 times table), and 119 = 7 × 17. 71 cannot be divided exactly by 2, 3, 5 or 7, and 9 × 9 = 81 is already more than 71, so no bigger number needs checking. 71 is prime.
The trap: 119 tempts children because it is odd, does not end in 0 or 5, and its digits add to 11, so it passes the quick tests for 2, 3 and 5. It is 7 × 17.
Why the other options are wrong
A (51): 51 = 3 × 17; its digits add to 6.
B (69): 69 = 3 × 23; its digits add to 15.
D (119): 119 = 7 × 17.
Worked explanation 2
45 × 45 = 2025. Using this fact, work out 46 × 46.
AA.
2026
BB.
2070
CC.
2071
DD.
2116
Answer: D
Answer: D (2116)
46 × 46 is one more 46 than 45 × 46, and 45 × 46 is one more 45 than 45 × 45. So 46 × 46 = 2025 + 45 + 46 = 2116. Check: 40 × 46 + 6 × 46 = 1840 + 276 = 2116.
The trap: 2071 tempts children who add just one extra 46 to 2025. Going from 45 × 45 to 46 × 46 adds an extra 45 and an extra 46.
Why the other options are wrong
A (2026): Adds 1, as if the answer goes up by one when the number does.
B (2070): Adds only one extra 45.
C (2071): Adds only one extra 46.
Worked explanation 3
Mira writes down every factor of 144, writing each number once. How many numbers are on her list?
AA.
13
BB.
14
CC.
15
DD.
16
Answer: C
Answer: C (15)
List the factors in pairs that multiply to 144: 1 × 144, 2 × 72, 3 × 48, 4 × 36, 6 × 24, 8 × 18, 9 × 16 and 12 × 12. That is 8 pairs, but 12 × 12 gives only one number. So there are 7 × 2 + 1 = 15 factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.
The trap: 16 tempts children who find all 8 pairs and double it, writing 12 twice.
Why the other options are wrong
A (13): Misses one pair, such as 9 × 16, and writes 12 once.
B (14): Misses the pair 12 × 12, so 12 is left off the list.
D (16): Doubles the 8 pairs, writing 12 twice.
Worked explanation 4
The whole numbers from 1 to 40 add up to 820. What do the whole numbers from 41 to 80 add up to?
AA.
1640
BB.
2420
CC.
2460
DD.
3240
Answer: B
Answer: B (2420)
Each number from 41 to 80 is 40 more than a number from 1 to 40 (41 = 1 + 40, 42 = 2 + 40, and so on up to 80 = 40 + 40). There are 40 of them, so the total is 820 + 40 × 40 = 820 + 1600 = 2420. Check: 1 to 80 adds to 80 × 81 ÷ 2 = 3240, and 3240 − 820 = 2420.
The trap: 1640 tempts children who simply double 820, as if the second forty numbers were the same size as the first forty.
Why the other options are wrong
A (1640): Doubles 820, ignoring that every number is 40 bigger.
C (2460): Adds 41 × 40 = 1640 instead of 40 × 40 = 1600.
D (3240): 3240 is the total of all the numbers from 1 to 80.
What traps should your child watch for?
Each trap below leads to a wrong option that sits right beside the answer. If your child picks one, name the slip together, then check for it on the next few number questions.
A number that looks prime. 119 is odd, doesn't end in 5 and isn't divisible by 3, yet it is 7 × 17. Always try 7 before deciding.
A square root counted twice. When a number is a square, its square root pairs with itself. For 144, the pair twelve times twelve adds one factor to the list, not two.
Changing only one side. Going from 45 squared to 46 squared adds a 45 and a 46. Adding a single 46 lands on a tempting wrong option.
Scaling the wrong thing. The numbers from 41 to 80 are each bigger than the numbers from 1 to 40, so their total isn't simply double.
Why does mental arithmetic matter so much?
Because there is nothing to lean on: Edutest doesn't allow calculators, rulers, dictionaries, working-out paper, mobile phones, smart watches and fitness trackers. If a number question feels slow, look for a quicker route before pushing on.
Split numbers so that each part is easy. 24 × 375 is 3 × (8 × 375), and 8 × 375 is 3000. In the same way, 46 squared is 40 × 46 plus 6 × 46.
Knowing that 25 × 4 = 100 and 125 × 8 = 1000 saves time again and again. Estimating first matters as much: when the options are far apart, a rough answer can rule some out before any exact working, and it flags a slip straight away.
How do number skills link to the rest of the test?
Number sits under almost every other maths skill. Simplifying fractions needs factors, pattern questions need multiples, and counting outcomes in probability is careful number work. Time lost here is lost across the whole paper.
It also overlaps with Edutest's Numerical Reasoning test, which covers series, matrices, arithmetical reasoning and deduction. Those questions use number to test reasoning rather than school knowledge; the number series page covers that side.
Turn number plates and house numbers into quick questions: is it prime, what are its factors, which tables is it in? A few minutes a day builds the instinct the test rewards. Learn the square numbers up to 225 until they come without thinking.
In the app, the Number lesson has an Interactive version and Notes. There are also drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest. For worked examples from every skill, see the maths sample questions page.
Four questions show the method; the Mathematics section of Practice test 1 shows whether your child can use it against the clock. Afterwards, results by skill show whether number is the area costing marks.
