Every question here is written by Prism in the style of the tests. None is copied from a real paper, and a fresh one is drawn each time a child practises.
From foundation to exam standard
Two questions at each level. Tap an option to check it.
Foundation where a child in Year 3 or 4 starts
Question 1Aim for about 60 seconds
One number is in the wrong place in this Venn diagram. Which one?
Show the worked answer
Answer: E, 26
How to work it out
Check every number against both labels.
26 is not a square number and an even number, so it belongs in the “even numbers” circle only, not in the “square numbers” circle only.
Why the other options are wrong
A (9): 9 is correctly placed in the “square numbers” circle only.
B (8): 8 is correctly placed in the “even numbers” circle only.
C (16): 16 is correctly placed in both circles.
D (4): 4 is correctly placed in both circles.
Question 2Aim for about 60 seconds
Which whole number is closest to the square root of 50?
Show the worked answer
Answer: D, 7
How to work it out
7² = 49 and 8² = 64, so the square root of 50 lies between 7 and 8, nearer 7 because 50 is nearer 49.
Why the other options are wrong
A (13): Quartering is not finding a square root.
B (25): Halving is not finding a square root.
C (49): 49 is the square, not the root.
E (8): 8² = 64, which is further from 50 than 7² = 49.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
Which whole number is closest to the square root of 147?
Show the worked answer
Answer: C, 12
How to work it out
12² = 144 and 13² = 169, so the square root of 147 lies between 12 and 13, nearer 12 because 147 is nearer 144.
Why the other options are wrong
A (13): 13² = 169, which is further from 147 than 12² = 144.
B (144): 144 is the square, not the root.
D (37): Quartering is not finding a square root.
E (74): Halving is not finding a square root.
Question 4Aim for about 60 seconds
Which of these numbers is a common factor of 90 and 72?
Show the worked answer
Answer: C, 3
How to work it out
A common factor divides into both exactly: 90 ÷ 3 = 30 and 72 ÷ 3 = 24.
Why the other options are wrong
A (8): 8 is a factor of 72 but not of 90.
B (5): 5 is a factor of 90 but not of 72.
D (12): 12 is a factor of 72 but not of 90.
E (10): 10 is a factor of 90 but not of 72.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
Which of these numbers is a common factor of 60 and 48?
Show the worked answer
Answer: E, 4
How to work it out
A common factor divides into both exactly: 60 ÷ 4 = 15 and 48 ÷ 4 = 12.
Why the other options are wrong
A (5): 5 is a factor of 60 but not of 48.
B (24): 24 is a factor of 48 but not of 60.
C (8): 8 is a factor of 48 but not of 60.
D (10): 10 is a factor of 60 but not of 48.
Question 6Aim for about 60 seconds
Which shows 45 as a product of prime numbers?
Show the worked answer
Answer: B, 3 × 3 × 5
How to work it out
Keep dividing by the smallest prime that works: 45 = 3 × 3 × 5.
Every number in the answer must be prime; 1 is not prime.
Why the other options are wrong
A (3 × 3 × 7): Changing 5 to 7 means the product is no longer 45.
C (1 × 3 × 3 × 5): 1 is not a prime number, so it must not appear in the product.
D (3 × 15): 15 is not prime, so it still needs splitting into primes.
E (9 × 5): 9 is not prime: it is 3 × 3.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
What must be true of a number
A multiple of 4 and of 6 must be a multiple of what?
Exam standard
Question 7Aim for about 60 seconds
A whole number is a multiple of 6 and a multiple of 8. Which statement must be true?
Show the worked answer
Answer: C, It is a multiple of 24
How to work it out
The lowest common multiple of 6 and 8 is 24, and every common multiple is a multiple of 24.
Why the other options are wrong
A (It is 24): 24 is the smallest such number, but 48 and 72 also work.
B (It is a factor of 24): Multiples of 24 such as 48 are not factors of 24.
D (It is odd): Every multiple of 6 is even.
E (It is a multiple of 48): 24 is a multiple of both 6 and 8 but not of 48; the lowest common multiple is 24, not 48.
How many factors
Count every factor of 36 without missing one.
Exam standard
Question 8Aim for about 60 seconds
How many factors does 64 have?
Show the worked answer
Answer: D, 7
How to work it out
The factors of 64 are 1, 2, 4, 8, 16, 32, 64: 7 of them.
Pairing them (1 × 64, 2 × 32, and so on) makes sure none are missed.
Why the other options are wrong
A (32): This is half the number, not the number of its factors.
B (6): One short: 1 and the number itself are both factors, and one is easily missed.
C (8): One too many: check that each number really divides exactly.
E (5): Two short: factors come in pairs, so list them as pairs to catch them all.
Tell without dividing
How can you tell 4,572 is divisible by 3?
Exam standard
Question 9Aim for about 60 seconds
Without dividing, how can you tell that 2,292 is divisible by 4?
Show the worked answer
Answer: C, Its last two digits, 92, make a multiple of 4
How to work it out
Its last two digits, 92, make a multiple of 4.
Why the other options are wrong
A (It ends in 2): The last digit tells you about 2, 5 and 10, not about 4.
B (Its first digit is 2): The first digit alone tells you nothing about divisibility.
D (It has 4 digits): The number of digits says nothing about its factors.
E (It is even): Being even says nothing about dividing by 4.
Nearest square root
Which whole number is closest to the square root of 50?
Exam standard
Question 10Aim for about 60 seconds
Which whole number is closest to the square root of 140?
Show the worked answer
Answer: B, 12
How to work it out
11² = 121 and 12² = 144, so the square root of 140 lies between 11 and 12, nearer 12 because 140 is nearer 144.
Why the other options are wrong
A (11): 11² = 121, which is further from 140 than 12² = 144.
C (70): Halving is not finding a square root.
D (144): 144 is the square, not the root.
E (35): Quartering is not finding a square root.
Consecutive numbers
Two numbers next to each other multiply to 132.
Exam standard
Question 11Aim for about 60 seconds
Two consecutive whole numbers multiply to make 182. What is the smaller of the two?
Show the worked answer
Answer: B, 13
How to work it out
13 × 14 = 182.
Try squares as a guide: 13² = 169 is just below 182.
Why the other options are wrong
A (15): 15 × 16 = 240, too big.
C (12): 12 × 13 = 156, not 182.
D (91): Halving the product does not give either number.
E (14): 14 is the larger of the pair, not the smaller.
Odd one out
Four numbers share a property; one does not.
Exam standard
Question 12Aim for about 60 seconds
Four of these numbers share a property. Which one does not belong?
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