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
On the island of Tumbo the coins are pips, toks and muns: 5 pips make 1 tok, and 12 toks make 1 mun. What is 5 toks 2 pips + 2 toks 4 pips? Give the answer with the fewest coins.
Show the worked answer
Answer: A, 8 toks 1 pip
How to work it out
2 + 4 = 6 pips, which is 1 tok and 1 pip.
5 + 2 + 1 = 8 toks.
So the answer is 8 toks 1 pip.
Why the other options are wrong
B (8 toks 6 pips): This adds a tok but keeps all 6 pips; the 5 pips swapped for it must be taken away.
C (7 toks 1 pip): This takes away 5 pips but never adds the tok they make.
D (9 toks 1 pip): This adds one tok too many; only one lot of 5 pips was swapped.
E (7 toks 6 pips): This leaves 6 pips; 5 pips make a tok, so 5 of them must be swapped for a tok.
Question 2Aim for about 60 seconds
Two whole numbers add up to 42, and one is 6 more than the other. What are the two numbers?
Show the worked answer
Answer: B, 18 and 24
How to work it out
Take the difference away and halve: (42 − 6) ÷ 2 = 18.
The other is 18 + 6 = 24.
Check: 18 + 24 = 42.
So the numbers are 18 and 24.
Why the other options are wrong
A (19 and 23): 19 and 23 do not fit: their difference is 4, not 6.
C (17 and 25): 17 and 25 do not fit: their difference is 8, not 6.
D (19 and 25): 19 and 25 do not fit: they add up to 44, not 42.
E (6 and 36): 6 and 36 do not fit: their difference is 30, not 6.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
Look at the pattern in the table. Which line of the pattern starts with 30²?
Line
Calculation
1
3² = 1² + 4 × 2
2
4² = 2² + 4 × 3
3
5² = 3² + 4 × 4
Show the worked answer
Answer: C, 30² = 28² + 4 × 29
How to work it out
In every line the number squared on the right is 2 less than the one on the left, and the number multiplied by 4 is the one in between.
So 30² = 28² + 4 × 29.
Check: 900 = 784 + 116.
Why the other options are wrong
A (30² = 28² + 2 × 29): Every line of the pattern multiplies by 4, not 2.
B (30² = 29² + 4 × 29): The number squared on the right is always 2 less than the one on the left, so 28, not 29.
D (30² = 28² + 4 × 28): The number multiplied by 4 is 1 less than 30, so 29, not 28.
E (30² = 28² + 4 × 30): The number multiplied by 4 is the one between the two squared numbers, 29, not 30.
Question 4Aim for about 60 seconds
Look at the pattern in the table. Which line of the pattern starts with 18²?
Line
Calculation
1
3² = 1² + 4 × 2
2
4² = 2² + 4 × 3
3
5² = 3² + 4 × 4
Show the worked answer
Answer: A, 18² = 16² + 4 × 17
How to work it out
In every line the number squared on the right is 2 less than the one on the left, and the number multiplied by 4 is the one in between.
So 18² = 16² + 4 × 17.
Check: 324 = 256 + 68.
Why the other options are wrong
B (18² = 16² + 4 × 18): The number multiplied by 4 is the one between the two squared numbers, 17, not 18.
C (18² = 16² + 4 × 16): The number multiplied by 4 is 1 less than 18, so 17, not 16.
D (18² = 16² + 2 × 17): Every line of the pattern multiplies by 4, not 2.
E (18² = 17² + 4 × 17): The number squared on the right is always 2 less than the one on the left, so 16, not 17.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
5! (said “five factorial”) is a quick way of writing 5 × 4 × 3 × 2 × 1 = 120. What is 7! ÷ 6!?
A (1): This works out (7 − 6)!; dividing 7! by 6! is not the same as taking 6 from 7 first.
B (5040): This is 7! on its own; it still has to be divided by 6! as well.
C (42): This keeps one factor too many: 6! cancels everything from 6 down to 1, including the 6.
D (8): This is one more than 7 = 7; check the multiplying.
Question 6Aim for about 60 seconds
On the island of Tumbo the coins are pips, toks and muns: 8 pips make 1 tok, and 8 toks make 1 mun. What is 6 toks 3 pips multiplied by 4? Give the answer with the fewest coins.
Show the worked answer
Answer: E, 3 muns 1 tok 4 pips
How to work it out
4 × 3 = 12 pips = 1 tok and 4 pips.
4 × 6 + 1 = 25 toks = 3 muns and 1 tok.
4 × 0 + 3 = 3 muns.
So the answer is 3 muns 1 tok 4 pips.
Why the other options are wrong
A (3 muns 4 pips): This swaps 8 pips away but never adds the toks they make.
B (24 toks 12 pips): This multiplies each part but never swaps 8 pips for a tok or 8 toks for a mun.
C (25 toks 4 pips): This swaps the pips for toks but leaves 25 toks; 8 toks make a mun.
D (4 muns 1 tok 4 pips): This has one mun too many: 25 toks make 3 muns.
Practise straight away at your child’s school year in maths and English, with verbal and non-verbal reasoning for the 11 Plus, and every answer explained. A free check, whenever you like, shows what to practise next and builds a weekly plan, for their year or for your target schools. Parents follow progress free.