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
What is 313 as an improper fraction?
Show the worked answer
Answer: C, 103
How to work it out
Each whole is 33, so 3 wholes are 93.
Add the 13: 9 + 1 = 10, giving 103.
Why the other options are wrong
A (13): This drops the whole number altogether.
B (93): This leaves out the 13.
D (43): This just adds the whole number to the top. Each whole is worth 3 parts, not 1.
E (63): This multiplies the whole number by the top instead of by the bottom.
Question 2Aim for about 60 seconds
Which fraction is the smallest?
Show the worked answer
Answer: B, 1/10
How to work it out
With 1 on top, the more pieces the whole is cut into, the smaller each piece.
10 is the largest bottom number, so 1/10 is the smallest.
Why the other options are wrong
A (1/6): 1/6 is bigger than 1/10: a whole cut into 6 pieces has bigger pieces than one cut into 10.
C (1/8): 1/8 is bigger than 1/10: a whole cut into 8 pieces has bigger pieces than one cut into 10.
D (1/5): 1/5 is bigger than 1/10: a whole cut into 5 pieces has bigger pieces than one cut into 10.
E (1/2): 1/2 is bigger than 1/10: a whole cut into 2 pieces has bigger pieces than one cut into 10.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
What is 2/3 of 21?
Show the worked answer
Answer: E, 14
How to work it out
Divide by the bottom number, then multiply by the top: 21 ÷ 3 = 7, and × 2 = 14.
Why the other options are wrong
A (4): This is 10 less than the correct answer, so the tens column is out. Recheck the working.
B (21): This is 3/3 of 21: one 1/3 too many.
C (7): This is only 1/3 of 21; it still needs multiplying by 2.
D (24): This is 10 more than the correct answer, so the tens column is out. Recheck the working.
Question 4Aim for about 60 seconds
Work out:
58 − 14
Show the worked answer
Answer: B, 38
How to work it out
Make the bottom numbers the same.
4 × 2 = 8, so 14 = 28.
Then 58 − 28 = 38.
Why the other options are wrong
A (432): This multiplies the bottom numbers without changing the tops to match.
C (48): This takes away 1 twelfths-style parts without changing 14 to match the bottom number 8.
D (78): This adds the fractions instead of subtracting.
E (44): This subtracts the bottom numbers too. Only the top numbers are subtracted, once the bottoms match.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
Priya ran 115 km, Ben ran 2310 km and Hamza ran 94 km. Which distance is the smallest?
Show the worked answer
Answer: D, 115
How to work it out
Change each to a decimal (or to twentieths): 115 = 2.2, 2310 = 2.3, 94 = 2.25.
The smallest is 115.
Why the other options are wrong
A (94): 94 = 2.25, which is bigger than 2.2. A bigger bottom number does not make the fraction smaller when the tops differ.
B (135): 135 km is not one of the three distances in the question.
C (125): 125 km is not one of the three distances in the question.
E (2310): 2310 = 2.3, which is bigger than 2.2. A bigger bottom number does not make the fraction smaller when the tops differ.
Question 6Aim for about 60 seconds
What is 225 as an improper fraction?
Show the worked answer
Answer: E, 125
How to work it out
Each whole is 55, so 2 wholes are 105.
Add the 25: 10 + 2 = 12, giving 125.
Why the other options are wrong
A (45): This just adds the whole number to the top. Each whole is worth 5 parts, not 1.
B (105): This leaves out the 25.
C (25): This drops the whole number altogether.
D (95): This multiplies the whole number by the top instead of by the bottom.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Between two fractions
Which fraction lies between a third and a half?
Exam standard
Question 7Aim for about 60 seconds
Which fraction lies between 7/12 and 2/3?
Show the worked answer
Answer: E, 5/8
How to work it out
Give them the same denominator or turn them into decimals.
7/12 = 0.58, 5/8 = 0.63, 2/3 = 0.67, so 5/8 sits between them.
Why the other options are wrong
A (1/4): 1/4 is less than 7/12, so it is below the range.
B (1/6): 1/6 is less than 7/12, so it is below the range.
C (5/12): 5/12 is less than 7/12, so it is below the range.
D (1/5): 1/5 is less than 7/12, so it is below the range.
Of what is left
A quarter of the money, then a third of what remains.
Exam standard
Question 8Aim for about 60 seconds
Aisha has £20. Aisha spends 1/2 of it on a book, then 1/2 of what is left on a pen. How much is left?
Show the worked answer
Answer: D, £5
How to work it out
1/2 of £20 is £10, leaving £10.
1/2 of £10 is £5, leaving £5.
Why the other options are wrong
A (£15): This is the total spent, not what is left.
B (£4): This is £1 less than the correct answer, so the last step of the working is out by one.
C (£0): This takes 1/2 of the whole £20 for a pen; the second fraction is of what was left, £10.
E (£10): £10 is what was left after a book only; a pen still has to come off.
The one that is not equivalent
Four fractions equal two thirds; one does not.
Exam standard
Question 9Aim for about 60 seconds
Which of these is NOT equivalent to 2/5?
Show the worked answer
Answer: B, 13/30
How to work it out
Equivalent fractions multiply top and bottom by the same number.
13/30 has the bottom multiplied by 6 but the top is 13, not 12.
Why the other options are wrong
A (2/5): 2/5 is the fraction itself; the question asks for the one that is not equal to it.
C (10/25): 10/25 is 2/5 with both parts multiplied by 5, so it is equivalent.
D (4/10): 4/10 is 2/5 with both parts multiplied by 2, so it is equivalent.
E (16/40): 16/40 is 2/5 with both parts multiplied by 8, so it is equivalent.
What is left in the jug
Two pours from a full jug: what fraction remains?
Exam standard
Question 10Aim for about 60 seconds
A jug is full. 6/12 of it is poured out, then 1/4 of the whole jug. What fraction of the jug is left?
Show the worked answer
Answer: C, 1/4
How to work it out
Out of 12 equal parts, 6 + 3 = 9 are poured out, leaving 3/12 = 1/4.
Why the other options are wrong
A (1/2): 1/2 is what was left after the first pour only; the second pour still has to come off.
B (1/3): One part too many is left; add the two pours carefully before subtracting.
D (3/24): The denominator stays 12; the parts of the jug do not double when you subtract.
E (3/4): 3/4 is the amount poured out, not the amount left.
Largest of fractions, decimals and percentages
Compare 0.6, a half and 55%.
Exam standard
Question 11Aim for about 60 seconds
Which is the largest: 3/4, 0.9, 65%, 70%, 0.35?
Show the worked answer
Answer: B, 0.9
How to work it out
Turn each into a decimal: 3/4 = 0.75, 0.9 = 0.9, 65% = 0.65, 70% = 0.7, 0.35 = 0.35.
The largest is 0.9.
Why the other options are wrong
A (3/4): 3/4 is 0.75 as a decimal, which is less than 0.9 (0.9).
C (65%): 65% is 0.65 as a decimal, which is less than 0.9 (0.9).
D (70%): 70% is 0.7 as a decimal, which is less than 0.9 (0.9).
E (0.35): 0.35 is less than 0.9, which is 0.9 as a decimal.
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