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
Which percentage is the same as 1/4?
Show the worked answer
Answer: D, 25%
How to work it out
Per cent means out of 100.
1/4 of 100 is 25, so 1/4 = 25%.
Why the other options are wrong
A (10%): 10% means 10 out of 100, which is not the same as 1/4.
B (50%): 50% means 50 out of 100, which is not the same as 1/4.
C (75%): 75% means 75 out of 100, which is not the same as 1/4.
E (40%): 40% means 40 out of 100, which is not the same as 1/4.
Question 2Aim for about 60 seconds
10% of the players are Year 6, and 50% of those are wearing glasses. What percentage of all the players are Year 6 and wearing glasses?
Show the worked answer
Answer: B, 5%
How to work it out
Take 50% of the 10%: 50% of 10 = 5.
So 5% of all the players.
Why the other options are wrong
A (10%): 10% is all the Year 6 players, including those who are not wearing glasses.
C (50%): 50% is the share of the Year 6 players only, not of all the players.
D (60%): This adds the percentages; the second group is a part of the first, so take 50% of 10%.
E (40%): This takes one percentage from the other; the second is a share of the first, not a separate group.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
What is 25% of 783,000?
Show the worked answer
Answer: A, 195,750
How to work it out
10% of 783,000 is 78,300.
Build 25% from that: 195,750.
Why the other options are wrong
B (587,250): This is what is left after taking 25% away.
C (31,320): This divides by 25 instead of finding 25 hundredths.
D (1,957,500): This is ten times too big: the answer has one digit too many.
E (78,300): This is 10%, not 25%.
Question 4Aim for about 60 seconds
Which list is in order from smallest to largest?
18 0.2 15%
Show the worked answer
Answer: E, 18, 15%, 0.2
How to work it out
Change them all to the same form, such as decimals: 18 = 0.125, 0.2 = 0.2, 15% = 0.15.
Smallest to largest: 18, 15%, 0.2.
Why the other options are wrong
A (0.2, 18, 15%): In this order 0.2 comes first, right before 18, but 0.2 is bigger than 18 = 0.125.
B (15%, 18, 0.2): In this order 15% comes first, right before 18, but 15% = 0.15 is bigger than 18 = 0.125.
C (18, 0.2, 15%): In this order 0.2 comes second, right before 15%, but 0.2 is bigger than 15% = 0.15.
D (0.2, 15%, 18): This list is in order from largest to smallest, the wrong way round.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
Which list is in order from smallest to largest?
25 0.45 35%
Show the worked answer
Answer: B, 35%, 25, 0.45
How to work it out
Change them all to the same form, such as decimals: 25 = 0.4, 0.45 = 0.45, 35% = 0.35.
Smallest to largest: 35%, 25, 0.45.
Why the other options are wrong
A (25, 0.45, 35%): In this order 0.45 comes second, right before 35%, but 0.45 is bigger than 35% = 0.35.
C (0.45, 35%, 25): In this order 0.45 comes first, right before 35%, but 0.45 is bigger than 35% = 0.35.
D (25, 35%, 0.45): In this order 25 comes first, right before 35%, but 25 = 0.4 is bigger than 35% = 0.35.
E (0.45, 25, 35%): This list is in order from largest to smallest, the wrong way round.
Question 6Aim for about 60 seconds
What is 35% of 337,000?
Show the worked answer
Answer: D, 117,950
How to work it out
10% of 337,000 is 33,700.
Build 35% from that: 117,950.
Why the other options are wrong
A (9628.57143): This divides by 35 instead of finding 35 hundredths.
B (1,179,500): This is ten times too big: the answer has one digit too many.
C (33,700): This is 10%, not 35%.
E (219,050): This is what is left after taking 35% away.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Which is larger
25% of 80 or 20% of 110?
Exam standard
Question 7Aim for about 60 seconds
Which is larger: 10% of 160 or 50% of 200?
Show the worked answer
Answer: A, 50% of 200, which is 100 against 16
How to work it out
Work both out.
10% of 160 = 16.
50% of 200 = 100.
So the larger is 50% of 200, which is 100 against 16.
Why the other options are wrong
B (50% of 200, because 200 is the bigger number): A percentage of a bigger number is not always more; it depends on the percentage too.
C (10% of 160, which is 16 against 100): The two amounts are worked out correctly here but the smaller one has been chosen.
D (They are equal): They are not equal: 10% of 160 is 16 and 50% of 200 is 100.
E (50% of 200, because 50 is the bigger percentage): A bigger percentage of a smaller number can be less; work both amounts out.
Up then down
A price rises by 20% then falls by 20%: where does it end?
Exam standard
Question 8Aim for about 60 seconds
A game costs £400. Its price goes up by 25%, then the new price is cut by 25%. How does the final price compare with the start?
Show the worked answer
Answer: C, 6.25% lower than the start
How to work it out
Up 25%: £400 becomes £500.
Down 25% of £500: £500 becomes £375. £375 is 6.25% lower than the start, £400.
Why the other options are wrong
A (25% lower than the start): The fall is 25% of the raised price, not of the start; the overall change is smaller than 25%.
B (25% higher than the start): The fall undoes the rise and more; the price ends lower than it started, not higher.
D (50% lower than the start): The two changes do not add up to a double fall; the rise came first and the fall partly cancels it.
E (The same as the start): The 25% fall is taken from the higher price, so it takes off more than the rise added: £400 rises to £500 and falls to £375.
A percentage of a percentage
40% of the pupils, and half of those: what share of everyone?
Exam standard
Question 9Aim for about 60 seconds
60% of the members are Year 6, and 25% of those are left-handed. What percentage of all the members are Year 6 and left-handed?
Show the worked answer
Answer: D, 15%
How to work it out
Take 25% of the 60%: 25% of 60 = 15.
So 15% of all the members.
Why the other options are wrong
A (85%): This adds the percentages; the second group is a part of the first, so take 25% of 60%.
B (25%): 25% is the share of the Year 6 members only, not of all the members.
C (60%): 60% is all the Year 6 members, including those who are not left-handed.
E (35%): This takes one percentage from the other; the second is a share of the first, not a separate group.
Percentage change
From 40 to 50 is what percentage increase?
Exam standard
Question 10Aim for about 60 seconds
A sunflower grows from 50 cm to 70 cm. What is the percentage increase?
Show the worked answer
Answer: C, 40%
How to work it out
The increase is 20.
As a fraction of the start, 20/50 = 40%.
Why the other options are wrong
A (70%): 70 is the new amount, not the change.
B (20%): 20 is the increase itself, not the percentage; divide it by the starting amount.
D (140%): This is the new amount as a percentage of the old; the increase is that less 100.
E (29%): This divides the increase by the new amount; a percentage increase is out of the starting amount.
Which method works
Without a calculator, which way finds 15% of 60?
Exam standard
Question 11Aim for about 60 seconds
Without a calculator, which is a correct way to find 35% of 140?
Show the worked answer
Answer: E, 25% of 140 plus 10% of 140
How to work it out
35% = 25% plus 10%, so 25% of 140 plus 10% of 140: find a quarter and a tenth, and add them.
That gives 49.
Why the other options are wrong
A (140 − 35): Taking 35 away from 140 ignores that a percentage is a share, not a number to subtract.
B (35 × 140): Multiplying by 35 gives 35 times the amount, not 35 hundredths of it.
C (10% of 140 three times): That combination does not make 35%; check that the parts add or subtract to 35.
D (140 ÷ 35): Dividing by 35 does not give 35%; 35% means 35 out of every 100.
The rest
If 45% chose tea and 30% coffee, how many chose neither?
Exam standard
Question 12Aim for about 60 seconds
120 people were asked. 30% chose football and 30% chose the red team. The rest chose neither. How many chose neither?
Show the worked answer
Answer: E, 48
How to work it out
30% + 30% = 60%, so 40% chose neither.
40% of 120 = 48.
Why the other options are wrong
A (40): 40 is the percentage who chose neither, not the number of people.
B (72): This is the number who chose football or the red team, not the rest.
C (58): This is 10 more than the correct answer, so the tens column is out. Recheck the working.
D (36): This is the number who chose football only.
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