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
7 oranges cost 56p. How much do 8 oranges cost?
Show the worked answer
Answer: A, 64p
How to work it out
One orange costs 56p ÷ 7 = 8p, so 8 oranges cost 8 × 8p = 64p.
Why the other options are wrong
B (56p): This multiplies the two numbers of items, 8 × 7, and ignores the price.
C (63p): This is 1p less than the correct answer, so the last step of the working is out by one.
D (54p): This is 10p less than the correct answer, so the tens column is out. Recheck the working.
E (72p): This is the cost of 9, one too many.
Question 2Aim for about 60 seconds
6 pencils cost 42p. How much do 4 pencils cost?
Show the worked answer
Answer: E, 28p
How to work it out
One pencil costs 42p ÷ 6 = 7p, so 4 pencils cost 4 × 7p = 28p.
Why the other options are wrong
A (46p): This adds 4 to the cost of 6; find the cost of one first.
B (14p): This is half the correct answer, 28p. Check whether you halved when you should not have.
C (35p): This is the cost of 5, one too many.
D (24p): This multiplies the two numbers of items, 4 × 6, and ignores the price.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
A recipe for 4 people uses 150 g of flour. How much flour is needed for 6 people?
Show the worked answer
Answer: B, 225 g
How to work it out
Flour for one person: 150 ÷ 4 = 37.5 g.
For 6 people: 37.5 × 6 = 225 g.
Why the other options are wrong
A (300 g): This is double the recipe, but 6 people is 1.5 times 4 people.
C (226 g): This is 1 g more than the correct answer, so the last step of the working is out by one.
D (156 g): This adds the 6 people to the flour; find the flour for one person first.
E (275 g): This is 50 g too much; check the multiplication.
Question 4Aim for about 60 seconds
On a map, 1 cm stands for 10 km. Two villages are 9.5 cm apart on the map. How far apart are they in real life?
Show the worked answer
Answer: D, 95 km
How to work it out
Each centimetre is 10 km, so 9.5 cm is 9.5 × 10 = 95 km.
Why the other options are wrong
A (0.95 km): This divides by the scale; it should multiply.
B (90 km): The half centimetre has been left out.
C (950 km): One zero too many.
E (19.5 km): This adds the numbers; each centimetre is worth the scale.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
1 kg is about 2.2 lbs. About how many kilograms are there in 13.2 lbs?
Show the worked answer
Answer: D, 6 kg
How to work it out
Each kilogram is 2.2 lbs, so divide: 13.2 ÷ 2.2 = 6.
Check: 6 × 2.2 = 13.2.
Why the other options are wrong
A (5 kg): 5 kg is about 11 lbs, not 13.2. Multiply back by 2.2 to check.
B (29 kg): This multiplies by 2.2 again. Changing pounds to kilograms makes the number smaller.
C (11 kg): This takes away 2.2 instead of dividing by it.
E (7 kg): 7 kg is about 15 lbs, not 13.2. Multiply back by 2.2 to check.
Question 6Aim for about 60 seconds
Priya and Grace share £99 in the ratio 5 : 6. How much does Grace get?
Show the worked answer
Answer: B, £54
How to work it out
There are 5 + 6 = 11 parts.
One part is £99 ÷ 11 = £9.
Grace gets 6 parts: 6 × £9 = £54.
Why the other options are wrong
A (£9): This is the value of one part; Grace gets 6 parts.
C (£27): This is half the correct answer, £54. Check whether you halved when you should not have.
D (£50): This shares the money equally, but the ratio is 5 : 6.
E (£45): This is Priya's share (5 parts), not Grace's.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Simplest form
Write a ratio with the smallest whole numbers.
Exam standard
Question 7Aim for about 60 seconds
Write the ratio 35 : 42 in its simplest form.
Show the worked answer
Answer: C, 5 : 6
How to work it out
Divide both parts by their highest common factor, 7: 35 ÷ 7 = 5 and 42 ÷ 7 = 6, giving 5 : 6.
Why the other options are wrong
A (6 : 7): Adding or taking away the same number from both parts changes the ratio; only dividing both by the same factor keeps it.
B (1 : 7): This takes the difference between the numbers; a ratio is found by dividing both by the same factor, not subtracting.
D (6 : 5): The parts are the right size but the wrong way round; keep the order of the question.
E (5 : 11): This compares the first part with the whole (35 out of 77); a ratio compares part with part.
Which mix is stronger
Two squashes mixed in different ratios: which tastes stronger?
Exam standard
Question 8Aim for about 60 seconds
Squash A mixes cordial and water in the ratio 3 : 4. Squash B mixes them 3 : 9. Which tastes stronger?
Show the worked answer
Answer: D, Squash A: cordial is 43% of it against 25%
How to work it out
Find cordial as a share of the whole.
A: 3 of 7 parts, 43%.
B: 3 of 12 parts, 25%.
The bigger share is stronger.
Why the other options are wrong
A (They taste the same): They are not the same: 3 out of 7 is 43% cordial and 3 out of 12 is 25%.
B (Squash B, because it has more parts of cordial): More parts of cordial means nothing on its own; 3 parts in a lot of water can be weaker than fewer parts in less water.
C (Squash A, because it has less water): Less water on its own does not settle it; what matters is cordial as a share of the whole drink.
E (Squash B: cordial is 25% of it against 43%): The fractions are the right way round in the words but the conclusion is backwards: the bigger share of cordial is the stronger drink.
What must be true of a ratio
A class is 3 to 4: what is certain, and what only could be?
Exam standard
Question 9Aim for about 60 seconds
In a class the ratio of boys to girls is 3 : 5. Which statement must be true?
Show the worked answer
Answer: A, The number of pupils is a multiple of 8
How to work it out
Think of the class as groups of 8: 3 boys and 5 girls in each.
The exact numbers are unknown, but the number of pupils is a multiple of 8 whatever the class size.
Why the other options are wrong
B (Boys make up 3/5 of the class): 3/5 compares boys with girls, not boys with the whole class; boys are 3/8 of the class.
C (There are more boys than girls): For every 3 boys there are 5 girls, and 5 is more than 3.
D (There are exactly 3 boys): 3 : 5 is only the proportion; there could be 6 boys and 10 girls, or 9 and 15.
E (There are 8 pupils in the class): 8 is the smallest possible class; any multiple of 8 fits the ratio.
Map scales
Centimetres on the map to kilometres on the ground.
Exam standard
Question 10Aim for about 60 seconds
A map has a scale of 1 : 100,000. Two villages are 6 cm apart on the map. How far apart are they really, in kilometres?
Show the worked answer
Answer: E, 6 km
How to work it out
1 cm on the map is 100,000 cm on the ground.
6 × 100,000 = 600,000 cm.
There are 100,000 cm in a kilometre, so that is 6 km.
Why the other options are wrong
A (16 km): This is 10 km more than the correct answer, so the tens column is out. Recheck the working.
B (60 km): Ten times too far: check the change from centimetres to kilometres (100,000 cm in a km).
C (1 km): Ten times too close: check the change from centimetres to kilometres.
D (600 km): A hundred times too far: there are 100,000 cm in a kilometre, not 1,000.
Best buy
Two pack sizes, two prices: which is better value?
Exam standard
Question 11Aim for about 60 seconds
Pack A has 5 bars for £1.05. Pack B has 10 bars for £1.30. Which is better value?
Show the worked answer
Answer: B, Pack B: 13p each against 21p
How to work it out
Work out the cost of one.
A: £1.05 ÷ 5 = 21p.
B: £1.30 ÷ 10 = 13p.
The lower cost for one is the better value.
Why the other options are wrong
A (They are the same value): They are not: £1.05 ÷ 5 = 21p and £1.30 ÷ 10 = 13p.
C (Pack B, because it has more bars): More in the pack is not better value on its own; the pack with more may cost more for each one.
D (Pack A, because it costs less): Cheaper overall is not better value when it holds fewer bars; compare the cost of one.
E (Pack A: 21p each against 13p): The prices for one are the wrong way round: the lower price for one is the better value.
From a fraction to a ratio
If three fifths are boys, what is boys to girls?
Exam standard
Question 12Aim for about 60 seconds
In a class, 6/7 of the pupils are boys. What is the ratio of boys to girls?
Show the worked answer
Answer: B, 6 : 1
How to work it out
If 6 of every 7 pupils are boys, the other 1 are girls, so boys : girls = 6 : 1.
Why the other options are wrong
A (6 : 7): 6/7 compares boys with the whole class; the ratio asked for compares boys with girls, who are the other 1 of every 7.
C (6 : 13): Adding the numerator to the denominator does not give the girls; girls are 7 take away 6.
D (7 : 6): This puts the whole class against the boys; a ratio of boys to girls compares the two groups.
E (1 : 6): This is girls to boys; the question asks for boys to girls, so the boys come first.
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