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
Calculate 638 + 854.
Show the worked answer
Answer: E, 1,492
How to work it out
Add the ones, then the tens, then the hundreds, carrying when a column passes 9: 1,492.
Why the other options are wrong
A (1,592): This is 100 too big: a carry into the hundreds was counted twice.
B (1,482): This is 10 too small: the carry from the ones into the tens was missed.
C (1,392): This is 100 too small: the carry into the hundreds was missed.
D (1,502): This is 10 more than the correct answer, so the tens column is out. Recheck the working.
Question 2Aim for about 60 seconds
One shelf has 108 books and another has 18. How many altogether? Which calculation gives the answer?
Show the worked answer
Answer: B, 108 + 18
How to work it out
The story puts two amounts together, so add: 108 + 18.
Why the other options are wrong
A (108 + 18 + 18): This uses 18 twice; it appears once in the story.
C (108 − 18): This takes one from the other, but the story does not take anything away.
D (108 ÷ 18): This divides, but the story does not share or split anything.
E (108 × 18): This multiplies, but the story does not have equal groups to count up.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
Calculate:
174 − 66 ÷ 6
Show the worked answer
Answer: D, 163
How to work it out
Divide before you subtract (BIDMAS): 66 ÷ 6 = 11.
Then 174 − 11 = 163.
Why the other options are wrong
A (11): This is only 66 ÷ 6; it still has to be taken from 174.
B (185): This adds instead of subtracting.
C (18): This subtracts first: (174 − 66) ÷ 6. Division comes before subtraction.
E (108): This subtracts 66 and forgets to divide it by 6.
Question 4Aim for about 60 seconds
What is 4.16 − 3.068?
Show the worked answer
Answer: A, 1.092
How to work it out
Line up the decimal points and fill the gap with a zero: 4.16 is 4.160.
Then 4.160 − 3.068 = 1.092.
Why the other options are wrong
B (1.082): This takes one hundredth too many: check the hundredths column.
C (1.192): This forgets an exchange in the tenths column.
D (7.228): This adds the numbers instead of subtracting.
E (3.853): This lines up the last digits instead of the decimal points.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
What is 5.89 − 3.154?
Show the worked answer
Answer: B, 2.736
How to work it out
Line up the decimal points and fill the gap with a zero: 5.89 is 5.890.
Then 5.890 − 3.154 = 2.736.
Why the other options are wrong
A (2.836): This forgets an exchange in the tenths column.
C (5.575): This lines up the last digits instead of the decimal points.
D (9.044): This adds the numbers instead of subtracting.
E (2.726): This takes one hundredth too many: check the hundredths column.
Question 6Aim for about 60 seconds
What is the missing digit in this addition?
4
3
6
8
□
7
+
1
2
1
2
6
6
5
5
8
1
0
3
Show the worked answer
Answer: C, 3
How to work it out
Work from the right, carrying as you go.
The column with the box receives a carry of 1 from the column to its right, so □ + 6 + 1 must end in 0.
That makes □ = 3.
Why the other options are wrong
A (0): This is the digit in the answer, not the missing digit in the number being added.
B (6): With 6 in the box the first number is 436,867, and 436,867 + 121,266 does not make 558,103.
D (4): This forgets the 1 carried in from the column to the right.
E (2): With 2 in the box the first number is 436,827, and 436,827 + 121,266 does not make 558,103.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
The missing digit
Four something times three is 141: which digit?
Exam standard
Question 7Aim for about 60 seconds
A digit is missing. ?9 × 6 = 474. What is the missing digit?
Show the worked answer
Answer: A, 7
How to work it out
474 ÷ 6 = 79, so the missing digit is 7.
Why the other options are wrong
B (8): One too many: check by multiplying the whole number back.
C (17): This is 10 more than the correct answer, so the tens column is out. Recheck the working.
D (79): 79 is the whole number; the question asks for the one missing digit.
E (6): One too few: check by multiplying the whole number back.
Which calculation
Read a story and choose the sum that answers it.
Exam standard
Question 8Aim for about 60 seconds
One shelf has 72 books and another has 18. How many altogether? Which calculation gives the answer?
Show the worked answer
Answer: A, 72 + 18
How to work it out
The story puts two amounts together, so add: 72 + 18.
Why the other options are wrong
B (72 + 18 + 18): This uses 18 twice; it appears once in the story.
C (72 − 18): This takes one from the other, but the story does not take anything away.
D (72 ÷ 18): This divides, but the story does not share or split anything.
E (72 × 18): This multiplies, but the story does not have equal groups to count up.
Place the brackets
Put brackets into a sum so that it gives the target.
Exam standard
Question 9Aim for about 60 seconds
Put brackets in 8 + 6 × 2 so that it equals 28.
Show the worked answer
Answer: E, (8 + 6) × 2
How to work it out
Without brackets, multiplication comes first: 8 + 12 = 20.
Brackets round 8 + 6 make that happen first: 14 × 2 = 28.
Why the other options are wrong
A (8 + (6 × 2)): 8 + (6 × 2) = 20, which is what the sum already gives without brackets.
B (8 + 6 × (2)): Brackets round a single number change nothing: it is still 20.
C ((8 + 6 × 2)): Brackets round the whole thing change nothing: it is still 20.
D ((8) + 6 × 2): Brackets round 8 alone change nothing: it is still 20.
Check with the inverse
Which calculation checks that 384 divided by 6 is 64?
Exam standard
Question 10Aim for about 60 seconds
Layla works out 731 − 158 = 573. Which calculation checks the answer using the inverse?
Show the worked answer
Answer: B, 573 + 158
How to work it out
The inverse undoes the operation: 573 + 158 should give back 731.
Why the other options are wrong
A (573 − 158): Taking away again does not undo a subtraction; adding does.
C (731 + 158): Adding to 731 does not undo taking 158 away from it; add 158 back to the answer.
D (158 + 731): Adding the two starting numbers checks nothing.
E (731 + 573): Adding the answer to the starting number checks nothing.
Decimal times decimal
0.3 times 0.4, with the decimal point in the right place.
Exam standard
Question 11Aim for about 60 seconds
Calculate 0.2 × 0.04.
Show the worked answer
Answer: D, 0.008
How to work it out
2 × 4 = 8.
There are 3 decimal places in the question altogether, so the answer has 3: 0.008.
Why the other options are wrong
A (0.240): This adds the decimals instead of multiplying.
B (0.001): Ten times too small: count the decimal places in both numbers.
C (8.000): 8 is the product of the whole numbers; the decimal point still has to be placed.
E (0.080): Ten times too big: count the decimal places in both numbers.
The quick way
The fastest correct way to do 199 times 5 in your head.
Exam standard
Question 12Aim for about 60 seconds
Which is the quickest correct way to work out 199 × 5 in your head?
Show the worked answer
Answer: E, 200 × 5 − 5
How to work it out
199 is 1 less than 200, so 200 × 5 − 5 is the quick way: 200 × 5 = 1,000 is one lot of 5 too many, and 1,000 − 5 = 995.
Why the other options are wrong
A (200 × 5 + 5): Rounding up already added one lot of 5; it must be taken off, not added again.
B (200 × 5): 200 × 5 counts one 199 too many; one lot of 5 must come off.
C (200 × 5 − 1): Rounding 199 up by 1 adds 5 to the answer (one extra lot), not 1.
D (199 + 5): Adding is a different calculation; the question is a multiplication.
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