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
8 goes into this machine. What comes out?
Show the worked answer
Answer: D, 73
How to work it out
Follow the steps in order: 8 × 8 = 64, then + 9 = 73.
Why the other options are wrong
A (136): This adds 9 first and multiplies after. Follow the machine from left to right.
B (64): This stops after the first step: it still needs + 9.
C (55): This subtracts 9 instead of adding it.
E (25): This adds every number instead of multiplying first.
Question 2Aim for about 60 seconds
2 goes into this machine. What comes out?
Show the worked answer
Answer: A, 13
How to work it out
Follow the steps in order: 2 × 2 = 4, then + 9 = 13.
Why the other options are wrong
B (14): This is 1 more than the right answer. No common slip leads to it, so recheck the working.
C (4): This stops after the first step: it still needs + 9.
D (−5): This subtracts 9 instead of adding it.
E (22): This adds 9 first and multiplies after. Follow the machine from left to right.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
7 goes into this machine. What comes out?
Show the worked answer
Answer: E, 31
How to work it out
Follow the steps in order: 7 × 4 = 28, then + 3 = 31.
Why the other options are wrong
A (25): This subtracts 3 instead of adding it.
B (40): This adds 3 first and multiplies after. Follow the machine from left to right.
C (14): This adds every number instead of multiplying first.
D (28): This stops after the first step: it still needs + 3.
Question 4Aim for about 60 seconds
If n = 4, what is the value of 4n − 4?
Show the worked answer
Answer: B, 12
How to work it out
4n means 4 × n.
Put 4 in place of n: 4 × 4 − 4 = 16 − 4 = 12.
Why the other options are wrong
A (4): This adds 4 + 4; 4n means 4 × 4.
C (16): This leaves out the − 4.
D (2): This is 10 less than the correct answer, so the tens column is out. Recheck the working.
E (20): This adds 4 instead of taking it away.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
9 goes into this machine. What comes out?
Show the worked answer
Answer: D, 56
How to work it out
Follow the steps in order: 9 × 5 = 45, then + 11 = 56.
Why the other options are wrong
A (34): This subtracts 11 instead of adding it.
B (100): This adds 11 first and multiplies after. Follow the machine from left to right.
C (25): This adds every number instead of multiplying first.
E (45): This stops after the first step: it still needs + 11.
Question 6Aim for about 60 seconds
Solve the equation to find the value of y.
10y + 10 = 6y + 18
Show the worked answer
Answer: B, 2
How to work it out
Take 6y from both sides: 4y + 10 = 18.
Take 10 from both sides: 4y = 8.
Divide by 4: y = 2.
Why the other options are wrong
A (1): This is 1 less than the right answer. No common slip leads to it, so recheck the working.
C (3): Check by putting your answer back into both sides.
D (8): This stops before dividing by 4.
E (7): This adds 10 instead of taking it 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 expression
Four pencils at p pence and a 30p rubber: which expression?
Exam standard
Question 7Aim for about 60 seconds
A apple costs p pence. Which expression gives the cost in pence of 6 apples and a 10p drink?
Show the worked answer
Answer: A, 6p + 10
How to work it out
6 apples cost 6 × p = 6p, and the drink adds 10: 6p + 10.
Why the other options are wrong
B (6p − 10): The drink costs money, so its price is added, not taken away.
C (10p + 6): The letter goes with the 6 apples, so it is 6p; 10 is a plain number of pence.
D (p + 60): This buys one apple and 6 drinks; it is the other way round.
E (6(p + 10)): This charges 10p for every apple as well; the drink is bought once.
Two facts, two unknowns
a plus b is 12 and a minus b is 4: what is a?
Exam standard
Question 8Aim for about 60 seconds
Two numbers, a and b, satisfy a + b = 37 and a − b = 11. What is a?
Show the worked answer
Answer: A, 24
How to work it out
Adding the two facts: 2a = 48, so a = 24.
Then b = 37 − 24 = 13.
Why the other options are wrong
B (37): 37 is the sum of the two numbers, not either one.
C (11): 11 is the difference, not either number.
D (25): Off by one; add the two facts and halve, then check both facts.
E (13): 13 is the other number, b.
Undo a formula
The cost is 40 plus 5n; the bill is 75: what is n?
Exam standard
Question 9Aim for about 60 seconds
The cost in pounds of a plumber is 30 + 3n, where n is the number of hours. If the cost is £54, what is n?
Show the worked answer
Answer: A, 8
How to work it out
Undo the formula: take off the fixed £30 to leave £24, then divide by 3: 24 ÷ 3 = 8.
Why the other options are wrong
B (18): This divides the whole cost by 3 without first taking off the fixed £30.
C (24): £24 is the cost after the fixed part is removed; it still needs dividing by 3.
D (9): One too many; check by putting n back into the formula.
E (28): This adds the fixed £30 instead of taking it away.
Which equation
Which equation has the solution x equals 5?
Exam standard
Question 10Aim for about 60 seconds
Which equation has the solution x = 11?
Show the worked answer
Answer: C, 3x + 9 = 42
How to work it out
Put x = 11 into each.
3 × 11 + 9 = 42, so 3x + 9 = 42 is true.
Why the other options are wrong
A (3x + 9 = 45): With x = 11, 3x + 9 = 42, not 45; this would need x = 12.
B (x + 3 = 11): This would need x to be 8, since adding 3 must give 11.
D (3x = 42): 3 × 11 = 33, not 42.
E (3x − 9 = 42): With x = 11, 3x − 9 = 24, not 42.
What must be true of a and b
If 2a equals 3b, which statement is certain?
Exam standard
Question 11Aim for about 60 seconds
a and b are whole numbers bigger than 0, and 5a = 6b. Which statement must be true?
Show the worked answer
Answer: D, a is bigger than b
How to work it out
5a = 6b means a : b = 6 : 5; a = 6, b = 5 is the smallest case and every case is a multiple of it.
So a is bigger than b and a is a multiple of 6.
Why the other options are wrong
A (a = 6): a = 6, b = 5 works, but so does a = 12, b = 10; a is not fixed.
B (a + b = 11): a = 6, b = 5 gives 11, but a = 12, b = 10 gives 22.
C (b is bigger than a): 5 lots of a equal 6 lots of b, and 5 is fewer than 6, so a must be the bigger number.
E (a = b): If a = b then 5a = 6a, which is only true when a = 0, and the numbers are bigger than 0.
Which rule fits the pattern
Sticks in patterns 1, 2 and 3: which rule gives pattern n?
Exam standard
Question 12Aim for about 60 seconds
A pattern of sticks uses 12 sticks for pattern 1, 18 for pattern 2 and 24 for pattern 3. Which rule gives the number of sticks for pattern n?
Show the worked answer
Answer: C, 6n + 6
How to work it out
Each pattern adds 6 sticks, so the rule starts 6n.
Pattern 1 would then be 6, but it is 12, so add 6: 6n + 6.
Why the other options are wrong
A (6n): 6n gives 6, 12, 18: the right step but each term is 6 short.
B (n + 6): n + 6 gives 7, 8, 9, which grows by 1 each time, not 6.
D (6n − 6): 6n − 6 gives 0, 6, 12; the sign is wrong.
E (12n): 12n gives 12, 24, 36; the first term is right but the pattern grows by 6, not 12.
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