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
Two rules take turns. What is the next number?
6, 7, 14, 15, 30, ?
Show the worked answer
Answer: B, 31
How to work it out
The rules alternate: add 1, then multiply by 2.
15 × 2 = 30, so the next step adds 1: 30 + 1 = 31.
Why the other options are wrong
A (32): One too many: this step adds exactly 1.
C (60): This multiplies by 2 again, but the rules take turns: this step adds 1.
D (29): This takes 1 away instead of adding it.
E (61): This does both rules at once; only one applies at each step.
Question 2Aim for about 60 seconds
What is the next number in the sequence?
41, 38, 35, 32, 29, ?
Show the worked answer
Answer: D, 26
How to work it out
Write the gaps between the numbers to find the rule.
Take away 3 each time, so the next number is 26.
Why the other options are wrong
A (25): This is one less than the next term. Check the rule: take away 3 each time.
B (28): This is two more than the next term. Check the rule: take away 3 each time.
C (27): This is one more than the next term. Check the rule: take away 3 each time.
E (16): This is 10 less than the correct answer, so the tens column is out. Recheck the working.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
What is the next number in the sequence?
6, 10, 15, 21, 28, ?
Show the worked answer
Answer: B, 36
How to work it out
The gaps are 4, 5, 6, 7: each gap is one bigger than the last.
These are the triangle numbers.
28 + 8 = 36.
Why the other options are wrong
A (35): This repeats the last gap (7); the gaps grow by one each time, so the next gap is 8.
C (45): This adds two gaps at once.
D (37): One too many: the next gap is exactly one more than the last.
E (56): This doubles the last number; the sequence grows by a gap, not by doubling.
Question 4Aim for about 60 seconds
What is the next number in the sequence?
16, 25, 36, 49, 64, ?
Show the worked answer
Answer: A, 81
How to work it out
Write the gaps between the numbers to find the rule.
These are the square numbers, so the next number is 81.
Why the other options are wrong
B (80): This is one less than the next term. Check the rule: these are the square numbers.
C (79): This adds the last gap, 15, again to 64, but the gaps in this sequence are not the same each time.
D (83): This is two more than the next term. Check the rule: these are the square numbers.
E (82): This is one more than the next term. Check the rule: these are the square numbers.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
What is the next number in the sequence?
4, 11, 32, 95, 284, ?
Show the worked answer
Answer: C, 851
How to work it out
Write the gaps between the numbers to find the rule.
Multiply by 3, then take away 1, so the next number is 851.
Why the other options are wrong
A (473): This adds the last gap, 189, again to 284, but the gaps in this sequence are not the same each time.
B (850): This is one less than the next term. Check the rule: multiply by 3, then take away 1.
D (852): This is one more than the next term. Check the rule: multiply by 3, then take away 1.
E (853): This is two more than the next term. Check the rule: multiply by 3, then take away 1.
Question 6Aim for about 60 seconds
Each row and each column of this grid follows a pattern. What is the missing number?
4
7
10
?
14
17
18
21
24
Show the worked answer
Answer: C, 11
How to work it out
Along each row the numbers go up by 3; down each column they go up by 7.
So the missing number is 11.
Check it against its row and its column.
Why the other options are wrong
A (15): This mixes up the row step and the column step.
B (4): This uses the number above; the pattern goes up as you go down.
D (14): This goes one step too far along the row.
E (18): One step too far down the column.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Two sequences woven together
Every other number follows its own rule; find the next one.
Exam standard
Question 7Aim for about 60 seconds
Two sequences take turns. What is the next number?
7, 54, 10, 51, 13, 48, ?
Show the worked answer
Answer: E, 16
How to work it out
Look at every other number.
7, 10, 13 add 3; 54, 51, 48 take away 3.
The next number continues the first sequence: 16.
Why the other options are wrong
A (45): This continues the other sequence, the one that goes down; the next number belongs to the one that goes up.
B (51): This adds 3 to the last number shown, but that number belongs to the other sequence.
C (19): One step too far: the going-up sequence adds 3 once more, not twice.
D (13): This repeats the last number of the going-up sequence instead of moving it on.
Two rules taking turns
Add, then multiply, then add again: what comes next?
Exam standard
Question 8Aim for about 60 seconds
Two rules take turns. What is the next number?
6, 9, 18, 21, 42, ?
Show the worked answer
Answer: C, 45
How to work it out
The rules alternate: add 3, then multiply by 2.
21 × 2 = 42, so the next step adds 3: 42 + 3 = 45.
Why the other options are wrong
A (84): This multiplies by 2 again, but the rules take turns: this step adds 3.
B (46): One too many: this step adds exactly 3.
D (87): This does both rules at once; only one applies at each step.
E (39): This takes 3 away instead of adding it.
Dividing sequences
Each number is the one before divided by the same amount.
Exam standard
Question 9Aim for about 60 seconds
What is the next number in the sequence?
25000, 5000, 1000, 200, 40, ?
Show the worked answer
Answer: E, 8
How to work it out
Each number is the one before divided by 5: 40 ÷ 5 = 8.
Why the other options are wrong
A (9): This is 1 more than the correct answer, so the last step of the working is out by one.
B (40): This repeats the last number instead of dividing it.
C (7): One less than the answer: 40 ÷ 5 is exactly 8.
D (35): This subtracts 5 instead of dividing by 5.
Triangle numbers
The gaps grow by one each time.
Exam standard
Question 10Aim for about 60 seconds
What is the next number in the sequence?
15, 21, 28, 36, 45, ?
Show the worked answer
Answer: C, 55
How to work it out
The gaps are 6, 7, 8, 9: each gap is one bigger than the last.
These are the triangle numbers.
45 + 10 = 55.
Why the other options are wrong
A (56): One too many: the next gap is exactly one more than the last.
B (66): This adds two gaps at once.
D (54): This repeats the last gap (9); the gaps grow by one each time, so the next gap is 10.
E (90): This doubles the last number; the sequence grows by a gap, not by doubling.
The tenth or twentieth term
Not the next number but one far along the sequence.
Exam standard
Question 11Aim for about 60 seconds
What is the 20th number in this sequence?
2, 8, 14, 20, ...
Show the worked answer
Answer: B, 116
How to work it out
The sequence adds 6 each time.
The 20th number is the first number plus 19 steps: 2 + 19 × 6 = 116.
Why the other options are wrong
A (110): One step short: the 20th number is 19 steps after the first.
C (120): This is 20 × 6 and forgets the first number, 2.
D (122): One step too many: the 20th number is 19 steps after the first, not 20.
E (115): This is 1 less than the correct answer, so the last step of the working is out by one.
A gap in the middle
The missing number is between two shown ones.
Exam standard
Question 12Aim for about 60 seconds
Which number is missing from the sequence?
18, 27, 36, ?, 54
Show the worked answer
Answer: E, 45
How to work it out
The numbers go up by 9 each time (36 to 54 is 18, two steps).
So the missing number is 36 + 9 = 45.
Why the other options are wrong
A (44): One less than the answer; the step is a whole number of the same size every time.
B (54): This jumps two steps from the number before the gap; the gap is one step.
C (63): This continues the sequence past the gap instead of filling it.
D (46): One more than the midpoint of its neighbours; the missing number sits exactly halfway between them.
Which number breaks the rule
One term in the sequence is wrong; find it.
Exam standard
Question 13Aim for about 60 seconds
The sequence should add the same number each time. One number is wrong. Which one?
2, 8, 15, 20, 26, 32
Show the worked answer
Answer: E, 15
How to work it out
The rule is add 6.
15 should be 14: 8 + 6 = 14.
Why the other options are wrong
A (8): 8 fits the rule: it is 6 more than the number before it (or the first number), so it belongs.
B (2): 2 fits the rule: it is 6 more than the number before it (or the first number), so it belongs.
C (32): 32 fits the rule: it is 6 more than the number before it (or the first number), so it belongs.
D (20): 20 fits the rule: it is 6 more than the number before it (or the first number), so it belongs.
Which rule explains it
Choose the rule in words, not the next number.
Exam standard
Question 14Aim for about 60 seconds
Which rule explains this sequence?
7, 13, 25, 49, 97
Show the worked answer
Answer: E, Double, then take away 1
How to work it out
Write the gaps: 6, 12, 24, 48.
The rule that fits every step is: double, then take away 1.
Why the other options are wrong
A (The gap grows by 2 each time): The gaps are 6, 12, 24, 48; they do not grow by 2.
B (Multiply by 2 each time): 7 × 2 is 14, which does not give 13 and 25 together.
C (Add 6 each time): From 7 to 13 is 6, but from 13 to 25 is 12, so the gap is not always the same.
D (Double, then take away 2): 7 × 2 − 2 = 12, which is not 13.
Find the first term
Work back from later terms to the start.
Exam standard
Question 15Aim for about 60 seconds
A sequence adds the same number each time. Its 6th, 7th and 8th numbers are shown. What is the first number?
..., 39, 46, ...
Show the worked answer
Answer: E, 4
How to work it out
The gap is 7.
Go back 5 steps from 39: 39 − 5 × 7 = 4.
Why the other options are wrong
A (11): One step short: go back 5 steps of 7, not 4.
B (32): This goes back only one step from the first number shown.
C (5): One more than the first number; count the steps back exactly.
D (2): This is half the correct answer, 4. Check whether you halved when you should not have.
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