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
This large cube is made of small cubes, 2 along each edge. How many small cubes are there altogether?
Show the worked answer
Answer: C, 8
How to work it out
2 along, 2 across and 2 up: 2 × 2 × 2 = 8.
Why the other options are wrong
A (6): This adds 2 three times; multiply instead.
B (24): This counts the small squares on all six faces; cubes on an edge are counted more than once and the middle is missed.
D (12): This counts the small squares on the three faces you can see; some cubes are hidden inside.
E (4): This is one layer; there are 2 layers.
Question 2Aim for about 60 seconds
This large cube is made of small cubes, 4 along each edge. How many small cubes are there altogether?
Show the worked answer
Answer: D, 64
How to work it out
4 along, 4 across and 4 up: 4 × 4 × 4 = 64.
Why the other options are wrong
A (48): This counts the small squares on the three faces you can see; some cubes are hidden inside.
B (16): This is one layer; there are 4 layers.
C (12): This adds 4 three times; multiply instead.
E (96): This counts the small squares on all six faces; cubes on an edge are counted more than once and the middle is missed.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 60 seconds
This large cube is made of small cubes, 3 along each edge. The outside of the large cube is painted, then it is taken apart. How many small cubes have exactly 3 painted faces?
Show the worked answer
Answer: B, 8
How to work it out
Cubes with exactly 3 painted faces are the corners: a cube always has 8, so 8.
Why the other options are wrong
A (1): This is the number with no painted faces.
C (6): This is the number with exactly one painted face.
D (12): This is the number with exactly 2 painted faces.
E (27): This is every small cube.
Question 4Aim for about 60 seconds
This shows the start of a board with 10 squares in each row. The numbers snake: the first row goes left to right, the next right to left, and so on. Which number is directly above 57?
40
39
38
37
36
35
34
33
32
31
21
22
23
24
25
26
27
28
29
30
20
19
18
17
16
15
14
13
12
11
1
2
3
4
5
6
7
8
9
10
Show the worked answer
Answer: E, 64
How to work it out
57 is 4 squares from the left in row 6.
Going up 1 row, the same column holds 64, because each row runs the opposite way to the one below.
Why the other options are wrong
A (65): This is one square along from the right answer; count the columns again.
B (67): This adds a whole row of 10, as if every row ran the same way; the rows snake.
C (63): This is one square along the other way; count the columns again.
D (44): This is the square directly below, not above.
Exam standard what the papers ask in Year 6
Question 5Aim for about 60 seconds
A red dice and a blue dice, each numbered 1 to 6, are thrown together. What is the probability that the two scores add up to 3? Give the answer as a fraction in its lowest terms.
Show the worked answer
Answer: E, 1/18
How to work it out
There are 6 × 6 = 36 equally likely throws.
2 of them make 3 (red 1 and blue 2 and red 2 and blue 1), so the probability is 2/36 = 1/18.
Why the other options are wrong
A (1/21): This counts 21 different pairs of numbers, but they are not equally likely: a pair of different numbers can be thrown two ways.
B (1/6): This shares between the 12 faces of the two dice; there are 36 different throws.
C (2/36): This is the right chance, but not in its lowest terms.
D (1/11): There are 11 totals, but they are not equally likely: 7 can be made in more ways than 2 or 12.
Question 6Aim for about 60 seconds
This shows the start of a board with 9 squares in each row. The numbers snake: the first row goes left to right, the next right to left, and so on. Which number is two squares directly above 52?
36
35
34
33
32
31
30
29
28
19
20
21
22
23
24
25
26
27
18
17
16
15
14
13
12
11
10
1
2
3
4
5
6
7
8
9
Show the worked answer
Answer: E, 70
How to work it out
52 is 3 squares from the left in row 6.
Going up 2 rows, the same column holds 70, because each row runs the opposite way to the one below.
Why the other options are wrong
A (71): This is one square along from the right answer; count the columns again.
B (66): This counts the columns from the wrong end of the row.
C (69): This is one square along the other way; count the columns again.
D (39): This is the square directly below, not above.
Practise straight away at your child’s school year in maths and English, with verbal and non-verbal reasoning for the 11 Plus, and every answer explained. A free check, whenever you like, shows what to practise next and builds a weekly plan, for their year or for your target schools. Parents follow progress free.