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 45 seconds
The three figures are alike in some way. Which figure goes with them?
Show the worked answer
Answer: E
How to work it out
All the figures are circles.
Shading, size and angle change, so they do not matter.
Why the other options are wrong
A: This is a teardrop. The three are all circles; the shading and size do not matter.
B: This is a octagon. The three are all circles; the shading and size do not matter.
C: This is a house. The three are all circles; the shading and size do not matter.
D: This is a trapezium. The three are all circles; the shading and size do not matter.
Question 2Aim for about 45 seconds
The three figures are alike in some way. Which figure goes with them?
Show the worked answer
Answer: E
How to work it out
All the figures are squares.
Shading, size and angle change, so they do not matter.
Why the other options are wrong
A: This is a cross. The three are all squares; the shading and size do not matter.
B: This is a octagon. The three are all squares; the shading and size do not matter.
C: This is a arrow. The three are all squares; the shading and size do not matter.
D: This is a triangle. The three are all squares; the shading and size do not matter.
Standard the 11 Plus standard, Year 5
Question 3Aim for about 45 seconds
All the figures in this group follow the same two rules. Which statement MUST be true of a figure that could join it?
The group
Show the worked answer
Answer: A, It is grey
How to work it out
The rules: every figure is grey, and every figure has an even number of sides (octagon 8, hexagon 6, square 4, trapezium 4).
So a figure that joins must be grey.
Why the other options are wrong
B (It is white): Every member is grey, so a white figure cannot join.
C (It has an odd number of sides): Every member has an even number of sides, so a figure that joins cannot have an odd number.
D (It has 8 sides): Some members have 8 sides, but others have 6; the rule is an even number, not one count.
E (It is a kite): A kite could join (it has an even number of sides), but a figure need not be a kite: any even-sided grey shape fits.
Question 4Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: E
How to work it out
The hidden rule: in every figure the number of sides plus the number of dots is 8.
Shading and angle do not matter.
Why the other options are wrong
A: This unshaded square (turned 0°) has 2 dots: 4 sides plus 2 is 6, not 8.
B: This striped pentagon (turned 0°) has 2 dots: 5 sides plus 2 is 7, not 8.
C: This grey hexagon (turned 90°) has 0 dots: 6 sides plus 0 is 6, not 8.
D: This grey square (turned 90°) has 5 dots: 4 sides plus 5 is 9, not 8.
Exam standard what the papers ask in Year 6
Question 5Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: B
How to work it out
A rule with a condition: a shape with an even number of sides is black, and one with an odd number is unshaded.
Angle does not matter.
Why the other options are wrong
A: This hexagon (turned 45°) has 6 sides, an even number, so it should be black, not unshaded.
C: This pentagon (turned 45°) has 5 sides, an odd number, so it should be unshaded, not black.
D: This triangle (turned 45°) has 3 sides, an odd number, so it should be unshaded, not black.
E: This hexagon (turned 90°) has 6 sides, an even number, so it should be black, not unshaded.
Question 6Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: A
How to work it out
A rule with a condition: a shape with an even number of sides is black, and one with an odd number is unshaded.
Angle does not matter.
Why the other options are wrong
B: This hexagon (turned 0°) has 6 sides, an even number, so it should be black, not unshaded.
C: This hexagon (turned 90°) has 6 sides, an even number, so it should be black, not unshaded.
D: This triangle (turned 0°) has 3 sides, an odd number, so it should be unshaded, not black.
E: This square (turned 45°) has 4 sides, an even number, so it should be black, not unshaded.
The kinds of question in this topic
Each kind asks something different of a child, even when the numbers or shapes look alike.
Two rules at once
Every member obeys two rules; which figure could join?
Standard
Question 7Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: B
How to work it out
Two rules at once: every figure is striped, and its number of dots matches its number of sides.
Only one option keeps both.
Why the other options are wrong
A: This hexagon is striped, but it has one dot too few for its sides.
C: This square is striped, but it has one dot too many for its sides.
D: This hexagon's dots match its sides, but it is black: every figure in the group is striped.
E: The dots match the sides, but this triangle is unshaded: the group is all striped.
The hidden sum
Dots plus sides make the same total in every member.
Exam standard
Question 8Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: C
How to work it out
The hidden rule: in every figure the number of sides plus the number of dots is 8.
Shading and angle do not matter.
Why the other options are wrong
A: This striped triangle (turned 0°) has 4 dots: 3 sides plus 4 is 7, not 8.
B: This unshaded hexagon (turned 90°) has 3 dots: 6 sides plus 3 is 9, not 8.
D: This striped triangle (turned 90°) has 3 dots: 3 sides plus 3 is 6, not 8.
E: This grey hexagon (turned 0°) has 0 dots: 6 sides plus 0 is 6, not 8.
If this then that
Shapes with an even number of sides are shaded; the rest are not.
Exam standard
Question 9Aim for about 45 seconds
Which of the shapes below could join this group?
The group
Show the worked answer
Answer: C
How to work it out
A rule with a condition: a shape with an even number of sides is black, and one with an odd number is unshaded.
Angle does not matter.
Why the other options are wrong
A: This triangle (turned 45°) has 3 sides, an odd number, so it should be unshaded, not black.
B: This pentagon (turned 45°) has 5 sides, an odd number, so it should be unshaded, not black.
D: This pentagon (turned 0°) has 5 sides, an odd number, so it should be unshaded, not black.
E: This pentagon (turned 90°) has 5 sides, an odd number, so it should be unshaded, not black.
Which cannot belong
Four figures could join the group; one never could.
Standard
Question 10Aim for about 45 seconds
Four of the shapes below could join this group. One cannot. Which one?
The group
Show the worked answer
Answer: A
How to work it out
Every figure in the group is a grey square; size and angle change freely.
The hexagon cannot belong.
Why the other options are wrong
B: This smaller square turned 90° is grey, like every figure in the group, so it could belong.
C: This smaller square turned 45° is grey, like every figure in the group, so it could belong.
D: This square turned 45° is grey, like every figure in the group, so it could belong.
E: This square turned 180° is grey, like every figure in the group, so it could belong.
Must or cannot be true
What is certain, and what is impossible, for any figure that joins.
Standard
Question 11Aim for about 45 seconds
All the figures in this group follow the same two rules. Which statement MUST be true of a figure that could join it?
The group
Show the worked answer
Answer: C, It is grey
How to work it out
The rules: every figure is grey, and every figure has an even number of sides (trapezium 4, square 4, octagon 8, hexagon 6).
So a figure that joins must be grey.
Why the other options are wrong
A (It has an odd number of sides): Every member has an even number of sides, so a figure that joins cannot have an odd number.
B (It has 4 sides): Some members have 4 sides, but others have 4; the rule is an even number, not one count.
D (It is checked): Every member is grey, so a checked figure cannot join.
E (It is a kite): A kite could join (it has an even number of sides), but a figure need not be a kite: any even-sided grey shape fits.
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