Figure series, mirrors, embedded shapes and paper folding.
About Analogy
An analogy question gives two figures that are related in one particular way, then a third figure, and asks which fourth figure is related to the third in the same way. Finding the change shown by the first pair is the whole task; once it is named, the answer follows.
What you need to understand
The change is a reflection or a turn. It is never a change of size and never a rotation by a part turn.
A mirror reflection swaps left and right and leaves top and bottom alone.
A water reflection swaps top and bottom and leaves left and right alone.
A half turn swaps both at once, which makes it different from either reflection.
The change is applied to the whole figure, including any internal marks and any detail at the edges.
Two figures that are the same picture show no change at all, so a pair like that cannot be the model for the answer.
The third figure is the starting point for the answer, not the second figure of the pair.
How to work through these questions
Pick the most distinctive feature of the first figure, such as a corner, a notch or a mark.
Note exactly where it sits: left or right, high or low.
Find the same feature in the second figure and note where it has moved to.
Name the change in words: left and right swapped, or top and bottom swapped, or both.
Check the reading against a second feature of the figure, because the first feature alone can be misleading in a symmetric figure.
Apply the named change to the third figure, moving each feature in turn.
Compare the result with the four options and choose the one that matches exactly.
Mistakes that cost marks
Applying the change backwards, that is changing the second figure as though it were the third.
Confusing a mirror reflection with a water reflection. They are different pictures and the first pair tells you which one is meant.
Taking the second figure of the pair as the base for the answer.
Assuming the figures are being enlarged or shrunk, which these questions never do.
Reading a half turn as a reflection, which gives a figure with one axis right and the other wrong.
Choosing the option that leaves the third figure unchanged, which is the commonest wrong answer.
Worked example
The first figure has a dot in its top-left corner. The second figure has the dot in its top-right corner. The third figure has the dot in its bottom-left corner. Which figure comes next?
Compare the first pair. The dot moved from the left to the right and stayed at the top.
Left and right changed places while top and bottom did not, so the change is a reflection in a vertical mirror.
Confirm with the rest of the figure rather than the dot alone, since one mark can be read in more than one way.
Apply the same change to the third figure: the dot is in the bottom-left, so it moves to the bottom-right and stays at the bottom.
Choose the option with the dot in the bottom-right corner.
Answer: The figure with the dot in the bottom-right corner.
Practice questions with answers
A few Analogy questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
The second figure is obtained from the first by changing it in one particular way. Apply the same change to the third figure.
A
B
C
D
Answer: Option C — with explanation
The first pair shows the figure reflecting it in water lying below it, which swaps top and bottom.
Applying that same change to the third figure gives the answer.
The other three options are the third figure left unchanged, and the third figure changed in one of the other two ways.
Common mistakes
- leaving the figure exactly as it was instead of doing to the third figure what the first pair shows
- turning it through half a turn, which swaps both instead of doing to the third figure what the first pair shows
- reflecting it in a mirror standing on its right, which swaps left and right instead of doing to the third figure what the first pair shows
Question 2
The second figure is obtained from the first by changing it in one particular way. Apply the same change to the third figure.
A
B
C
D
Answer: Option B — with explanation
The first pair shows the figure turning it through half a turn, which swaps both.
Applying that same change to the third figure gives the answer.
The other three options are the third figure left unchanged, and the third figure changed in one of the other two ways.
Common mistakes
- reflecting it in a mirror standing on its right, which swaps left and right instead of doing to the third figure what the first pair shows
- leaving the figure exactly as it was instead of doing to the third figure what the first pair shows
- reflecting it in water lying below it, which swaps top and bottom instead of doing to the third figure what the first pair shows
Question 3
The second figure is obtained from the first by changing it in one particular way. Apply the same change to the third figure.
A
B
C
D
Answer: Option C — with explanation
The first pair shows the figure reflecting it in water lying below it, which swaps top and bottom.
Applying that same change to the third figure gives the answer.
The other three options are the third figure left unchanged, and the third figure changed in one of the other two ways.
Common mistakes
- reflecting it in a mirror standing on its right, which swaps left and right instead of doing to the third figure what the first pair shows
- leaving the figure exactly as it was instead of doing to the third figure what the first pair shows
- turning it through half a turn, which swaps both instead of doing to the third figure what the first pair shows
Question 4
The second figure is obtained from the first by changing it in one particular way. Apply the same change to the third figure.
A
B
C
D
Answer: Option B — with explanation
The first pair shows the figure reflecting it in water lying below it, which swaps top and bottom.
Applying that same change to the third figure gives the answer.
The other three options are the third figure left unchanged, and the third figure changed in one of the other two ways.
Common mistakes
- reflecting it in a mirror standing on its right, which swaps left and right instead of doing to the third figure what the first pair shows
- turning it through half a turn, which swaps both instead of doing to the third figure what the first pair shows
- leaving the figure exactly as it was instead of doing to the third figure what the first pair shows
Question 5
The second figure is obtained from the first by changing it in one particular way. Apply the same change to the third figure.
A
B
C
D
Answer: Option D — with explanation
The first pair shows the figure reflecting it in water lying below it, which swaps top and bottom.
Applying that same change to the third figure gives the answer.
The other three options are the third figure left unchanged, and the third figure changed in one of the other two ways.
Common mistakes
- turning it through half a turn, which swaps both instead of doing to the third figure what the first pair shows
- leaving the figure exactly as it was instead of doing to the third figure what the first pair shows
- reflecting it in a mirror standing on its right, which swaps left and right instead of doing to the third figure what the first pair shows
Frequently asked questions
How do I tell a mirror reflection from a water reflection?
In a mirror reflection left and right change places. In a water reflection top and bottom change places. Whichever happened in the first pair is what must happen to the third figure.
How is a half turn different from the two reflections?
A half turn changes both pairs of directions at once, so it is not the same as either reflection on its own. A figure turned through half a turn is the mirror image of its own water image.
What if the first two figures look identical?
Then the pair shows no change, so it cannot be the model for the answer. A well-formed question avoids that, because it would leave the answer undetermined.
Does the change ever mean making the figure bigger?
No. These questions only ever reflect or turn the figure, so a larger or smaller option can be discarded at once.
Which figure do I start from?
The third one. The first pair exists only to show the change; the answer is the third figure with that change applied.
Take the Analogy test
Two timed papers on the same syllabus — sit the foundation paper first,
then the advanced one. Both use the real exam paper format with a full
step-by-step review of every question once you submit.
