Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 8 (Level 13/14). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
70 questions available · medium difficulty · CogAT Grade 8 · Free, no registration required
What Figure Matrices measures
Four cells sit in a square with three of them filled. Whatever change turns the top-left figure into the top-right one is the same change that applies to the bottom-left figure, and the child picks the figure completing the grid. It is the closest thing on the CogAT to a classic non-verbal reasoning item, measuring the ability to notice a rule and apply it rather than any learned knowledge.
What a grade 8 figure matrices question looks like
Identical in form to grade 7, since both grades take the same level. The items do not get harder between the two grades - the comparison group gets older, so the same performance places lower. Pace is therefore worth more to a grade 8 student than any additional technique.
At level 13/14 — grade 8
Eighth graders take the same Level 13/14 form as seventh graders and are scored against an older-age norm, so the practical target is the same accuracy at a faster pace. If your child is getting these right but running out of time, pace is the thing to work on, not reasoning.
Where children go wrong
Being right too slowly
At roughly half a minute a question, a correct answer arrived at in ninety seconds has cost two other items. When accuracy is already good, the remaining gains are almost entirely in deciding faster and in abandoning an item that is not resolving.
Assuming the rule is the obvious one
Counting is the easiest relationship to see, so items at this level often hold the count constant and change something less visible. If the count is the same everywhere, that is a signal it is not the rule rather than a signal that it is.
Trusting an option that is right about something
By this level nearly every wrong answer matches the correct figure in some respect, so recognising a familiar feature carries almost no information. Eliminating against each rule separately is what works; picturing the answer and hunting for it does not.
How to practise this at home
The habit worth building is looking for the second rule after finding the first. Have your child state both changes explicitly, then eliminate options against each rule separately rather than trying to picture the answer and match it. Elimination is faster under time pressure and far less vulnerable to a distractor built to get one rule right.
Common questions about Figure Matrices
How many rules does one item apply?
One at the easier levels and two together from around grade 5 upward. Assuming a second rule exists and checking for it costs a few seconds and prevents the most common error at this level.
What should my child do when they cannot see the rule at all?
Eliminate and move on. Comparing the options against each other sometimes reveals what varies, and an item that has resisted thirty seconds is usually better abandoned, since every question carries equal weight.
Is this the hardest of the nonverbal subtests?
It is the one most often reported as hardest at these levels, mainly because of the two-rule items. Paper folding is more demanding on visualisation specifically, but its method is more learnable.
Sample Figure Matrices Questions with Answers
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Question 1medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large half-filled flag, rotated 315 degrees✓
B.one large half-filled flag, rotated 225 degrees
C.one large half-filled flag, rotated 135 degrees
D.one large half-filled flag, rotated 180 degrees
Correct answer: A
Look at the top row first: the figure changes by one step — turn the figure 180 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large half-filled flag, rotated 315 degrees, which is option A. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is applied a different change (turn the figure 45 degrees) instead of the one shown. Option B is applied a different change (turn the figure 90 degrees) instead of the one shown.
Question 2medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.three small half-filled flags✓
B.three small half-filled flags, rotated 225 degrees
C.three small half-filled flags, rotated 270 degrees
D.three small half-filled flags, rotated 180 degrees
Correct answer: A
Look at the top row first: the figure changes by one step — turn the figure 180 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives three small half-filled flags, which is option A. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option B is applied a different change (turn the figure 45 degrees) instead of the one shown. Option C is applied a different change (turn the figure 90 degrees) instead of the one shown.
Question 3medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large half-filled flag, rotated 270 degrees
B.one large half-filled flag
C.one large half-filled flag, rotated 180 degrees
D.one large half-filled flag, rotated 90 degrees✓
Correct answer: D
Look at the top row first: the figure changes by one step — turn the figure 90 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large half-filled flag, rotated 90 degrees, which is option D. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is turned the right amount but the wrong way. Option C is turned twice as far as the top row does.
Question 4medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large dotted ell, rotated 270 degrees✓
B.one large dotted ell, rotated 90 degrees
C.one large dotted ell, rotated 180 degrees
D.one large dotted ell, rotated 135 degrees
Correct answer: A
Look at the top row first: the figure changes by one step — turn the figure 180 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large dotted ell, rotated 270 degrees, which is option A. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is applied a different change (turn the figure 45 degrees) instead of the one shown. Option C is applied a different change (turn the figure 90 degrees) instead of the one shown.
Question 5medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large solid arrow, rotated 45 degrees
B.one large solid arrow, rotated 225 degrees✓
C.one large solid arrow, rotated 135 degrees
D.one large solid arrow, rotated 90 degrees
Correct answer: B
Look at the top row first: the figure changes by one step — turn the figure 180 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large solid arrow, rotated 225 degrees, which is option B. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is applied a different change (turn the figure 45 degrees) instead of the one shown. Option C is applied a different change (turn the figure 90 degrees) instead of the one shown.
Question 6medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small half-filled flags, rotated 315 degrees
B.two small half-filled flags, rotated 45 degrees
C.two small half-filled flags, rotated 225 degrees
D.two small half-filled flags, rotated 135 degrees✓
Correct answer: D
Look at the top row first: the figure changes by one step — turn the figure 90 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives two small half-filled flags, rotated 135 degrees, which is option D. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is turned the right amount but the wrong way. Option C is turned twice as far as the top row does.
Question 7medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one medium half-filled ell, rotated 135 degrees
B.one medium half-filled ell, rotated 45 degrees
C.one medium half-filled ell, rotated 90 degrees✓
D.one medium half-filled ell
Correct answer: C
Look at the top row first: the figure changes by one step — turn the figure 45 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one medium half-filled ell, rotated 90 degrees, which is option C. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is turned the right amount but the wrong way. Option A is turned twice as far as the top row does.
Question 8medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one small dotted flag, rotated 135 degrees
B.one small dotted flag, rotated 180 degrees
C.one small dotted flag, rotated 270 degrees
D.one small dotted flag, rotated 225 degrees✓
Correct answer: D
Look at the top row first: the figure changes by one step — turn the figure 45 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one small dotted flag, rotated 225 degrees, which is option D. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is turned the right amount but the wrong way. Option C is turned twice as far as the top row does.
Question 9medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one medium solid ell, rotated 135 degrees
B.one medium solid ell, rotated 180 degrees✓
C.one medium solid ell, rotated 225 degrees
D.one medium solid ell, rotated 90 degrees
Correct answer: B
Look at the top row first: the figure changes by one step — turn the figure 45 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives one medium solid ell, rotated 180 degrees, which is option B. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is turned the right amount but the wrong way. Option C is turned twice as far as the top row does.
Question 10medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small unfilled ells, rotated 225 degrees
B.two small unfilled ells, rotated 135 degrees✓
C.two small unfilled ells, rotated 45 degrees
D.two small unfilled ells, rotated 315 degrees
Correct answer: B
Look at the top row first: the figure changes by one step — turn the figure 90 degrees. The same change must happen from the bottom-left figure to the missing one. Applying it gives two small unfilled ells, rotated 135 degrees, which is option B. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is turned the right amount but the wrong way. Option A is turned twice as far as the top row does.