Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 5 (Level 11). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
77 questions available · medium difficulty · CogAT Grade 5 · 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 5 figure matrices question looks like
Two changes applied at once become common rather than occasional - a figure may rotate and change fill, or shrink and gain a shape. Crucially, the wrong answers are built so each of them gets one of the two changes right, so an option can look correct while being half wrong.
At level 11 — grade 5
At Level 11 compound items become the norm. This is where stating the rule aloud stops being a teaching aid and becomes the actual method, because holding two simultaneous transformations in mind without articulating them is unreliable at any age.
Where children go wrong
Finding only one of two rules
Most items at this level apply two changes together, and the distractors are built so each one satisfies a single rule correctly. Finding one rule and answering confidently is therefore worse than useless - it leads directly to a wrong option someone prepared in advance.
Mistaking rotation for reflection
A shape turned ninety degrees and the same shape flipped look identical when the figure is close to symmetric, and different when it is not. Checking one asymmetric detail - a notch, an off-centre dot, a shaded segment - resolves it in a second.
Picking the figure that looks most similar
The most visually familiar option is rarely the answer. Wrong choices are commonly built by taking the correct figure and undoing the change, so they resemble the cell beside the gap more closely than the answer does.
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 1easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one small half-filled square✓
B.two small dotted squares
C.one small dotted square
D.one medium dotted square
Correct answer: A
Look at the top row first: the figure changes by one step — change to the next pattern. The same change must happen from the bottom-left figure to the missing one. Applying it gives one small half-filled square, 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 (make the figure bigger) instead of the one shown. Option B is applied a different change (add one more copy) instead of the one shown.
Question 2easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one medium hatched hexagon
B.one small hatched hexagon
C.one medium dotted hexagon✓
D.one large hatched hexagon
Correct answer: C
Look at the top row first: the figure changes by one step — change to the next pattern. The same change must happen from the bottom-left figure to the missing one. Applying it gives one medium dotted hexagon, which is option C. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is applied a different change (make the figure bigger) instead of the one shown. Option B is applied a different change (make the figure smaller) instead of the one shown.
Question 3easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large hatched circle
B.two small hatched circles
C.one large dotted circle✓
D.one medium hatched circle
Correct answer: C
Look at the top row first: the figure changes by one step — change to the next pattern. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large dotted circle, which is option C. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option D is applied a different change (make the figure smaller) instead of the one shown. Option B is applied a different change (add one more copy) instead of the one shown.
Question 4medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.three small dotted ells, rotated 225 degrees✓
B.three small dotted ells, rotated 90 degrees
C.three small dotted ells, rotated 135 degrees
D.three small dotted ells, rotated 45 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 dotted ells, rotated 225 degrees, 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 5easy
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 triangles✓
B.one large half-filled triangle
C.two small half-filled triangles
D.two small solid triangles
Correct answer: A
Look at the top row first: the figure changes by one step — add one more copy. The same change must happen from the bottom-left figure to the missing one. Applying it gives three small half-filled triangles, which is option A. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option B is changed the number of copies in the wrong direction. Option D is applied a different change (fill the figure in) instead of the one shown.
Question 6easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small hatched hexagons
B.one large hatched hexagon
C.one medium hatched hexagon
D.one small hatched hexagon✓
Correct answer: D
Look at the top row first: the figure changes by one step — make the figure smaller. The same change must happen from the bottom-left figure to the missing one. Applying it gives one small hatched hexagon, which is option D. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option B is changed the size in the wrong direction. Option A is applied a different change (add one more copy) instead of the one shown.
Question 7easy
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 triangle✓
B.one large half-filled triangle
C.one large solid triangle
D.two small half-filled triangles
Correct answer: A
Look at the top row first: the figure changes by one step — make the figure smaller. The same change must happen from the bottom-left figure to the missing one. Applying it gives one medium half-filled triangle, 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 (add one more copy) instead of the one shown. Option C is applied a different change (fill the figure in) instead of the one shown.
Question 8medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one medium solid flag, rotated 225 degrees✓
B.one medium solid flag, rotated 135 degrees
C.one medium solid flag, rotated 45 degrees
D.one medium solid flag, rotated 315 degrees
Correct answer: A
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 medium solid flag, rotated 225 degrees, which is option A. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option C is turned the right amount but the wrong way. Option D 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.three small half-filled arrows, rotated 270 degrees
B.three small half-filled arrows, rotated 90 degrees
C.three small half-filled arrows, rotated 180 degrees✓
D.three small half-filled arrows
Correct answer: C
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 three small half-filled arrows, rotated 180 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 10easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small dotted pentagons✓
B.one medium hatched pentagon
C.three small hatched pentagons
D.two small hatched pentagons
Correct answer: A
Look at the top row first: the figure changes by one step — change to the next pattern. The same change must happen from the bottom-left figure to the missing one. Applying it gives two small dotted pentagons, which is option A. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option C is applied a different change (add one more copy) instead of the one shown. Option B is applied a different change (take one copy away) instead of the one shown.