Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 4 (Level 10). 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 4 · 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 4 figure matrices question looks like
The same grid, but which attribute carries the rule now varies from item to item, so a child cannot settle into expecting rotation every time. Most items still apply a single change; among the harder ones, two changes start appearing together for the first time.
At level 10 — grade 4
Level 10 keeps most items to one rule but varies which attribute carries it, so expecting rotation every time stops working. Two-rule items appear among the harder questions, which is usually a fourth grader's first encounter with a distractor built to satisfy half a pattern.
Where children go wrong
Expecting the same attribute every time
After a run of rotation items a child starts looking for rotation, and the item that changes fill instead goes unnoticed. Which attribute carries the rule varies deliberately, and the assumption that it will not is a reliable source of lost marks.
Stopping at the first rule found
A child who notices the shape rotated may stop looking and miss that it also changed colour. Getting into the habit of asking what else changed, once, before choosing catches most of these.
Reading the grid the wrong way
The rule can be read across the rows or down the columns, and in a well-built item both readings give the same answer. Where they disagree, the child has found a pattern the item did not intend. Checking that the rule works both ways catches this before it costs a mark.
How to practise this at home
Ask your child to say the rule aloud before looking at the options - 'it turned and it got bigger'. Saying it forces the rule into words, which is where an incomplete rule becomes obvious. If they cannot finish the sentence they have not found the rule yet, and picking from the options at that point is how careless errors happen. Then have them check the rule against the second row before answering.
Common questions about Figure Matrices
Should the rule be read across or down?
Either - a properly built item gives the same answer both ways. If the two readings disagree, look again, because one of them is a pattern that happens to fit rather than the intended rule.
My child gets these right but slowly. Does that matter?
It does, because the CogAT is timed at roughly half a minute per question. Accuracy first and then pace, but a slow correct answer is not yet a solved problem.
Are figure matrices the same as IQ test puzzles?
They are closely related in form, and the reasoning resembles matrix items used in a range of ability tests. The CogAT reports a percentile against other children of the same age rather than an IQ.
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 medium dotted arrow
B.one medium dotted arrow, rotated 180 degrees
C.one medium dotted arrow, rotated 90 degrees
D.one medium dotted arrow, rotated 270 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 medium dotted arrow, rotated 270 degrees, which is option D. 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 A is turned twice as far as the top row does.
Question 2medium
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 45 degrees
B.one large dotted ell, rotated 225 degrees
C.one large dotted ell, rotated 315 degrees
D.one large dotted ell, 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 one large dotted ell, rotated 135 degrees, which is option D. Option A 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 B is turned twice as far as the top row does.
Question 3medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small solid ells, rotated 90 degrees✓
B.two small solid ells
C.two small solid ells, rotated 180 degrees
D.two small solid ells, rotated 270 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 two medium solid ells, rotated 90 degrees, which is option A. 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 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 medium solid arrow, rotated 135 degrees
B.one medium solid arrow, rotated 225 degrees✓
C.one medium solid arrow, rotated 45 degrees
D.one medium solid arrow, 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 one medium 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 C is turned the right amount but the wrong way. Option D is turned twice as far as the top row does.
Question 5medium
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 90 degrees
B.two small unfilled ells, rotated 270 degrees✓
C.two small unfilled ells, rotated 180 degrees
D.two small unfilled ells
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 large unfilled ells, rotated 270 degrees, which is option B. Option C 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 D is turned twice as far as the top row does.
Question 6easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one small solid flag✓
B.one large solid flag
C.one medium solid flag
D.two small solid flags
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 small solid flag, 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 size in the wrong direction. Option D 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 large hatched circle✓
B.one small hatched circle
C.two small hatched circles
D.one medium hatched circle
Correct answer: A
Look at the top row first: the figure changes by one step — make the figure bigger. The same change must happen from the bottom-left figure to the missing one. Applying it gives one large hatched circle, which is option A. Option D 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 C is applied a different change (add one more copy) instead of the one shown.
Question 8easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one small unfilled hexagon
B.two small solid hexagons✓
C.three small unfilled hexagons
D.two small unfilled hexagons
Correct answer: B
Look at the top row first: the figure changes by one step — fill the figure in. The same change must happen from the bottom-left figure to the missing one. Applying it gives two small solid hexagons, which is option B. 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 A is applied a different change (take one copy away) instead of the one shown.
Question 9medium
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one small solid flag, rotated 90 degrees
B.one small solid flag
C.one small solid flag, rotated 270 degrees
D.one small solid flag, rotated 180 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 small solid flag, rotated 180 degrees, which is option D. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option B is turned the right amount but the wrong way. Option C 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.three small solid pentagons✓
B.two small unfilled pentagons
C.one medium solid pentagon
D.two small solid pentagons
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 solid pentagons, which is option A. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option C is changed the number of copies in the wrong direction. Option B is applied a different change (empty the figure out) instead of the one shown.