Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 3 (Level 9). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
57 questions available · medium difficulty · CogAT Grade 3 · 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 3 figure matrices question looks like
A two-by-two grid with the last cell marked by a question mark, then five answer figures. One thing changes between cells and it is usually something a child can name unprompted - the shape gets bigger, turns, changes colour, or there is one more of it. The same change runs along both rows.
At level 9 — grade 3
Level 9 matrices apply a single change, usually one a child can name without help. The reasoning demand is low; what is really being tested is whether the child notices that a rule exists at all and thinks to check it against the second row.
Where children go wrong
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.
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.
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.
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 1easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.two small solid pentagons
B.one medium solid pentagon
C.one small unfilled pentagon✓
D.one small solid pentagon
Correct answer: C
Look at the top row first: the figure changes by one step — empty the figure out. The same change must happen from the bottom-left figure to the missing one. Applying it gives one small unfilled pentagon, which is option C. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option B is applied a different change (make the figure bigger) instead of the one shown. Option A 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 large solid diamond
B.two small hatched diamonds✓
C.one large hatched diamond
D.one medium hatched diamond
Correct answer: B
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 two large hatched diamonds, which is option B. 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 smaller) instead of the one shown. Option A is applied a different change (fill the figure in) 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 medium unfilled arrow, rotated 135 degrees
B.one medium unfilled arrow, rotated 225 degrees
C.one medium unfilled arrow, rotated 315 degrees✓
D.one medium unfilled arrow, rotated 180 degrees
Correct answer: C
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 medium unfilled arrow, rotated 315 degrees, 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 (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 4easy
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
B.one medium half-filled arrow✓
C.one large half-filled arrow
D.two small half-filled arrows
Correct answer: B
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 arrow, which is option B. Option C 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 A is applied a different change (fill the figure in) 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 small dotted ell, rotated 45 degrees
B.one small dotted ell, rotated 180 degrees✓
C.one small dotted ell
D.one small dotted ell, 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 small dotted ell, rotated 180 degrees, which is option B. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is applied a different change (turn the figure 45 degrees) instead of the one shown. Option D is applied a different change (turn the figure 90 degrees) 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.one medium hatched hexagon
B.one small hatched hexagon
C.one medium solid hexagon✓
D.one large hatched hexagon
Correct answer: C
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 one medium solid 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 7easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large dotted arrow
B.two small dotted arrows
C.one small dotted arrow✓
D.one medium dotted arrow
Correct answer: C
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 dotted arrow, which is option C. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is changed the size in the wrong direction. Option B 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 large unfilled arrow
B.one medium solid arrow✓
C.one medium unfilled arrow
D.one small unfilled arrow
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 one medium solid arrow, which is option B. Option C is the figure from the bottom-left cell, unchanged — the change was never applied. Option A is applied a different change (make the figure bigger) instead of the one shown. Option D is applied a different change (make the figure smaller) instead of the one shown.
Question 9easy
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 square✓
B.one large half-filled square
C.one large solid square
D.two small half-filled squares
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 square, 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 10easy
Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?
A.one large solid diamond
B.one large unfilled diamond
C.one medium unfilled diamond✓
D.two small unfilled diamonds
Correct answer: C
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 unfilled diamond, which is option C. 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 A is applied a different change (fill the figure in) instead of the one shown.