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CogAT Grade 6 Figure Matrices Practice Questions

Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 6 (Level 12). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.

82 questions available · medium difficulty · CogAT Grade 6 · 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 6 figure matrices question looks like

Still two rules, but the individual rules get subtler: rotations of forty-five degrees rather than ninety, size changes of one step rather than two. The grid looks less dramatic than at grade 5 and is not easier, because the differences now have to be looked for rather than noticed.

At level 12 — grade 6

Level 12 keeps the two-rule structure but shrinks the individual changes. The items reward careful looking more than clever reasoning, and a child who is racing will lose marks on questions they could comfortably have answered.

Where children go wrong

Missing a change too small to notice

A rotation of forty-five degrees or a single step in size does not announce itself the way a colour change does. Items at this level reward careful looking more than clever reasoning, and children who race through tend to lose marks that were available to them.

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.

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.

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 two-by-two grid. Top row: two small unfilled ells, rotated 135 degrees, then two small unfilled ells, rotated 315 degrees. Bottom row: two small unfilled arrows, then the missing figure.?
  • A.two small unfilled arrowstwo small unfilled arrows
  • B.two small unfilled arrows, rotated 90 degreestwo small unfilled arrows, rotated 90 degrees
  • C.two small unfilled arrows, rotated 45 degreestwo small unfilled arrows, rotated 45 degrees
  • D.two small unfilled arrows, rotated 180 degreestwo small unfilled arrows, rotated 180 degrees

Correct answer: D

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 two small unfilled arrows, rotated 180 degrees, which is option D. Option A is the figure from the bottom-left cell, unchanged — the change was never applied. Option C 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 2easy

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: one small dotted ell, then one medium dotted ell. Bottom row: one small dotted square, then the missing figure.?
  • A.two small dotted squarestwo small dotted squares
  • B.one medium dotted squareone medium dotted square
  • C.one small solid squareone small solid square
  • D.one small dotted squareone small dotted square

Correct answer: B

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 medium dotted square, which is option B. Option D is the figure from the bottom-left cell, unchanged — the change was never applied. Option A 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 3medium

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: two small unfilled arrows, rotated 135 degrees, then two small unfilled arrows, rotated 180 degrees. Bottom row: two small unfilled flags, then the missing figure.?
  • A.two small unfilled flags, rotated 45 degreestwo small unfilled flags, rotated 45 degrees
  • B.two small unfilled flagstwo small unfilled flags
  • C.two small unfilled flags, rotated 90 degreestwo small unfilled flags, rotated 90 degrees
  • D.two small unfilled flags, rotated 315 degreestwo small unfilled flags, rotated 315 degrees

Correct answer: A

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 two small unfilled flags, rotated 45 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 4easy

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: two small unfilled flags, then two small solid flags. Bottom row: two small unfilled pentagons, then the missing figure.?
  • A.two small unfilled pentagonstwo small unfilled pentagons
  • B.two small solid pentagonstwo small solid pentagons
  • C.one small unfilled pentagonone small unfilled pentagon
  • D.three small unfilled pentagonsthree small unfilled pentagons

Correct answer: B

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 solid pentagons, 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 (add one more copy) instead of the one shown. Option C is applied a different change (take one copy away) 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 two-by-two grid. Top row: two small unfilled ells, rotated 180 degrees, then two small unfilled ells, rotated 225 degrees. Bottom row: two small unfilled arrows, rotated 90 degrees, then the missing figure.?
  • A.two small unfilled arrows, rotated 45 degreestwo small unfilled arrows, rotated 45 degrees
  • B.two small unfilled arrows, rotated 180 degreestwo small unfilled arrows, rotated 180 degrees
  • C.two small unfilled arrows, rotated 90 degreestwo small unfilled arrows, rotated 90 degrees
  • D.two small unfilled arrows, rotated 135 degreestwo small unfilled arrows, rotated 135 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 two small unfilled arrows, rotated 135 degrees, which is option D. 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 B is turned twice as far as the top row does.

Question 6medium

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: one large unfilled ell, then one large unfilled ell, rotated 180 degrees. Bottom row: one large unfilled flag, rotated 45 degrees, then the missing figure.?
  • A.one large unfilled flag, rotated 90 degreesone large unfilled flag, rotated 90 degrees
  • B.one large unfilled flag, rotated 45 degreesone large unfilled flag, rotated 45 degrees
  • C.one large unfilled flag, rotated 225 degreesone large unfilled flag, rotated 225 degrees
  • D.one large unfilled flag, rotated 135 degreesone large unfilled flag, rotated 135 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 large unfilled flag, rotated 225 degrees, which is option C. Option B 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 7medium

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: one large hatched arrow, rotated 180 degrees, then one large hatched arrow. Bottom row: one large hatched ell, rotated 90 degrees, then the missing figure.?
  • A.one large hatched ell, rotated 180 degreesone large hatched ell, rotated 180 degrees
  • B.one large hatched ell, rotated 270 degreesone large hatched ell, rotated 270 degrees
  • C.one large hatched ell, rotated 90 degreesone large hatched ell, rotated 90 degrees
  • D.one large hatched ell, rotated 135 degreesone large hatched ell, rotated 135 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 hatched ell, rotated 270 degrees, 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 (turn the figure 45 degrees) instead of the one shown. Option A is applied a different change (turn the figure 90 degrees) 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 two-by-two grid. Top row: one small solid ell, rotated 45 degrees, then one small solid ell, rotated 90 degrees. Bottom row: one small solid flag, rotated 180 degrees, then the missing figure.?
  • A.one small solid flag, rotated 270 degreesone small solid flag, rotated 270 degrees
  • B.one small solid flag, rotated 180 degreesone small solid flag, rotated 180 degrees
  • C.one small solid flag, rotated 225 degreesone small solid flag, rotated 225 degrees
  • D.one small solid flag, rotated 135 degreesone small solid flag, rotated 135 degrees

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 small solid flag, rotated 225 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 9easy

Look at how the first figure changes into the second. Which figure completes the bottom row in the same way?

A two-by-two grid. Top row: one large hatched ell, then one large unfilled ell. Bottom row: one large hatched flag, then the missing figure.?
  • A.one large unfilled flagone large unfilled flag
  • B.one large hatched flagone large hatched flag
  • C.one medium hatched flagone medium hatched flag
  • D.two small hatched flagstwo small hatched flags

Correct answer: A

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 large unfilled flag, which is option A. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option C is applied a different change (make the figure smaller) instead of the one shown. Option D is applied a different change (add one more copy) 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 two-by-two grid. Top row: one medium unfilled arrow, then two small unfilled arrows. Bottom row: one medium unfilled cross, then the missing figure.?
  • A.one small unfilled crossone small unfilled cross
  • B.one medium unfilled crossone medium unfilled cross
  • C.one large unfilled crossone large unfilled cross
  • D.two small unfilled crossestwo small unfilled crosses

Correct answer: D

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 small unfilled crosses, which is option D. Option B is the figure from the bottom-left cell, unchanged — the change was never applied. Option C is applied a different change (make the figure bigger) instead of the one shown. Option A is applied a different change (make the figure smaller) instead of the one shown.