Loading questions…

CogAT Grade 7 Figure Matrices Practice Questions

Practice Figure Matrices questions for the Cognitive Abilities Test — Grade 7 (Level 13/14). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.

74 questions available · medium difficulty · CogAT Grade 7 · 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 7 figure matrices question looks like

Two rules, fine-grained, with a distractor set where nearly every option is correct in some respect. The reasoning demand has not risen much since grade 5; what has risen is the cost of answering from a partial rule, because a partial rule now leads straight to a prepared wrong answer.

At level 13/14 — grade 7

By Level 13/14 the distractor construction is the real difficulty. Nearly every wrong option is correct in some respect, so guessing from a partial rule is close to guaranteed wrong. Eliminating against each rule separately is worth more here than at any earlier level.

Where children go wrong

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.

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.

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.

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: one small dotted arrow, rotated 180 degrees, then one small dotted arrow. Bottom row: one small dotted flag, rotated 90 degrees, then the missing figure.?
  • A.one small dotted flag, rotated 90 degreesone small dotted flag, rotated 90 degrees
  • B.one small dotted flag, rotated 270 degreesone small dotted flag, rotated 270 degrees
  • C.one small dotted flag, rotated 135 degreesone small dotted flag, rotated 135 degrees
  • D.one small dotted flag, rotated 180 degreesone small dotted flag, rotated 180 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 flag, rotated 270 degrees, which is option B. 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 D 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 two-by-two grid. Top row: three small half-filled ells, rotated 135 degrees, then three small half-filled ells, rotated 180 degrees. Bottom row: three small half-filled arrows, rotated 45 degrees, then the missing figure.?
  • A.three small half-filled arrows, rotated 90 degreesthree small half-filled arrows, rotated 90 degrees
  • B.three small half-filled arrows, rotated 135 degreesthree small half-filled arrows, rotated 135 degrees
  • C.three small half-filled arrowsthree small half-filled arrows
  • D.three small half-filled arrows, rotated 45 degreesthree small half-filled arrows, rotated 45 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 three small half-filled arrows, rotated 90 degrees, which is option A. Option D 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-by-two grid. Top row: two small half-filled ells, rotated 135 degrees, then two small half-filled ells, rotated 225 degrees. Bottom row: two small half-filled arrows, then the missing figure.?
  • A.two small half-filled arrows, rotated 180 degreestwo small half-filled arrows, rotated 180 degrees
  • B.two small half-filled arrows, rotated 270 degreestwo small half-filled arrows, rotated 270 degrees
  • C.two small half-filled arrows, rotated 90 degreestwo small half-filled arrows, rotated 90 degrees
  • D.two small half-filled arrowstwo 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 two small half-filled arrows, rotated 90 degrees, which is option C. Option D 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 A 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 two-by-two grid. Top row: one medium unfilled ell, rotated 90 degrees, then one medium unfilled ell, rotated 180 degrees. Bottom row: one medium unfilled flag, rotated 45 degrees, then the missing figure.?
  • A.one medium unfilled flag, rotated 225 degreesone medium unfilled flag, rotated 225 degrees
  • B.one medium unfilled flag, rotated 45 degreesone medium unfilled flag, rotated 45 degrees
  • C.one medium unfilled flag, rotated 135 degreesone medium unfilled flag, rotated 135 degrees
  • D.one medium unfilled flag, rotated 315 degreesone medium unfilled flag, rotated 315 degrees

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 one medium unfilled flag, rotated 135 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 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: one small dotted arrow, then one small dotted arrow, rotated 180 degrees. Bottom row: one small dotted ell, rotated 45 degrees, then the missing figure.?
  • A.one small dotted ell, rotated 90 degreesone small dotted ell, rotated 90 degrees
  • B.one small dotted ell, rotated 225 degreesone small dotted ell, rotated 225 degrees
  • C.one small dotted ell, rotated 135 degreesone small dotted ell, rotated 135 degrees
  • D.one small dotted ell, rotated 45 degreesone small dotted ell, rotated 45 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 225 degrees, 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 (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-by-two grid. Top row: one small dotted ell, rotated 90 degrees, then one small dotted ell, rotated 180 degrees. Bottom row: one small dotted flag, rotated 45 degrees, then the missing figure.?
  • A.one small dotted flag, rotated 45 degreesone small dotted flag, rotated 45 degrees
  • B.one small dotted flag, rotated 225 degreesone small dotted flag, rotated 225 degrees
  • C.one small dotted flag, rotated 135 degreesone small dotted flag, rotated 135 degrees
  • D.one small dotted flag, rotated 315 degreesone small dotted flag, rotated 315 degrees

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 one small dotted flag, rotated 135 degrees, which is option C. 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 B 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 two-by-two grid. Top row: one medium half-filled flag, rotated 90 degrees, then one medium half-filled flag, rotated 270 degrees. Bottom row: one medium half-filled ell, rotated 45 degrees, then the missing figure.?
  • A.one medium half-filled ell, rotated 90 degreesone medium half-filled ell, rotated 90 degrees
  • B.one medium half-filled ell, rotated 45 degreesone medium half-filled ell, rotated 45 degrees
  • C.one medium half-filled ell, rotated 135 degreesone medium half-filled ell, rotated 135 degrees
  • D.one medium half-filled ell, rotated 225 degreesone medium half-filled ell, rotated 225 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 one medium half-filled ell, 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 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 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: two small half-filled flags, then two small half-filled flags, rotated 90 degrees. Bottom row: two small half-filled arrows, rotated 180 degrees, then the missing figure.?
  • A.two small half-filled arrows, rotated 270 degreestwo small half-filled arrows, rotated 270 degrees
  • B.two small half-filled arrows, rotated 180 degreestwo small half-filled arrows, rotated 180 degrees
  • C.two small half-filled arrowstwo small half-filled arrows
  • D.two small half-filled arrows, rotated 90 degreestwo small half-filled arrows, rotated 90 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 small half-filled arrows, 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 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 two-by-two grid. Top row: one medium hatched ell, rotated 90 degrees, then one medium hatched ell, rotated 180 degrees. Bottom row: one medium hatched arrow, rotated 135 degrees, then the missing figure.?
  • A.one medium hatched arrow, rotated 225 degreesone medium hatched arrow, rotated 225 degrees
  • B.one medium hatched arrow, rotated 135 degreesone medium hatched arrow, rotated 135 degrees
  • C.one medium hatched arrow, rotated 45 degreesone medium hatched arrow, rotated 45 degrees
  • D.one medium hatched arrow, rotated 315 degreesone medium hatched arrow, 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 hatched arrow, 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 10medium

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 half-filled ells, rotated 135 degrees, then two small half-filled ells, rotated 315 degrees. Bottom row: two small half-filled flags, rotated 45 degrees, then the missing figure.?
  • A.two small half-filled flags, rotated 225 degreestwo small half-filled flags, rotated 225 degrees
  • B.two small half-filled flags, rotated 45 degreestwo small half-filled flags, rotated 45 degrees
  • C.two small half-filled flags, rotated 135 degreestwo small half-filled flags, rotated 135 degrees
  • D.two small half-filled flags, rotated 90 degreestwo small half-filled flags, rotated 90 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 two small half-filled flags, rotated 225 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.