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Grade 5 Cognitive Skills (CogAT): 10 Free Practice Questions

A brand-new set of Grade 5 CogAT practice questions every single day, with the answer and a full explanation for each one. No account, no paywall — tap an answer to check it.

1Each box in the grid contains the same three shapes (square, diamond, parallelogram) stacked in a different vertical order. Study the pattern connecting the three boxes shown, then determine which answer choice correctly completes the missing box.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="170" height="262" viewBox="0 0 170 262"><rect x="0" y="0" width="170" height="262" fill="#ffffff"/><rect x="1" y="1" width="168" height="218" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="101.1,30.1 101.1,62.3 68.9,62.3 68.9,30.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,86.1 108.9,110.0 85.0,133.9 61.1,110.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="75.9,160.4 105.6,160.4 94.1,187.3 64.4,187.3" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="218.0" width="170" height="44" fill="#111827"/><text x="85.0" y="249.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">B</text></svg>
Rule: each successive box is generated by a single-step upward cyclic rotation of the stack — the shape that occupies the top position moves to the bottom, and the other two shapes shift down to fill the remaining slots. Box 1 shows square (top), diamond (middle), parallelogram (bottom). Applying the rotation gives Box 2: diamond (top), parallelogram (middle), square (bottom). Applying it again gives Box 3: parallelogram (top), square (middle), diamond (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: square (top), diamond (middle), parallelogram (bottom) — this is option B. Option D rotates the stack in the downward direction instead, which incorrectly reconstructs Box 2's arrangement rather than continuing the established rotation. Option A applies an incomplete transformation, swapping only the middle and bottom shapes of Box 3 rather than performing the full three-position rotation, so it fails to follow the rule consistently. Option C preserves the correct rotated order but replaces the shape in the middle position with a pentagon, a shape outside the shared set of square, diamond, parallelogram, violating the requirement that every box use only the same three shapes.

2Each stack rearranges the same set of shapes using one consistent rule. Study Step 1, Step 2, and Step 3 above, then choose the answer that continues the pattern into Step 4.

STEP 1STEP 2STEP 3STEP 4?
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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="52" height="216" viewBox="0 0 52 216"><polygon points="26.0,15.2 34.1,19.1 36.1,27.8 30.5,34.8 21.5,34.8 15.9,27.8 17.9,19.1" fill="#0f8f82" stroke="#1c1a15" stroke-width="1.6"/><polygon points="36.3,58.5 31.2,67.4 20.8,67.4 15.7,58.5 20.8,49.6 31.2,49.6" fill="#c98a10" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,81.2 34.9,96.7 17.1,96.7" fill="#2f8f52" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,114.2 35.8,121.3 32.1,132.8 19.9,132.8 16.2,121.3" fill="#7c3aed" stroke="#1c1a15" stroke-width="1.6"/><circle cx="26.0" cy="157.5" r="10.32" fill="#2f6fed" stroke="#1c1a15" stroke-width="1.6"/><polygon points="33.3,197.8 18.7,197.8 18.7,183.2 33.3,183.2" fill="#b3268f" stroke="#1c1a15" stroke-width="1.6"/></svg>
Step 1 is diamond → hexagon → triangle → pentagon → circle → heptagon. The rule is "swap only the top and bottom shapes; the middle stays put." Applying it once gives Step 2: heptagon → hexagon → triangle → pentagon → circle → diamond. Applying it again gives Step 3: diamond → hexagon → triangle → pentagon → circle → heptagon. Applying the same rule one more time to Step 3 produces the correct Step 4: heptagon → hexagon → triangle → pentagon → circle → diamond — this is choice D. Check it by re-deriving Step 3 → Step 4 independently and confirming every position matches. Each wrong choice fails for a specific, nameable reason: one choice swaps the direction of the rotation/reflection — a common error when a student applies the rule backward, one takes the correct order and swaps two shapes near the middle — a transcription slip, and one takes the correct order but replaces the last shape with the gray octagon, which never belonged to this set of 6 shapes. A careful student should be able to point to the exact position where each wrong choice breaks the rule, not just recognize that "it looks different."

3The 3x3 grid below follows two independent rules: every cell in a given row uses the same shape, and every cell in a given column uses the same size. Study the pattern across the completed rows and columns, then choose the option that correctly completes the missing bottom-right cell.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="150" height="232" viewBox="0 0 150 232"><rect x="0" y="0" width="150" height="232" fill="#ffffff"/><rect x="1" y="1" width="148" height="188" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="94.0,76.0 94.0,114.0 56.0,114.0 56.0,76.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="188.0" width="150" height="44" fill="#111827"/><text x="75.0" y="219.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">D</text></svg>
Rule: each row is assigned a fixed shape (parallelogram for row 1, diamond for row 2, square for row 3) that stays constant across all three columns, and each column is assigned a fixed size (small for column 1, medium for column 2, large for column 3) that stays constant across all three rows. The missing cell is row 3, column 3, so it must combine row 3's shape (square) with column 3's size (large) — this is option D. Option A uses the correct row-3 shape (square) but the wrong column size (small instead of large), violating the column rule. Option B uses the correct column-3 size (large) but the wrong shape (parallelogram instead of square), violating the row rule. Option C uses the correct size but substitutes a circle, a shape that does not appear anywhere in the grid, violating the row rule entirely.

4Each panel below shows one circle. Moving from panel 1 to panel 3, the circle's size changes by the same fixed amount at every step. Study the pattern, then choose the option that correctly completes the missing 4th panel.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="150" height="232" viewBox="0 0 150 232"><rect x="0" y="0" width="150" height="232" fill="#ffffff"/><rect x="1" y="1" width="148" height="188" fill="#ffffff" stroke="#111827" stroke-width="2"/><circle cx="75.0" cy="95.0" r="20.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="188.0" width="150" height="44" fill="#111827"/><text x="75.0" y="219.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">C</text></svg>
Rule: the circle's size increases by a constant step of 1 unit(s) per panel (size-scale index). Panel 1 = 16px diameter, panel 2 = 24px diameter, panel 3 = 32px diameter. Adding the same step once more gives the missing panel: 40px diameter — this is option C. Option D applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option B shows the same size as panel 2, reversing the progression instead of continuing it forward. Option A has the correct size value but substitutes a pentagon for the circle, breaking the requirement that the same shape appear in every panel.

5A square sheet is folded and then punched with a hole, as shown. Which answer choice shows the sheet fully unfolded?

START
AFTER FOLD 1
PUNCHED
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Answer: <svg width="72" height="72" viewBox="0 0 72 72"><rect x="0" y="0" width="72" height="72" fill="#dbe7f5" stroke="#2b4a72" stroke-width="1.6" rx="4"/><circle cx="9.0" cy="27.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="63.0" cy="27.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="9.0" cy="45.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="63.0" cy="45.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/></svg>
The sheet is folded 2 times — Fold 1: vertical crease at x=4; Fold 2: horizontal crease at y=4. Punch 1 at (1,3). To find the fully unfolded pattern, undo the folds in reverse order (last fold first), reflecting every hole across each crease line — unless a hole sits exactly ON that crease, in which case it reflects onto itself and does not create a new hole. Tracing punch 1 at (1,3) specifically: Undoing fold 2 (a horizontal crease at y=4): every current point reflects across this crease, doubling the hole count to 2. Undoing fold 1 (a vertical crease at x=4): every current point reflects across this crease, doubling the hole count to 4. Combining every traced hole (and removing any exact duplicates) gives 4 holes total in the fully unfolded sheet — choice D. Each wrong choice comes from one specific, common mistake: one forgets to undo the very last fold that was made (leaving the pattern only partly unfolded), one undoes a crease using the wrong axis (mirroring left-right instead of top-bottom, or vice versa), and one mishandles a punch that sits exactly on a crease — either wrongly doubling a hole that should stay single, or wrongly leaving a hole single that should have doubled.

6The 3x3 grid below follows two independent rules: every cell in a given row uses the same shape, and every cell in a given column uses the same size. Study the pattern across the completed rows and columns, then choose the option that correctly completes the missing bottom-right cell.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="150" height="232" viewBox="0 0 150 232"><rect x="0" y="0" width="150" height="232" fill="#ffffff"/><rect x="1" y="1" width="148" height="188" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="75.0,68.1 100.6,86.7 90.8,116.7 59.2,116.7 49.4,86.7" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="188.0" width="150" height="44" fill="#111827"/><text x="75.0" y="219.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">D</text></svg>
Rule: each row is assigned a fixed shape (diamond for row 1, hexagon for row 2, pentagon for row 3) that stays constant across all three columns, and each column is assigned a fixed size (small for column 1, medium for column 2, large for column 3) that stays constant across all three rows. The missing cell is row 3, column 3, so it must combine row 3's shape (pentagon) with column 3's size (large) — this is option D. Option A uses the correct row-3 shape (pentagon) but the wrong column size (medium instead of large), violating the column rule. Option C uses the correct column-3 size (large) but the wrong shape (hexagon instead of pentagon), violating the row rule. Option B uses the correct size but substitutes a square, a shape that does not appear anywhere in the grid, violating the row rule entirely.

7Each box in the grid contains the same three shapes (square, diamond, parallelogram) stacked in a different vertical order. Study the pattern connecting the three boxes shown, then determine which answer choice correctly completes the missing box.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="170" height="262" viewBox="0 0 170 262"><rect x="0" y="0" width="170" height="262" fill="#ffffff"/><rect x="1" y="1" width="168" height="218" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="75.9,32.7 105.6,32.7 94.1,59.6 64.4,59.6" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,86.1 108.9,110.0 85.0,133.9 61.1,110.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="101.1,157.7 101.1,189.9 68.9,189.9 68.9,157.7" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="218.0" width="170" height="44" fill="#111827"/><text x="85.0" y="249.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">B</text></svg>
Rule: each successive box is generated by a single-step downward cyclic rotation of the stack — the shape that occupies the bottom position moves to the top, and the other two shapes shift down to fill the remaining slots. Box 1 shows parallelogram (top), diamond (middle), square (bottom). Applying the rotation gives Box 2: square (top), parallelogram (middle), diamond (bottom). Applying it again gives Box 3: diamond (top), square (middle), parallelogram (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: parallelogram (top), diamond (middle), square (bottom) — this is option B. Option D rotates the stack in the upward direction instead, which incorrectly reconstructs Box 2's arrangement rather than continuing the established rotation. Option A applies an incomplete transformation, swapping only the top and middle shapes of Box 3 rather than performing the full three-position rotation, so it fails to follow the rule consistently. Option C preserves the correct rotated order but replaces the shape in the top position with a triangle, a shape outside the shared set of square, diamond, parallelogram, violating the requirement that every box use only the same three shapes.

8The relationship between the top-left and top-right box also applies from the bottom-left box to the missing box. Which picture goes best in the box with the question mark?

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="76" height="76" viewBox="0 0 76 76"><rect width="76" height="76" fill="#fffdf7" stroke="#211d16" stroke-width="1.4"/><line x1="38" y1="10.64" x2="38" y2="0" stroke="#211d16" stroke-width="1.4"/><polygon points="38,0 39.5576733692346,3.6842439760115404 36.4423266307654,3.6842439760115404" fill="#211d16"/><line x1="38" y1="65.36" x2="38" y2="76" stroke="#211d16" stroke-width="1.4"/><polygon points="38,76 36.4423266307654,72.31575602398846 39.5576733692346,72.31575602398846" fill="#211d16"/><line x1="10.64" y1="38" x2="0" y2="38" stroke="#211d16" stroke-width="1.4"/><polygon points="0,38 3.6842439760115404,36.4423266307654 3.684243976011541,39.5576733692346" fill="#211d16"/><line x1="65.36" y1="38" x2="76" y2="38" stroke="#211d16" stroke-width="1.4"/><polygon points="76,38 72.31575602398846,39.5576733692346 72.31575602398846,36.4423266307654" fill="#211d16"/><polygon points="38.0,21.9 51.9,46.0 24.1,46.0" fill="#1c1a15" stroke="#1c1a15" stroke-width="2"/></svg>
Compare the top-left box (small outlined (white) triangle) to the top-right box (small filled (black) triangle): the rule changes fill (invert white/black). Everything else about the shape stays exactly the same — that is the trap. Applying that identical rule to the bottom-left box (large outlined (white) triangle) gives large filled (black) triangle — choice D. Verify it attribute by attribute: fill should invert, shape should stay the same, and size should stay the same. Each wrong choice gets every attribute right except exactly one: one choice has the wrong fill, one has the wrong shape, and one has the wrong size — find the single attribute that breaks in each wrong choice rather than judging the picture as a whole.

9The 3x3 grid below follows two independent rules: every cell in a given row uses the same shape, and every cell in a given column uses the same size. Study the pattern across the completed rows and columns, then choose the option that correctly completes the missing bottom-right cell.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="150" height="232" viewBox="0 0 150 232"><rect x="0" y="0" width="150" height="232" fill="#ffffff"/><rect x="1" y="1" width="148" height="188" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="75.0,68.9 97.6,81.9 97.6,108.1 75.0,121.1 52.4,108.1 52.4,81.9" fill="#6b7280" stroke="#111827" stroke-width="2"/><rect x="0" y="188.0" width="150" height="44" fill="#111827"/><text x="75.0" y="219.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">D</text></svg>
Rule: each row is assigned a fixed shape (square for row 1, triangle for row 2, hexagon for row 3) that stays constant across all three columns, and each column is assigned a fixed size (small for column 1, medium for column 2, large for column 3) that stays constant across all three rows. The missing cell is row 3, column 3, so it must combine row 3's shape (hexagon) with column 3's size (large) — this is option D. Option B uses the correct row-3 shape (hexagon) but the wrong column size (medium instead of large), violating the column rule. Option C uses the correct column-3 size (large) but the wrong shape (triangle instead of hexagon), violating the row rule. Option A uses the correct size but substitutes a pentagon, a shape that does not appear anywhere in the grid, violating the row rule entirely.

10Each panel below shows one parallelogram. Moving from panel 1 to panel 3, the parallelogram's shading (darkness) changes by the same fixed amount at every step. Study the pattern, then choose the option that correctly completes the missing 4th panel.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="150" height="232" viewBox="0 0 150 232"><rect x="0" y="0" width="150" height="232" fill="#ffffff"/><rect x="1" y="1" width="148" height="188" fill="#ffffff" stroke="#111827" stroke-width="2"/><polygon points="62.5,76.4 103.5,76.4 87.5,113.6 46.5,113.6" fill="#374151" stroke="#111827" stroke-width="2"/><rect x="0" y="188.0" width="150" height="44" fill="#111827"/><text x="75.0" y="219.0" font-size="22" font-weight="bold" font-family="Arial, sans-serif" text-anchor="middle" fill="#ffffff">D</text></svg>
Rule: the parallelogram's shading (darkness) increases by a constant step of 1 unit(s) per panel (shading-scale index). Panel 1 = shading level 2 of 6 (darker = higher), panel 2 = shading level 3 of 6 (darker = higher), panel 3 = shading level 4 of 6 (darker = higher). Adding the same step once more gives the missing panel: shading level 5 of 6 (darker = higher) — this is option D. Option A applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option C shows the same shading (darkness) as panel 2, reversing the progression instead of continuing it forward. Option B has the correct shading (darkness) value but substitutes a hexagon for the parallelogram, breaking the requirement that the same shape appear in every panel.

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