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Archive · November 2, 2026

Grade 4 Cognitive Skills (CogAT): 10 Free Practice Questions

A brand-new set of Grade 4 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.

1A square sheet is folded and then punched with a hole, as shown. Which answer choice shows the sheet fully unfolded?

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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="54.0" cy="27.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="54.0" cy="45.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/></svg>
The sheet is folded 1 time — Fold 1: horizontal crease at y=4. Punch 1 at (6,3). 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 (6,3) specifically: Undoing fold 1 (a horizontal crease at y=4): every current point reflects across this crease, doubling the hole count to 2. Combining every traced hole (and removing any exact duplicates) gives 2 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.

2Each panel below shows one square. Moving from panel 1 to panel 3, the square'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="97.3,72.7 97.3,117.3 52.7,117.3 52.7,72.7" fill="#1f2937" 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 square's shading (darkness) increases by a constant step of 1 unit(s) per panel (shading-scale index). Panel 1 = shading level 3 of 6 (darker = higher), panel 2 = shading level 4 of 6 (darker = higher), panel 3 = shading level 5 of 6 (darker = higher). Adding the same step once more gives the missing panel: shading level 6 of 6 (darker = higher) — this is option C. Option A applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option D 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 square, breaking the requirement that the same shape appear in every panel.

3Each panel below shows one pentagon. Moving from panel 1 to panel 3, the pentagon'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"/><polygon points="75.0,69.8 99.0,87.2 89.8,115.4 60.2,115.4 51.0,87.2" 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 pentagon's size increases by a constant step of 1 unit(s) per panel (size-scale index). Panel 1 = 24px diameter, panel 2 = 32px diameter, panel 3 = 40px diameter. Adding the same step once more gives the missing panel: 48px diameter — this is option C. Option A applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option D shows the same size as panel 2, reversing the progression instead of continuing it forward. Option B has the correct size value but substitutes a square for the pentagon, breaking the requirement that the same shape appear in every panel.

4Each panel below shows one square. Moving from panel 1 to panel 3, the square'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"/><polygon points="89.8,80.2 89.8,109.8 60.2,109.8 60.2,80.2" 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">A</text></svg>
Rule: the square'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 A. Option D applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option C shows the same size as panel 2, reversing the progression instead of continuing it forward. Option B has the correct size value but substitutes a diamond for the square, breaking the requirement that the same shape appear in every panel.

5Each box in the grid contains the same three shapes (square, triangle, diamond) 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="85.0,21.2 106.6,58.7 63.4,58.7" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="101.1,93.9 101.1,126.1 68.9,126.1 68.9,93.9" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,149.9 108.9,173.8 85.0,197.7 61.1,173.8" 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">A</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 triangle (top), square (middle), diamond (bottom). Applying the rotation gives Box 2: diamond (top), triangle (middle), square (bottom). Applying it again gives Box 3: square (top), diamond (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), square (middle), diamond (bottom) — this is option A. Option B rotates the stack in the upward direction instead, which incorrectly reconstructs Box 2's arrangement rather than continuing the established rotation. Option C 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 D preserves the correct rotated order but replaces the shape in the top position with a pentagon, a shape outside the shared set of square, triangle, diamond, violating the requirement that every box use only the same three shapes.

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"/><circle cx="75.0" cy="95.0" r="25.6" 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, circle 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 (circle) with column 3's size (large) — this is option D. Option C uses the correct row-3 shape (circle) but the wrong column size (medium instead of large), violating the column rule. Option A uses the correct column-3 size (large) but the wrong shape (diamond instead of circle), violating the row rule. Option B uses the correct size but substitutes a triangle, a shape that does not appear anywhere in the grid, violating the row rule entirely.

7Each panel below shows one pentagon. Moving from panel 1 to panel 3, the pentagon's number of copies 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="7.0,81.3 20.0,90.8 15.0,106.0 -1.0,106.0 -6.0,90.8" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="41.0,81.3 54.0,90.8 49.0,106.0 33.0,106.0 28.0,90.8" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="75.0,81.3 88.0,90.8 83.0,106.0 67.0,106.0 62.0,90.8" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="109.0,81.3 122.0,90.8 117.0,106.0 101.0,106.0 96.0,90.8" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="143.0,81.3 156.0,90.8 151.0,106.0 135.0,106.0 130.0,90.8" 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 pentagon's number of copies increases by a constant step of 1 unit(s) per panel (count-scale index). Panel 1 = 2 copies, panel 2 = 3 copies, panel 3 = 4 copies. Adding the same step once more gives the missing panel: 5 copies — this is option C. Option B applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option A shows the same number of copies as panel 2, reversing the progression instead of continuing it forward. Option D has the correct number of copies value but substitutes a hexagon for the pentagon, breaking the requirement that the same shape appear in every panel.

8The 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="64.3,79.1 99.3,79.1 85.7,110.9 50.7,110.9" 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">A</text></svg>
Rule: each row is assigned a fixed shape (pentagon for row 1, square for row 2, parallelogram 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 (parallelogram) with column 3's size (large) — this is option A. Option C uses the correct row-3 shape (parallelogram) but the wrong column size (medium instead of large), violating the column rule. Option D uses the correct column-3 size (large) but the wrong shape (square instead of parallelogram), violating the row rule. Option B uses the correct size but substitutes a triangle, a shape that does not appear anywhere in the grid, violating the row rule entirely.

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="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 (medium instead of large), violating the column rule. Option B uses the correct column-3 size (large) but the wrong shape (diamond instead of square), violating the row rule. Option C uses the correct size but substitutes a triangle, a shape that does not appear anywhere in the grid, violating the row rule entirely.

10The 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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Show answer & explanation
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 (parallelogram for row 1, diamond 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 (small instead of large), violating the column rule. Option A uses the correct column-3 size (large) but the wrong shape (parallelogram instead of hexagon), 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.

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