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Archive · October 31, 2026

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.

1Frame A and Frame B combine into Frame C, keeping every dot that appears in either frame. Study the two worked examples above, then choose the option that correctly completes Frame A + Frame B in the last row.

EXAMPLE 1+=EXAMPLE 2+=YOUR TURN+=?
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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="62" height="62" viewBox="0 0 62 62"><rect x="0" y="0" width="62" height="62" fill="#efeade" stroke="#211d16" stroke-width="1.4" rx="4"/><polygon points="31.0,6.0 52.7,18.5 52.7,43.5 31.0,56.0 9.3,43.5 9.3,18.5" fill="#fffdf7" stroke="#3a4a63" stroke-width="1.8"/><circle cx="31.0" cy="6.0" r="4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1.1"/><circle cx="52.7" cy="18.5" r="4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1.1"/><circle cx="52.7" cy="43.5" r="4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1.1"/></svg>
FRAME C must contain every dot that appears in FRAME A or FRAME B — a logical OR of the two source frames, not an overlap-only AND. Example 1 shows A={0,4} combined with B={3,4} to make C={0,3,4}: every dot from either source survives. Example 2 confirms the same rule with A={3,5} and B={0,4} making C={0,3,4,5}. For the final row, A={0,2} and B={1,2}, so the correct sum is every corner in either set: {0,1,2} — choice D. Verify by listing A3's corners, then B3's corners, then merging the two lists and removing repeats; that merged list should match choice D exactly. Each wrong choice fails for a specific, checkable reason: one keeps only the corners common to both frames (an AND instead of an OR), one is missing a dot that should have carried over from one of the source frames, and one has an extra dot at a corner that never appeared in A3 or B3 at all.

2Each 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 B 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 A has the correct size value but substitutes a parallelogram for the circle, 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 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="75.0,63.5 105.0,85.3 93.5,120.5 56.5,120.5 45.0,85.3" 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">B</text></svg>
Rule: the pentagon'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 B. Option D applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option A shows the same shading (darkness) as panel 2, reversing the progression instead of continuing it forward. Option C has the correct shading (darkness) value but substitutes a circle for the pentagon, breaking the requirement that the same shape appear in every panel.

4The 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 (circle for row 1, pentagon 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 B uses the correct row-3 shape (parallelogram) but the wrong column size (small instead of large), violating the column rule. Option D uses the correct column-3 size (large) but the wrong shape (circle instead of parallelogram), violating the row rule. Option C uses the correct size but substitutes a hexagon, a shape that does not appear anywhere in the grid, violating the row rule entirely.

5Each box in the grid contains the same three shapes (square, hexagon, 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="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="85.0,151.7 104.2,162.7 104.2,184.9 85.0,195.9 65.8,184.9 65.8,162.7" 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">C</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), square (middle), hexagon (bottom). Applying the rotation gives Box 2: hexagon (top), parallelogram (middle), square (bottom). Applying it again gives Box 3: square (top), hexagon (middle), parallelogram (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: parallelogram (top), square (middle), hexagon (bottom) — this is option C. Option D rotates the stack in the upward direction instead, which incorrectly reconstructs Box 2's arrangement rather than continuing the established rotation. Option B applies an incomplete transformation, swapping only the top and bottom shapes (leaving the middle shape fixed) of Box 3 rather than performing the full three-position rotation, so it fails to follow the rule consistently. Option A preserves the correct rotated order but replaces the shape in the bottom position with a triangle, a shape outside the shared set of square, hexagon, parallelogram, violating the requirement that every box use only the same three shapes.

6Each box in the grid contains the same three shapes (circle, 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"/><circle cx="85.0" cy="46.2" r="21.7" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="75.9,96.5 105.6,96.5 94.1,123.5 64.4,123.5" 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 circle (top), parallelogram (middle), diamond (bottom). Applying the rotation gives Box 2: diamond (top), circle (middle), parallelogram (bottom). Applying it again gives Box 3: parallelogram (top), diamond (middle), circle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: circle (top), parallelogram (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 D 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 hexagon, a shape outside the shared set of circle, diamond, parallelogram, violating the requirement that every box use only the same three shapes.

7The 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">D</text></svg>
Rule: each row is assigned a fixed shape (triangle for row 1, diamond 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 D. Option C uses the correct row-3 shape (parallelogram) 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 parallelogram), violating the row rule. Option A uses the correct size but substitutes a square, a shape that does not appear anywhere in the grid, violating the row rule entirely.

8A square sheet is folded and then punched with a hole, as shown. Which answer choice shows the sheet fully unfolded?

START
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.

9Each box in the grid contains the same three shapes (triangle, hexagon, 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="85.0,22.3 108.9,46.2 85.0,70.1 61.1,46.2" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,85.0 106.6,122.5 63.4,122.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,151.7 104.2,162.7 104.2,184.9 85.0,195.9 65.8,184.9 65.8,162.7" 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">C</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 diamond (top), triangle (middle), hexagon (bottom). Applying the rotation gives Box 2: triangle (top), hexagon (middle), diamond (bottom). Applying it again gives Box 3: hexagon (top), diamond (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: diamond (top), triangle (middle), hexagon (bottom) — this is option C. Option B rotates the stack in the downward direction instead, which incorrectly reconstructs Box 2's arrangement rather than continuing the established rotation. Option D 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 A preserves the correct rotated order but replaces the shape in the top position with a circle, a shape outside the shared set of triangle, hexagon, diamond, violating the requirement that every box use only the same three shapes.

10Each panel below shows one triangle. Moving from panel 1 to panel 3, the triangle'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="-10.0,80.0 2.9,102.5 -22.9,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="24.0,80.0 36.9,102.5 11.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="58.0,80.0 70.9,102.5 45.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="92.0,80.0 104.9,102.5 79.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="126.0,80.0 138.9,102.5 113.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="160.0,80.0 172.9,102.5 147.1,102.5" 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 triangle's number of copies increases by a constant step of 1 unit(s) per panel (count-scale index). Panel 1 = 3 copies, panel 2 = 4 copies, panel 3 = 5 copies. Adding the same step once more gives the missing panel: 6 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 diamond for the triangle, breaking the requirement that the same shape appear in every panel.

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