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Archive · October 30, 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.

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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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="18.0" cy="27.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="54.0" cy="27.0" r="3.4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1"/><circle cx="18.0" cy="45.0" 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 2 times — Fold 1: vertical crease at x=4; Fold 2: horizontal crease at y=4. Punch 1 at (2,3). 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 (2,3) 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.

2Each panel below shows one diamond. Moving from panel 1 to panel 3, the diamond'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="-10.0,80.7 4.3,95.0 -10.0,109.3 -24.3,95.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="24.0,80.7 38.3,95.0 24.0,109.3 9.7,95.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="58.0,80.7 72.3,95.0 58.0,109.3 43.7,95.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="92.0,80.7 106.3,95.0 92.0,109.3 77.7,95.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="126.0,80.7 140.3,95.0 126.0,109.3 111.7,95.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="160.0,80.7 174.3,95.0 160.0,109.3 145.7,95.0" 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">A</text></svg>
Rule: the diamond'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 A. Option C applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option B 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 parallelogram for the diamond, breaking the requirement that the same shape appear in every panel.

3The 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="38.0,29.2 45.6,42.4 30.4,42.4" fill="#fffdf7" stroke="#1c1a15" stroke-width="2"/></svg>
Compare the top-left box (large filled (black) square) to the top-right box (large outlined (white) circle): the rule changes fill (invert white/black) and shape (advance square→circle→triangle), all at the same time. Everything else about the shape stays exactly the same — that is the trap. Applying that identical rule to the bottom-left box (small filled (black) circle) gives small outlined (white) triangle — choice D. Verify it attribute by attribute: fill should invert, shape should advance one step in the cycle, 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.

4Each row and column follows the same rule: every attribute is either the same across all three cards, or different across all three. Find the card that correctly completes the missing bottom-right cell.

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Answer: <svg xmlns="http://www.w3.org/2000/svg" width="68" height="68" viewBox="0 0 68 68"><defs><pattern id="patc_5_easy_10_0" width="4" height="4" patternTransform="rotate(45)" patternUnits="userSpaceOnUse"><rect width="4" height="4" fill="#fffdf7"/><line x1="0" y1="0" x2="0" y2="4" stroke="#c98a10" stroke-width="2"/></pattern></defs><rect x="0" y="0" width="68" height="68" fill="#fffdf7" stroke="#211d16" stroke-width="1.4" rx="4"/><polygon points="15.0,23.1 25.8,34.0 15.0,44.9 4.1,34.0" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/><polygon points="34.0,23.1 44.9,34.0 34.0,44.9 23.1,34.0" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/><polygon points="53.0,23.1 63.9,34.0 53.0,44.9 42.2,34.0" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/></svg>
Every row and every column must keep each of the 2 attributes (count and shape) either all-the-same or all-different — never matching on exactly two out of three. Look at Row 1: 2 solid hexagons | 3 solid squares | 1 solid triangle. Look at Row 2: 3 solid squares | 1 solid triangle | 2 solid hexagons. Now look at Column 1 (top two cells): 2 solid hexagons | 3 solid squares. For the missing bottom-right cell, work through each attribute one at a time: count must complete Row 3 and Column 3 correctly, shape must do the same, Solving all 2 attributes together gives exactly one answer: 3 solid squares — choice D. Each wrong choice satisfies 1 of the 2 attributes correctly but breaks exactly one (either the count is off by one, the shape is swapped, ) — that one-attribute slip is the single most common mistake on this item type, so double-check each attribute separately rather than eyeballing the whole card at once.

5Each 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.

6Each box in the grid contains the same three shapes (circle, triangle, pentagon) 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="85.0,23.4 106.7,39.1 98.4,64.6 71.6,64.6 63.3,39.1" 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"/><circle cx="85.0" cy="173.8" r="21.7" 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">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 pentagon (top), triangle (middle), circle (bottom). Applying the rotation gives Box 2: circle (top), pentagon (middle), triangle (bottom). Applying it again gives Box 3: triangle (top), circle (middle), pentagon (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: pentagon (top), triangle (middle), circle (bottom) — this is option A. 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 C preserves the correct rotated order but replaces the shape in the bottom position with a hexagon, a shape outside the shared set of circle, triangle, pentagon, violating the requirement that every box use only the same three shapes.

7Each panel below shows one parallelogram. Moving from panel 1 to panel 3, the parallelogram'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="-15.4,86.9 2.3,86.9 -4.6,103.1 -22.4,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="18.6,86.9 36.4,86.9 29.4,103.1 11.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="52.6,86.9 70.3,86.9 63.4,103.1 45.6,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="86.6,86.9 104.4,86.9 97.4,103.1 79.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="120.6,86.9 138.3,86.9 131.4,103.1 113.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="154.6,86.9 172.3,86.9 165.4,103.1 147.7,103.1" 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">B</text></svg>
Rule: the parallelogram'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 B. Option C applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option D shows the same number of copies as panel 2, reversing the progression instead of continuing it forward. Option A has the correct number of copies value but substitutes a circle for the parallelogram, breaking the requirement that the same shape appear in every panel.

8Each 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="75.0,65.6 103.0,85.9 92.3,118.8 57.7,118.8 47.0,85.9" 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">C</text></svg>
Rule: the pentagon's size increases by a constant step of 1 unit(s) per panel (size-scale index). Panel 1 = 32px diameter, panel 2 = 40px diameter, panel 3 = 48px diameter. Adding the same step once more gives the missing panel: 56px 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 hexagon for the pentagon, breaking the requirement that the same shape appear in every panel.

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">B</text></svg>
Rule: each row is assigned a fixed shape (circle for row 1, pentagon 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 B. Option A uses the correct row-3 shape (square) 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 (pentagon instead of square), 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.

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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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="75.0,65.6 100.5,109.7 49.5,109.7" 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">A</text></svg>
Rule: each row is assigned a fixed shape (parallelogram for row 1, square for row 2, triangle 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 (triangle) with column 3's size (large) — this is option A. Option B uses the correct row-3 shape (triangle) 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 triangle), violating the row rule. Option C uses the correct size but substitutes a pentagon, a shape that does not appear anywhere in the grid, violating the row rule entirely.

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