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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.

1Each 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_4_easy_9_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="24.5,23.1 33.9,28.6 33.9,39.4 24.5,44.9 15.1,39.4 15.1,28.6" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/><polygon points="43.5,23.1 52.9,28.6 52.9,39.4 43.5,44.9 34.1,39.4 34.1,28.6" 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: 1 solid triangle | 2 solid hexagons | 3 solid squares. Look at Row 2: 2 solid hexagons | 3 solid squares | 1 solid triangle. Now look at Column 1 (top two cells): 1 solid triangle | 2 solid hexagons. 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: 2 solid hexagons — 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.

2The 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 (diamond 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 D. Option A 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 (square instead of parallelogram), 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.

3Each box in the grid contains the same three shapes (triangle, pentagon, 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="85.0,21.2 106.6,58.7 63.4,58.7" 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="85.0,151.0 106.7,166.8 98.4,192.2 71.6,192.2 63.3,166.8" 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">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 triangle (top), parallelogram (middle), pentagon (bottom). Applying the rotation gives Box 2: pentagon (top), triangle (middle), parallelogram (bottom). Applying it again gives Box 3: parallelogram (top), pentagon (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), parallelogram (middle), pentagon (bottom) — this is option B. Option C 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 middle and bottom 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 middle position with a diamond, a shape outside the shared set of triangle, pentagon, parallelogram, violating the requirement that every box use only the same three shapes.

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_4_complex_1_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="#c23b3b" 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="#c23b3b" stroke="#c23b3b" stroke-width="1.7"/><polygon points="34.0,23.1 44.9,34.0 34.0,44.9 23.1,34.0" fill="#c23b3b" stroke="#c23b3b" stroke-width="1.7"/><polygon points="53.0,23.1 63.9,34.0 53.0,44.9 42.2,34.0" fill="#c23b3b" stroke="#c23b3b" stroke-width="1.7"/></svg>
Every row and every column must keep each of the 4 attributes (count, shape, fill, and color) either all-the-same or all-different — never matching on exactly two out of three. Look at Row 1: 3 cobalt outline squares | 2 crimson solid triangles | 1 forest striped hexagon. Look at Row 2: 1 crimson solid hexagon | 3 forest striped squares | 2 cobalt outline triangles. Now look at Column 1 (top two cells): 3 cobalt outline squares | 1 crimson solid hexagon. 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, fill must do the same, and color must do the same. Solving all 4 attributes together gives exactly one answer: 3 crimson solid squares — choice D. Each wrong choice satisfies 3 of the 4 attributes correctly but breaks exactly one (either the count is off by one, the shape is swapped, the fill pattern is wrong, or the color is wrong) — 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 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="26.0,48.2 34.9,63.7 17.1,63.7" fill="#2f8f52" stroke="#1c1a15" stroke-width="1.6"/><polygon points="33.3,98.8 18.7,98.8 18.7,84.2 33.3,84.2" fill="#b3268f" 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="36.3,190.5 26.0,200.8 15.7,190.5 26.0,180.2" fill="#c23b3b" stroke="#1c1a15" stroke-width="1.6"/></svg>
Step 1 is heptagon → triangle → diamond → pentagon → circle → square. The rule is "rotate the whole stack up by two." Applying it once gives Step 2: diamond → pentagon → circle → square → heptagon → triangle. Applying it again gives Step 3: circle → square → heptagon → triangle → diamond → pentagon. Applying the same rule one more time to Step 3 produces the correct Step 4: heptagon → triangle → diamond → pentagon → circle → square — 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."

6Each box in the grid contains the same three shapes (circle, square, 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="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"/><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">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 square (top), diamond (middle), circle (bottom). Applying the rotation gives Box 2: circle (top), square (middle), diamond (bottom). Applying it again gives Box 3: diamond (top), circle (middle), square (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: square (top), diamond (middle), circle (bottom) — this is option B. Option A 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 pentagon, a shape outside the shared set of circle, square, diamond, violating the requirement that every box use only the same three shapes.

7The 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 filled (black) triangle) to the top-right box (medium outlined (white) square): the rule changes fill (invert white/black) and shape (advance square→circle→triangle) and size (advance small→medium→large), all at the same time. Applying that identical rule to the bottom-left box (medium outlined (white) circle) gives large filled (black) triangle — choice D. Verify it attribute by attribute: fill should invert, shape should advance one step in the cycle, and size should advance one step in the cycle. 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.

8Each box in the grid contains the same three shapes (pentagon, 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="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="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="85.0,151.0 106.7,166.8 98.4,192.2 71.6,192.2 63.3,166.8" 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">D</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), parallelogram (middle), pentagon (bottom). Applying the rotation gives Box 2: parallelogram (top), pentagon (middle), diamond (bottom). Applying it again gives Box 3: pentagon (top), diamond (middle), parallelogram (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: diamond (top), parallelogram (middle), pentagon (bottom) — this is option D. Option B rotates the stack in the downward 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 A preserves the correct rotated order but replaces the shape in the top position with a circle, a shape outside the shared set of pentagon, diamond, parallelogram, violating the requirement that every box use only the same three shapes.

9Each panel below shows one triangle. Moving from panel 1 to panel 3, the triangle'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="75.0,60.5 104.9,112.2 45.1,112.2" fill="#5c6472" 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 triangle's shading (darkness) increases by a constant step of 1 unit(s) per panel (shading-scale index). Panel 1 = shading level 1 of 6 (darker = higher), panel 2 = shading level 2 of 6 (darker = higher), panel 3 = shading level 3 of 6 (darker = higher). Adding the same step once more gives the missing panel: shading level 4 of 6 (darker = higher) — 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 B 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 parallelogram for the triangle, breaking the requirement that the same shape appear in every panel.

10Each panel below shows one hexagon. Moving from panel 1 to panel 3, the hexagon'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="75.0,70.5 96.2,82.8 96.2,107.2 75.0,119.5 53.8,107.2 53.8,82.8" 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">B</text></svg>
Rule: the hexagon'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 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 size as panel 2, reversing the progression instead of continuing it forward. Option C has the correct size value but substitutes a parallelogram for the hexagon, breaking the requirement that the same shape appear in every panel.

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