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Archive · November 2, 2026

Grade 2 Cognitive Skills (CogAT): 10 Free Practice Questions

A brand-new set of Grade 2 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.

1The 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="50.2,38.0 38.0,50.2 25.8,38.0 38.0,25.8" fill="#fffdf7" stroke="#1c1a15" stroke-width="2"/></svg>
Compare the top-left box (medium filled (black) triangle) to the top-right box (large 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 (small filled (black) triangle) gives medium outlined (white) square — 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.

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="75.0,66.8 103.2,95.0 75.0,123.2 46.8,95.0" 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">C</text></svg>
Rule: each row is assigned a fixed shape (parallelogram for row 1, hexagon for row 2, diamond 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 (diamond) with column 3's size (large) — this is option C. Option D uses the correct row-3 shape (diamond) 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 (hexagon instead of diamond), violating the row rule. Option B uses the correct size but substitutes a pentagon, a shape that does not appear anywhere in the grid, violating the row rule entirely.

3Each 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_2_medium_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="34.0,23.1 43.4,39.4 24.6,39.4" fill="none" stroke="#7c3aed" stroke-width="1.7"/></svg>
Every row and every column must keep each of the 3 attributes (count, shape, and fill) either all-the-same or all-different — never matching on exactly two out of three. Look at Row 1: 2 outline triangles | 1 solid hexagon | 3 striped squares. Look at Row 2: 1 striped square | 3 outline triangles | 2 solid hexagons. Now look at Column 1 (top two cells): 2 outline triangles | 1 striped square. 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, Solving all 3 attributes together gives exactly one answer: 1 outline triangle — choice D. Each wrong choice satisfies 2 of the 3 attributes correctly but breaks exactly one (either the count is off by one, the shape is swapped, the fill pattern 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.

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

5Each 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_2_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="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: 1 solid triangle | 3 solid squares | 2 solid hexagons. Look at Row 2: 3 solid squares | 2 solid hexagons | 1 solid triangle. Now look at Column 1 (top two cells): 1 solid triangle | 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.

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

7Each box in the grid contains the same three shapes (square, triangle, 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="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="85.0,148.9 106.6,186.3 63.4,186.3" 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), parallelogram (middle), triangle (bottom). Applying the rotation gives Box 2: parallelogram (top), triangle (middle), square (bottom). Applying it again gives Box 3: triangle (top), square (middle), parallelogram (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: square (top), parallelogram (middle), triangle (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 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 square, triangle, parallelogram, violating the requirement that every box use only the same three shapes.

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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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="75.0,68.1 100.6,86.7 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">A</text></svg>
Rule: each row is assigned a fixed shape (hexagon for row 1, circle 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 A. Option C uses the correct row-3 shape (pentagon) 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 (circle instead of pentagon), violating the row rule. Option D uses the correct size but substitutes a parallelogram, a shape that does not appear anywhere in the grid, violating the row rule entirely.

9Each box in the grid contains the same three shapes (square, triangle, 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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Show answer & explanation
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="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">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 triangle (top), square (middle), parallelogram (bottom). Applying the rotation gives Box 2: parallelogram (top), triangle (middle), square (bottom). Applying it again gives Box 3: square (top), parallelogram (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), square (middle), parallelogram (bottom) — this is option C. Option A 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 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 pentagon, a shape outside the shared set of square, triangle, parallelogram, violating the requirement that every box use only the same three shapes.

10Each 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">A</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 A. 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 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.

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