Grade 3 Cognitive Skills (CogAT): 10 Free Practice Questions

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="85.0,87.9 104.2,98.9 104.2,121.1 85.0,132.1 65.8,121.1 65.8,98.9" 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 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), hexagon (middle), parallelogram (bottom). Applying the rotation gives Box 2: hexagon (top), parallelogram (middle), diamond (bottom). Applying it again gives Box 3: parallelogram (top), diamond (middle), hexagon (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: diamond (top), hexagon (middle), parallelogram (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 A 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 D preserves the correct rotated order but replaces the shape in the bottom position with a circle, a shape outside the shared set of hexagon, diamond, parallelogram, violating the requirement that every box use only the same three shapes.

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="85.0,87.9 104.2,98.9 104.2,121.1 85.0,132.1 65.8,121.1 65.8,98.9" 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">D</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), hexagon (middle), diamond (bottom). Applying the rotation gives Box 2: diamond (top), triangle (middle), hexagon (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: triangle (top), hexagon (middle), diamond (bottom) — this is option D. Option A 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 middle and bottom shapes 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 middle position with a square, a shape outside the shared set of triangle, hexagon, diamond, violating the requirement that every box use only the same three shapes.

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">B</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 B. Option A 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 D has the correct size value but substitutes a hexagon for the square, breaking the requirement that the same shape appear in every panel.

Answer: 7
The correct answer is 7, since each second number is one-third of the first. Identify the relationship between 15 and 5: 15 ÷ 3 = 5, so the rule is 'divide by 3.' Apply the same rule to 21: 21 ÷ 3 = 7. Students may subtract a fixed value (15 − 5 = 10) instead of dividing, incorrectly subtracting 10 from 21 to arrive at 11, or miscalculate the division to get 8 or 6.

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Step 1 is square → diamond → circle → pentagon → heptagon → triangle → hexagon. The rule is "the top and bottom shapes stay fixed while everything between them reverses." Applying it once gives Step 2: square → triangle → heptagon → pentagon → circle → diamond → hexagon. Applying it again gives Step 3: square → diamond → circle → pentagon → heptagon → triangle → hexagon. Applying the same rule one more time to Step 3 produces the correct Step 4: square → triangle → heptagon → pentagon → circle → diamond → hexagon — 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 7 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."

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="30.0" 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 circle'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 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 shading (darkness) as panel 2, reversing the progression instead of continuing it forward. Option D has the correct shading (darkness) value but substitutes a triangle for the circle, breaking the requirement that the same shape appear in every panel.

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"/><circle cx="38" cy="38" r="16.0512" fill="#1c1a15" stroke="#1c1a15" stroke-width="2"/></svg>
Compare the top-left box (large filled (black) triangle) to the top-right box (small 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) square) gives large filled (black) circle — 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.

Answer: accurate
'Accurate' is correct because repeating an experiment is done to confirm correctness, not other unrelated traits. The clue is 'repeated the experiment three times,' which is a strategy scientists use to check for correctness and reliability. 'Accurate' directly relates to confirming correct results, unlike the other unrelated adjectives. Students may select an unrelated adjective like 'colorful' or 'expensive' without connecting the purpose of repeating an experiment to accuracy.

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="85.0,151.7 104.2,162.7 104.2,184.9 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">A</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 triangle (top), square (middle), hexagon (bottom). Applying the rotation gives Box 2: square (top), hexagon (middle), triangle (bottom). Applying it again gives Box 3: hexagon (top), triangle (middle), square (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), square (middle), hexagon (bottom) — this is option A. Option D rotates the stack in the downward 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 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 circle, a shape outside the shared set of square, triangle, hexagon, violating the requirement that every box use only the same three shapes.

Answer: <svg xmlns="http://www.w3.org/2000/svg" width="68" height="68" viewBox="0 0 68 68"><defs><pattern id="patc_3_medium_6_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 35.4,34.0 24.5,44.9 13.6,34.0" fill="url(#patc_3_medium_6_0)" stroke="#7c3aed" stroke-width="1.7"/><polygon points="43.5,23.1 54.4,34.0 43.5,44.9 32.6,34.0" fill="url(#patc_3_medium_6_0)" 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: 3 striped hexagons | 2 outline squares | 1 solid triangle. Look at Row 2: 2 solid squares | 1 striped triangle | 3 outline hexagons. Now look at Column 1 (top two cells): 3 striped hexagons | 2 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, fill must do the same, Solving all 3 attributes together gives exactly one answer: 2 striped squares — 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.