Grade 5 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="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="85.0,87.2 106.7,103.0 98.4,128.4 71.6,128.4 63.3,103.0" 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">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 square (top), pentagon (middle), circle (bottom). Applying the rotation gives Box 2: circle (top), square (middle), pentagon (bottom). Applying it again gives Box 3: pentagon (top), circle (middle), square (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: square (top), pentagon (middle), circle (bottom) — this is option A. Option C 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 middle 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 top position with a parallelogram, a shape outside the shared set of circle, square, pentagon, violating the requirement that every box use only the same three shapes.

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) square) to the top-right box (medium 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 (medium 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 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.

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

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="85.0,24.1 104.2,35.1 104.2,57.3 85.0,68.3 65.8,57.3 65.8,35.1" 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="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">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 hexagon (top), diamond (middle), parallelogram (bottom). Applying the rotation gives Box 2: diamond (top), parallelogram (middle), hexagon (bottom). Applying it again gives Box 3: parallelogram (top), hexagon (middle), diamond (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: hexagon (top), diamond (middle), parallelogram (bottom) — this is option D. Option C 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 B preserves the correct rotated order but replaces the shape in the bottom position with a triangle, 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="52" height="150" viewBox="0 0 52 150"><polygon points="26.0,15.2 35.8,22.3 32.1,33.8 19.9,33.8 16.2,22.3" fill="#7c3aed" stroke="#1c1a15" stroke-width="1.6"/><circle cx="26.0" cy="58.5" r="10.32" fill="#2f6fed" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,81.2 34.9,96.7 17.1,96.7" fill="#2f8f52" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,114.2 34.1,118.1 36.1,126.8 30.5,133.8 21.5,133.8 15.9,126.8 17.9,118.1" fill="#0f8f82" stroke="#1c1a15" stroke-width="1.6"/></svg>
Step 1 is heptagon → pentagon → circle → triangle. The rule is "rotate the whole stack down by one." Applying it once gives Step 2: triangle → heptagon → pentagon → circle. Applying it again gives Step 3: circle → triangle → heptagon → pentagon. Applying the same rule one more time to Step 3 produces the correct Step 4: pentagon → circle → triangle → heptagon — 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 4 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="52" height="216" viewBox="0 0 52 216"><polygon points="33.3,32.8 18.7,32.8 18.7,18.2 33.3,18.2" fill="#b3268f" stroke="#1c1a15" stroke-width="1.6"/><polygon points="36.3,58.5 31.2,67.4 20.8,67.4 15.7,58.5 20.8,49.6 31.2,49.6" fill="#c98a10" stroke="#1c1a15" stroke-width="1.6"/><polygon points="36.3,91.5 26.0,101.8 15.7,91.5 26.0,81.2" fill="#c23b3b" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,114.2 34.9,129.7 17.1,129.7" fill="#2f8f52" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,147.2 34.1,151.1 36.1,159.8 30.5,166.8 21.5,166.8 15.9,159.8 17.9,151.1" fill="#0f8f82" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,180.2 35.8,187.3 32.1,198.8 19.9,198.8 16.2,187.3" fill="#7c3aed" stroke="#1c1a15" stroke-width="1.6"/></svg>
Step 1 is diamond → heptagon → triangle → square → hexagon → pentagon. The rule is "the top and bottom shapes stay fixed while everything between them reverses." Applying it once gives Step 2: diamond → hexagon → square → triangle → heptagon → pentagon. Applying it again gives Step 3: diamond → heptagon → triangle → square → hexagon → pentagon. Applying the same rule one more time to Step 3 produces the correct Step 4: diamond → hexagon → square → triangle → heptagon → pentagon — 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."

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="85.0,149.9 108.9,173.8 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">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), square (middle), diamond (bottom). Applying the rotation gives Box 2: diamond (top), triangle (middle), square (bottom). Applying it again gives Box 3: square (top), diamond (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), square (middle), diamond (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 middle and bottom 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 middle position with a pentagon, a shape outside the shared set of square, triangle, 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="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">B</text></svg>
Rule: each row is assigned a fixed shape (pentagon 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 B. Option C 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 (pentagon instead of parallelogram), violating the row rule. Option A uses the correct size but substitutes a circle, a shape that does not appear anywhere in the grid, violating the row rule entirely.

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="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 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), hexagon (middle), parallelogram (bottom). Applying the rotation gives Box 2: parallelogram (top), circle (middle), hexagon (bottom). Applying it again gives Box 3: hexagon (top), parallelogram (middle), circle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: circle (top), hexagon (middle), parallelogram (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 middle and bottom 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 middle position with a diamond, a shape outside the shared set of circle, hexagon, parallelogram, violating the requirement that every box use only the same three shapes.

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"/><circle cx="31.0" cy="56.0" r="4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1.1"/><circle cx="9.3" cy="43.5" r="4" fill="#8a3b2b" stroke="#1c1a15" stroke-width="1.1"/><circle cx="9.3" cy="18.5" 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={1,3,4,5} combined with B={1,3,4,5} to make C={1,3,4,5}: every dot from either source survives. Example 2 confirms the same rule with A={1,2,4,5} and B={0,1,2,4} making C={0,1,2,4,5}. For the final row, A={0,2,3,5} and B={0,1,3,4}, so the correct sum is every corner in either set: {0,1,2,3,4,5} — 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.