Grade 4 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="85.0,21.2 106.6,58.7 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"/><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 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), parallelogram (middle), circle (bottom). Applying the rotation gives Box 2: parallelogram (top), circle (middle), triangle (bottom). Applying it again gives Box 3: circle (top), triangle (middle), parallelogram (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), parallelogram (middle), circle (bottom) — this is option A. Option C 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 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 square, a shape outside the shared set of circle, triangle, parallelogram, 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_4_easy_2_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="#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 | 1 solid triangle | 3 solid squares. Look at Row 2: 1 solid triangle | 3 solid squares | 2 solid hexagons. Now look at Column 1 (top two cells): 2 solid hexagons | 1 solid triangle. 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: 1 solid triangle — 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.

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="85.0,87.2 106.7,103.0 98.4,128.4 71.6,128.4 63.3,103.0" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="101.1,157.7 101.1,189.9 68.9,189.9 68.9,157.7" 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 triangle (top), pentagon (middle), square (bottom). Applying the rotation gives Box 2: square (top), triangle (middle), pentagon (bottom). Applying it again gives Box 3: pentagon (top), square (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), pentagon (middle), square (bottom) — this is option B. Option D 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 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 A preserves the correct rotated order but replaces the shape in the bottom position with a parallelogram, a shape outside the shared set of square, triangle, pentagon, 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">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), 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 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 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 square, a shape outside the shared set of triangle, hexagon, diamond, violating the requirement that every box use only the same three shapes.

Answer: 44
The next number is 44. The gaps between the numbers are not equal — they themselves grow by 2 each time: +2, +4, +6, +8, +10. The next gap is 12, so the next number is 32 + 12 = 44.

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.

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="75.0,66.4 99.7,80.7 99.7,109.3 75.0,123.6 50.3,109.3 50.3,80.7" 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">D</text></svg>
Rule: the hexagon'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 D. 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 size as panel 2, reversing the progression instead of continuing it forward. Option A has the correct size value but substitutes a triangle for the hexagon, breaking the requirement that the same shape appear in every panel.

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"/><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">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 pentagon (top), triangle (middle), hexagon (bottom). Applying the rotation gives Box 2: triangle (top), hexagon (middle), pentagon (bottom). Applying it again gives Box 3: hexagon (top), pentagon (middle), triangle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: pentagon (top), triangle (middle), hexagon (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 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 C preserves the correct rotated order but replaces the shape in the bottom position with a circle, a shape outside the shared set of triangle, pentagon, hexagon, 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="75.0,68.9 97.6,81.9 97.6,108.1 75.0,121.1 52.4,108.1 52.4,81.9" 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">A</text></svg>
Rule: each row is assigned a fixed shape (triangle for row 1, diamond for row 2, hexagon 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 (hexagon) with column 3's size (large) — this is option A. Option C uses the correct row-3 shape (hexagon) 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 (triangle instead of hexagon), 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.

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="75.9,32.7 105.6,32.7 94.1,59.6 64.4,59.6" 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">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 parallelogram (top), diamond (middle), circle (bottom). Applying the rotation gives Box 2: diamond (top), circle (middle), parallelogram (bottom). Applying it again gives Box 3: circle (top), parallelogram (middle), diamond (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: parallelogram (top), diamond (middle), circle (bottom) — this is option C. 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 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 A preserves the correct rotated order but replaces the shape in the bottom position with a pentagon, a shape outside the shared set of circle, diamond, parallelogram, violating the requirement that every box use only the same three shapes.