XLTestPrep

Daily Practice › Grade 5 Cognitive Skills (CogAT) › October 28, 2026

Archive · October 28, 2026

Grade 5 Cognitive Skills (CogAT): 10 Free Practice Questions

A brand-new set of Grade 5 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 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.

?
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"/><circle cx="75.0" cy="95.0" r="25.6" 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, diamond for row 2, circle 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 (circle) with column 3's size (large) — this is option C. Option D uses the correct row-3 shape (circle) but the wrong column size (small instead of large), violating the column rule. Option A uses the correct column-3 size (large) but the wrong shape (parallelogram instead of circle), violating the row rule. Option B uses the correct size but substitutes a square, a shape that does not appear anywhere in the grid, violating the row rule entirely.

2Each 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?
Show answer & explanation
Answer: <svg xmlns="http://www.w3.org/2000/svg" width="52" height="216" viewBox="0 0 52 216"><polygon points="26.0,15.2 34.9,30.7 17.1,30.7" fill="#2f8f52" stroke="#1c1a15" stroke-width="1.6"/><polygon points="26.0,48.2 35.8,55.3 32.1,66.8 19.9,66.8 16.2,55.3" fill="#7c3aed" stroke="#1c1a15" stroke-width="1.6"/><circle cx="26.0" cy="91.5" r="10.32" fill="#2f6fed" stroke="#1c1a15" stroke-width="1.6"/><polygon points="36.3,124.5 26.0,134.8 15.7,124.5 26.0,114.2" fill="#c23b3b" stroke="#1c1a15" stroke-width="1.6"/><polygon points="33.3,164.8 18.7,164.8 18.7,150.2 33.3,150.2" fill="#b3268f" stroke="#1c1a15" stroke-width="1.6"/><polygon points="36.3,190.5 31.2,199.4 20.8,199.4 15.7,190.5 20.8,181.6 31.2,181.6" fill="#c98a10" stroke="#1c1a15" stroke-width="1.6"/></svg>
Step 1 is hexagon → pentagon → circle → square → diamond → triangle. The rule is "swap only the top and bottom shapes; the middle stays put." Applying it once gives Step 2: triangle → pentagon → circle → square → diamond → hexagon. Applying it again gives Step 3: hexagon → pentagon → circle → square → diamond → triangle. Applying the same rule one more time to Step 3 produces the correct Step 4: triangle → pentagon → circle → square → 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 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."

3Each box in the grid contains the same three shapes (pentagon, hexagon, 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.

?
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="85.0,23.4 106.7,39.1 98.4,64.6 71.6,64.6 63.3,39.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="85.0,87.9 104.2,98.9 104.2,121.1 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">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 pentagon (top), hexagon (middle), parallelogram (bottom). Applying the rotation gives Box 2: parallelogram (top), pentagon (middle), hexagon (bottom). Applying it again gives Box 3: hexagon (top), parallelogram (middle), pentagon (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: pentagon (top), hexagon (middle), parallelogram (bottom) — this is option D. 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 A preserves the correct rotated order but replaces the shape in the top position with a diamond, a shape outside the shared set of pentagon, hexagon, parallelogram, violating the requirement that every box use only the same three shapes.

4Look at this number series: 6, 5, 10, 9, 14, 13, ___ . The rule is not a single repeated step — work out the whole pattern, then give the next number.

Show answer & explanation
Answer: 18
The next number is 18. Two separate series are woven together. The 1st, 3rd and 5th numbers count up by 4 (6, 10, 14), while the 2nd, 4th and 6th count up by 4 (5, 9, 13). The blank is the 7th number, so it belongs to the first series: 14 + 4 = 18.

5Each box in the grid contains the same three shapes (circle, triangle, 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.

?
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"/><circle cx="85.0" cy="110.0" r="21.7" 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">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), circle (middle), diamond (bottom). Applying the rotation gives Box 2: circle (top), diamond (middle), triangle (bottom). Applying it again gives Box 3: diamond (top), triangle (middle), circle (bottom). Applying the same rotation a third time to Box 3 reproduces the missing stack: triangle (top), circle (middle), diamond (bottom) — this is option A. Option B rotates the stack in the downward 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 square, a shape outside the shared set of circle, triangle, diamond, violating the requirement that every box use only the same three shapes.

6Each 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.

?
Show answer & explanation
Answer: <svg xmlns="http://www.w3.org/2000/svg" width="68" height="68" viewBox="0 0 68 68"><defs><pattern id="patc_5_medium_8_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 24.4,39.4 5.5,39.4" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/><polygon points="34.0,23.1 43.4,39.4 24.6,39.4" fill="#c98a10" stroke="#7c3aed" stroke-width="1.7"/><polygon points="53.0,23.1 62.5,39.4 43.6,39.4" fill="#c98a10" 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: 1 solid square | 3 striped triangles | 2 outline hexagons. Look at Row 2: 3 outline triangles | 2 solid hexagons | 1 striped square. Now look at Column 1 (top two cells): 1 solid square | 3 outline triangles. 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: 3 solid triangles — 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.

7Each panel below shows one triangle. Moving from panel 1 to panel 3, the triangle's number of copies changes by the same fixed amount at every step. Study the pattern, then choose the option that correctly completes the missing 4th panel.

?
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="7.0,80.0 19.9,102.5 -5.9,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="41.0,80.0 53.9,102.5 28.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="75.0,80.0 87.9,102.5 62.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="109.0,80.0 121.9,102.5 96.1,102.5" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="143.0,80.0 155.9,102.5 130.1,102.5" 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: the triangle's number of copies increases by a constant step of 1 unit(s) per panel (count-scale index). Panel 1 = 2 copies, panel 2 = 3 copies, panel 3 = 4 copies. Adding the same step once more gives the missing panel: 5 copies — this is option C. Option A applies a step of 2 unit(s) instead of 1, over- or under-shooting the established rate of change. Option D shows the same number of copies as panel 2, reversing the progression instead of continuing it forward. Option B has the correct number of copies value but substitutes a square for the triangle, breaking the requirement that the same shape appear in every panel.

8The 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?

?
Show answer & explanation
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="12.16" fill="#fffdf7" stroke="#1c1a15" stroke-width="2"/></svg>
Compare the top-left box (large 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), 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) square) gives medium outlined (white) circle — 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.

9Each panel below shows one parallelogram. Moving from panel 1 to panel 3, the parallelogram's number of copies changes by the same fixed amount at every step. Study the pattern, then choose the option that correctly completes the missing 4th panel.

?
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="-15.4,86.9 2.3,86.9 -4.6,103.1 -22.4,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="18.6,86.9 36.4,86.9 29.4,103.1 11.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="52.6,86.9 70.3,86.9 63.4,103.1 45.6,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="86.6,86.9 104.4,86.9 97.4,103.1 79.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="120.6,86.9 138.3,86.9 131.4,103.1 113.7,103.1" fill="#6b7280" stroke="#111827" stroke-width="2"/><polygon points="154.6,86.9 172.3,86.9 165.4,103.1 147.7,103.1" 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: the parallelogram's number of copies increases by a constant step of 1 unit(s) per panel (count-scale index). Panel 1 = 3 copies, panel 2 = 4 copies, panel 3 = 5 copies. Adding the same step once more gives the missing panel: 6 copies — 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 number of copies as panel 2, reversing the progression instead of continuing it forward. Option D has the correct number of copies value but substitutes a circle for the parallelogram, breaking the requirement that the same shape appear in every panel.

10Each 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.

?
Show answer & explanation
Answer: <svg xmlns="http://www.w3.org/2000/svg" width="68" height="68" viewBox="0 0 68 68"><defs><pattern id="patc_5_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="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: 3 solid hexagons | 2 solid squares | 1 solid triangle. Look at Row 2: 2 solid triangles | 1 solid hexagon | 3 solid squares. Now look at Column 1 (top two cells): 3 solid hexagons | 2 solid triangles. 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.

More Grade 5 practice today

Math 1,403 questions in the bank English Language Arts 1,684 questions in the bank Science 794 questions in the bank

Previous days

Nov 2 Nov 1 Oct 31 Oct 30 Oct 29 Oct 27 Oct 26