Build a repeatable method for each PAT task. This collection includes five visual drills per type, labeled diagrams and explanations that show what to compare, count, rotate or unfold.
There are five items in each of the six filters. The first item of each type is also included in the mixed DAT practice collection.
Showing 30 of 30 questions
Answer E. Trace the broad face rather than the slanted extrusion edges. Its columns, from left to right in the object drawing, rise to 1, 3, 2 equal units. The correct aperture preserves those steps and proportions after rotation. The other apertures change the height or position of a step. This drill fixes the direction of passage to isolate silhouette matching.
Answer A. Trace the broad face rather than the slanted extrusion edges. Its columns, from left to right in the object drawing, rise to 2, 4, 1 equal units. The correct aperture preserves those steps and proportions after rotation. The other apertures change the height or position of a step. This drill fixes the direction of passage to isolate silhouette matching.
Answer C. Trace the broad face rather than the slanted extrusion edges. Its columns, from left to right in the object drawing, rise to 2, 1, 3, 2 equal units. The correct aperture preserves those steps and proportions after rotation. The other apertures change the height or position of a step. This drill fixes the direction of passage to isolate silhouette matching.
Answer D. Trace the broad face rather than the slanted extrusion edges. Its columns, from left to right in the object drawing, rise to 1, 3, 3, 2 equal units. The correct aperture preserves those steps and proportions after rotation. The other apertures change the height or position of a step. This drill fixes the direction of passage to isolate silhouette matching.
Answer E. Trace the broad face rather than the slanted extrusion edges. Its columns, from left to right in the object drawing, rise to 1, 4, 2, 3 equal units. The correct aperture preserves those steps and proportions after rotation. The other apertures change the height or position of a step. This drill fixes the direction of passage to isolate silhouette matching.
Answer A. Looking from the right collapses the left-to-right width. At each depth, keep the tallest column across that width. Reading from front to back gives heights 1, 3, 2. Only one choice preserves that profile. The 3D reference makes this silhouette drill fully specified; it is a practice aid beyond the two views used in an exam item.
Answer B. Looking from the right collapses the left-to-right width. At each depth, keep the tallest column across that width. Reading from front to back gives heights 3, 1, 2. Only one choice preserves that profile. The 3D reference makes this silhouette drill fully specified; it is a practice aid beyond the two views used in an exam item.
Answer A. Looking from the right collapses the left-to-right width. At each depth, keep the tallest column across that width. Reading from front to back gives heights 3, 2, 1. Only one choice preserves that profile. The 3D reference makes this silhouette drill fully specified; it is a practice aid beyond the two views used in an exam item.
Answer D. Looking from the right collapses the left-to-right width. At each depth, keep the tallest column across that width. Reading from front to back gives heights 2, 1, 3. Only one choice preserves that profile. The 3D reference makes this silhouette drill fully specified; it is a practice aid beyond the two views used in an exam item.
Answer B. Looking from the right collapses the left-to-right width. At each depth, keep the tallest column across that width. Reading from front to back gives heights 2, 3, 2. Only one choice preserves that profile. The 3D reference makes this silhouette drill fully specified; it is a practice aid beyond the two views used in an exam item.
Answer C. The angle sizes are 1: 48°, 2: 42°, 3: 39°, and 4: 45°. Therefore the increasing order is 3 < 2 < 4 < 1. Mentally rotate the angles to align one ray; compare the gap to the other ray instead of the slope on the page.
Answer C. The angle sizes are 1: 116°, 2: 120°, 3: 113°, and 4: 109°. Therefore the increasing order is 4 < 3 < 1 < 2. Mentally rotate the angles to align one ray; compare the gap to the other ray instead of the slope on the page.
Answer C. The angle sizes are 1: 69°, 2: 72°, 3: 62°, and 4: 65°. Therefore the increasing order is 3 < 4 < 1 < 2. Mentally rotate the angles to align one ray; compare the gap to the other ray instead of the slope on the page.
Answer D. The angle sizes are 1: 104°, 2: 98°, 3: 101°, and 4: 95°. Therefore the increasing order is 4 < 2 < 3 < 1. Mentally rotate the angles to align one ray; compare the gap to the other ray instead of the slope on the page.
Answer B. The angle sizes are 1: 127°, 2: 121°, 3: 130°, and 4: 124°. Therefore the increasing order is 2 < 4 < 1 < 3. Mentally rotate the angles to align one ray; compare the gap to the other ray instead of the slope on the page.
Answer B. Undo the folds in reverse order, reflecting the hole across each crease. These 2 half-folds create 4 layers at the punched location, so one punch produces 4 holes. Match their positions as well as their reflection symmetry; every choice has the same number of holes. In the four-row, four-column answer lattice, numbering from the top left starting at 1, the (row, column) positions are (2, 1), (2, 4), (3, 1), (3, 4).
Answer C. Undo the folds in reverse order, reflecting the hole across each crease. These 2 half-folds create 4 layers at the punched location, so one punch produces 4 holes. Match their positions as well as their reflection symmetry; every choice has the same number of holes. In the four-row, four-column answer lattice, numbering from the top left starting at 1, the (row, column) positions are (2, 1), (2, 4), (3, 1), (3, 4).
Answer E. Undo the folds in reverse order, reflecting the hole across each crease. These 2 half-folds create 4 layers at the punched location, so one punch produces 4 holes. Match their positions as well as their reflection symmetry; every choice has the same number of holes. In the four-row, four-column answer lattice, numbering from the top left starting at 1, the (row, column) positions are (1, 2), (1, 3), (4, 2), (4, 3).
Answer D. Undo the folds in reverse order, reflecting the hole across each crease. These 3 half-folds create 8 layers at the punched location, so one punch produces 8 holes. Match their positions as well as their reflection symmetry; every choice has the same number of holes. In the four-row, four-column answer lattice, numbering from the top left starting at 1, the (row, column) positions are (1, 2), (1, 3), (2, 2), (2, 3), (3, 2), (3, 3), (4, 2), (4, 3).
Answer A. Undo the folds in reverse order, reflecting the hole across each crease. These 2 half-folds create 4 layers at the punched location, so one punch produces 4 holes. Match their positions as well as their reflection symmetry; every choice has the same number of holes. In the four-row, four-column answer lattice, numbering from the top left starting at 1, the (row, column) positions are (1, 2), (1, 3), (4, 2), (4, 3).
Answer B. Count exposed faces cube by cube, including faces at the back and inside the steps. Do not count any face touching another cube or the tabletop. For this 10-cube assembly, the tally is 1 painted face: 2 cubes; 2 painted faces: 3 cubes; 3 painted faces: 4 cubes; 5 painted faces: 1 cube. Thus exactly 2 cubes have 1 painted face.
Answer B. Count exposed faces cube by cube, including faces at the back and inside the steps. Do not count any face touching another cube or the tabletop. For this 11-cube assembly, the tally is 1 painted face: 2 cubes; 2 painted faces: 4 cubes; 3 painted faces: 3 cubes; 4 painted faces: 2 cubes. Thus exactly 2 cubes have 4 painted faces.
Answer C. Count exposed faces cube by cube, including faces at the back and inside the steps. Do not count any face touching another cube or the tabletop. For this 12-cube assembly, the tally is 0 painted faces: 1 cube; 2 painted faces: 5 cubes; 3 painted faces: 3 cubes; 4 painted faces: 1 cube; 5 painted faces: 2 cubes. Thus exactly 5 cubes have 2 painted faces.
Answer B. Count exposed faces cube by cube, including faces at the back and inside the steps. Do not count any face touching another cube or the tabletop. For this 12-cube assembly, the tally is 1 painted face: 2 cubes; 2 painted faces: 5 cubes; 3 painted faces: 3 cubes; 4 painted faces: 2 cubes. Thus exactly 2 cubes have 4 painted faces.
Answer A. Count exposed faces cube by cube, including faces at the back and inside the steps. Do not count any face touching another cube or the tabletop. For this 11-cube assembly, the tally is 0 painted faces: 1 cube; 2 painted faces: 4 cubes; 3 painted faces: 4 cubes; 4 painted faces: 1 cube; 5 painted faces: 1 cube. Thus exactly 1 cube has 5 painted faces.
Answer C. The opposite face pairs are ● / ◇, + / □, × / ⊙. Opposite faces cannot share an edge. For the remaining candidates, preserve the order of the three faces around their shared corner: the valid view has ● on top, + on the left and ⊙ on the right. Swapping the two side faces gives a mirror image, which rotating the cube cannot produce.
Answer A. The opposite face pairs are × / ●, □ / ⊙, ◇ / +. Opposite faces cannot share an edge. For the remaining candidates, preserve the order of the three faces around their shared corner: the valid view has ⊙ on top, ● on the left and ◇ on the right. Swapping the two side faces gives a mirror image, which rotating the cube cannot produce.
Answer D. The opposite face pairs are ◇ / ×, ⊙ / +, ● / □. Opposite faces cannot share an edge. For the remaining candidates, preserve the order of the three faces around their shared corner: the valid view has ⊙ on top, ◇ on the left and ● on the right. Swapping the two side faces gives a mirror image, which rotating the cube cannot produce.
Answer A. The opposite face pairs are ● / ⊙, × / +, ◇ / □. Opposite faces cannot share an edge. For the remaining candidates, preserve the order of the three faces around their shared corner: the valid view has ⊙ on top, + on the left and □ on the right. Swapping the two side faces gives a mirror image, which rotating the cube cannot produce.
Answer B. The opposite face pairs are × / +, ◇ / □, ● / ⊙. Opposite faces cannot share an edge. For the remaining candidates, preserve the order of the three faces around their shared corner: the valid view has ● on top, × on the left and □ on the right. Swapping the two side faces gives a mirror image, which rotating the cube cannot produce.
Test Ninjas · Content checked October 23, 2026
Start with one task type using the section filter. Before selecting an answer, say what operation the question requires: compare a silhouette, reconcile orthographic views, rank angles, reverse a fold, count exposed faces or mentally fold a net. A consistent procedure is more reliable than choosing the first familiar-looking picture.
Work on a screen large enough to inspect the diagrams accurately. Open a full-size image when labels or edges are difficult to see. The comparison diagrams keep relevant alternatives together; where separate option images are provided, inspect each one before selecting its answer. Do not infer geometric differences from a browser’s scaling artifacts.
Use the first few attempts untimed. Once you can explain the result, use the elapsed timer for a short block of one type. Move to a mixed block only after you have a method for each type. The timer measures your practice session; it does not simulate the full PAT section.
In these constrained silhouette drills, trace the broad face and compare the relative heights and positions of its steps. Rotation preserves shape; reflection or moving one step does not. Ignore extrusion lines that do not belong to the outline being matched.
Check each candidate against all supplied orthographic views. Width, depth and height must be consistent across views. An object that fits one projection can still introduce an extra column or omit a required height in another.
Rank the size of the opening at the vertex, independent of the length or orientation of the rays. Compare close pairs directly, then assemble the full ordering. The diagrams are constructed with distinct angles so the intended order is unambiguous.
Start at the final folded state and reverse one fold at a time. Reflect the hole positions across each fold line, tracking which layers were punched. A visually symmetric pattern is not sufficient unless it follows the actual sequence.
List cubes systematically by stack and determine which faces are exposed to paint under the prompt’s rules. A shared face is not exposed. Keep supporting cubes in the count even when another cube hides part of them.
Choose an anchor face in the net and follow the rotation of adjacent faces. Preserve which edges touch and which markings meet after folding. A mirrored arrangement may look similar but cannot be obtained by rotating the object.
A mirror image changes handedness. Keep an asymmetric feature as an anchor while mentally rotating an outline or folded object, and check that its relationship to neighboring features is preserved.
A sequence of folds must be reversed from last to first. Apply one reflection at a time and keep the intermediate hole positions; jumping directly to a symmetric final pattern can add or omit holes.
A drawing shows faces, not an inventory of blocks. Reconstruct stacks and their contacts before counting painted faces. Follow the prompt’s rule for the underside rather than assuming all six faces can be painted.
Use the same vertex-centered comparison for each pair. Ray length and screen orientation are distractions; zoom only to make the drawing legible, not to measure pixel noise as if it were meaningful.
Yes. There are five questions each for keyholes, top–front–end views, angle ranking, hole punching, cube counting and pattern folding, for 30 total.
No. They isolate specific spatial operations. The keyhole questions explicitly constrain the direction of passage, and the bank does not reproduce a full official section’s difficulty distribution or timing.
The source bank defines the geometry of each item. Separate validation code reads the published SVG drawings and checks the relevant silhouettes, projections, angle order, reflections, exposed faces or folded relationships against the answer key.
The page works on a phone, but small diagrams can make spatial comparisons harder. Use the full-size image link or a larger screen when you cannot clearly distinguish edges and labels. Avoid treating rendering artifacts as geometric clues.
No. It reports correct answers in this collection. An official scaled score requires calibrated test forms, and these targeted drills are not designed for that conversion.
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