Spatial reasoning.
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Try eight original spatial ability questions covering rotation, cube nets, folding, viewpoints, and blocks.

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By Foldmetry · Updated

What this spatial reasoning test covers

Spatial reasoning involves keeping track of shapes, directions, and relationships as you rotate an object, fold a sheet, or change your viewpoint. A spatial visualization test asks you to picture those changes before you see the result. In this free spatial ability test, work through eight original questions, with diagrams and explanations for every item.

You will meet two rotation questions, cube opposites, net validity, a paper-hole pattern, a front view, block counting, and a cross section. The set is untimed. It is a learning exercise rather than a validated psychometric instrument: its score is a count of correct answers here, not an IQ estimate, percentile, hiring result, or school assessment prediction. No account is needed and answers stay in your browser.

Spatial reasoning test: eight questions

0 of 8 answered

Choose one answer for every question, then check your answers. Untimed, free, and no account. Answers are processed only in this browser; leaving the page clears them.

1. Which shape is a 90° clockwise turn of the target? Filled squares listed from top to bottom and left to right. Target: row 1, columns 2,3; row 2, columns 1,2; row 3, columns 2. A: row 1, columns 2,3; row 2, columns 1,2; row 3, columns 2. B: row 1, columns 1,2; row 2, columns 2,3; row 3, columns 2. C: row 1, columns 2; row 2, columns 1,2,3; row 3, columns 3. D: row 1, columns 2; row 2, columns 2,3; row 3, columns 1,2.

Answer and method

Option C. A clockwise quarter turn maps each square at (x, y) to (-y, x) when screen y increases downward, then shifts the shape into view. C preserves every connection and places the long branch correctly. A has not turned, B reverses handedness, and D turns twice as far.

2. Which option is a rotation, without a reflection? Filled squares listed from top to bottom and left to right. Target: row 1, columns 2,3; row 2, columns 1,2; row 3, columns 2. A: row 1, columns 1,2; row 2, columns 2,3; row 3, columns 2. B: row 1, columns 3; row 2, columns 1,2,3; row 3, columns 2. C: row 1, columns 2; row 2, columns 2,3; row 3, columns 1,2. D: row 1, columns 2; row 2, columns 1,2; row 3, columns 2,3.

Answer and method

Option C. C is the target turned through 180°. Trace the off-centre branch around the outline: its order stays the same. The other three options reverse that order. A different viewing direction does not authorize reflecting a flat shape through the paper.

3. In this net, which face is opposite C? A–C–E–F form a horizontal row; B is above C and D is below C.

Answer and method

F. F is opposite C. The four-face belt is A–C–E–F; faces two positions apart become opposite. The full set is A/E, C/F and B/D. Faces that share an edge in the net stay adjacent after folding.

4. Which drawing can fold into a cube? Left: a row of four squares with flaps above and below its second square. Right: a two-by-three rectangle.

Answer and method

Left only. The left net reaches all six cube faces without overlap. The two-by-three rectangle contains a four-square cycle: trying to fold all its shared edges forces conflicting orientations. Six connected squares alone are not sufficient.

5. Which option is the fully unfolded hole pattern? A four-by-four square folds right to left, then bottom to top, with one punch at (1, 0.75). Unfolded options: A has holes at (1,0.75), (3,0.75), (1,3.25), (3,3.25); B at (1,0.75), (1,3.25); C at (1,0.75), (3,0.75), (1,3.25); D at (0.5,0.75), (1,0.75), (0.5,1.25), (1,1.25).

Answer and method

Option A. A has holes at (1, 0.75), (3, 0.75), (1, 3.25), and (3, 3.25) on a four-by-four square. Undo the bottom-to-top fold first, reflecting y across 2; then reflect x across 2. The point is away from both creases, so all four positions are distinct.

6. Which is the front-view silhouette? Back row heights: 2, 0, 1. Front row heights: 1, 3, 1. Look from the front edge; compare the profiles pictured below.Four front profiles: A has column heights 2,3,1; B 1,3,1; C 2,0,1; D 3,3,3.

Answer and method

A: 2, 3, 1. A. Take the maximum height in each left-to-right column: max(2,1)=2, max(0,3)=3, max(1,1)=1. The rear two-high stack remains visible above the front one-high stack. Depth disappears in this orthographic view; height does not.

7. How many unit cubes are in these solid columns? Back row heights 2,0,1; front row heights 1,3,1. Each column is filled from the ground with no gaps.

Each column is solid from the ground, with no internal gaps.

Answer and method

8. Eight: (2+0+1)+(1+3+1)=8. Five is the number of occupied positions in the top view, not the number of cubes. The question specifies solid columns; without that condition, a silhouette alone could not prove the hidden total.

8. A cube is sliced by a plane parallel to one face. What is the section?

Answer and method

Square. A square, for a cut that passes through the interior. The plane is parallel to a square face and cuts the four perpendicular side faces at equal distances. Other plane directions can produce other polygons; the direction of this cut is part of the question.

Four methods to use across the set

For rotations, keep connections fixed and turn the entire object. Choose a landmark and check a second branch. For cube nets, follow shared edges as hinges and distinguish adjacent from opposite faces. For paper folding, undo folds in reverse order and reflect every hole across the crease. For a front view of solid block columns, take the tallest stack along each line of sight.

Each method has conditions. A four-face belt shortcut applies to a straight belt in a valid cube net. Doubling holes assumes distinct reflected positions and a punch through every relevant layer. Adding column heights assumes the stacks are solid from the ground. A front silhouette uses an orthographic view. The wording of these conditions is part of the problem, not a minor detail to skip.

Cross-section questions ask about the intersection of a solid with a plane. In this set, the cutting plane is parallel to a face of a cube and passes through its interior, so the section is a square. A differently oriented plane can produce another polygon. Always identify the direction of the cut before reaching for a memorized answer about the solid.

Reading your result without overinterpreting it

A correct answer shows that your method worked on one item. An incorrect answer tells you to inspect that transformation. It does not establish a general weakness, and a high score does not establish a standardized level of spatial ability. The set is small, its question mix is fixed, and a repeat attempt is affected by prior exposure. Use the detailed feedback to choose what to learn next.

Try reviewing without the diagrams first: can you state why the answer follows from the conditions? Then draw the missing step. A cube question may need one hinge turn; a paper-folding question may need one reflected pair; a viewpoint question may need one maximum-height calculation. Reconstructing that step is a useful way to discover whether the error came from geometry, the instructions, or a rushed choice.

Choose a guide for your next practice

Use mental rotation for angles, landmarks, and reflections. Use the interactive cube net tool to inspect all opposite pairs and the eleven distinct nets. Read paper folding for layers, holes, and crease symmetry. The perspective-taking guide covers front and top views plus a worked block count.

For sequences and classification, continue with the non-verbal reasoning test. If you are looking specifically for CAT4 information, read the CAT4 guide and the publisher’s advice before treating any online mini test as preparation. Foldmetry on iPhone and iPad extends general spatial learning with six skill paths, guided lessons, and mistake review; it remains a practice tool with no official examination affiliation.

Take the method into daily practice.

Foldmetry on iPhone and iPad brings six spatial skills into 36 guided lessons, daily practice, and local mistake review. Free to start, with optional Pro features.

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Actual Foldmetry app screen showing the six guided skill paths.