How These Are Formatted
Twenty items across the four families that appear in almost every spatial battery. Each carries the full reasoning and, where one exists, the trap it was built around.
One difference from a real paper is worth stating up front: these items are described in words rather than drawn. Real spatial tests are graphical, and you will be looking at figures rather than reading about them.
That makes these harder in one respect — you have to build the object before you can operate on it — and it makes the underlying principle far more visible, which is the point of practising.
Family 1: Mental Rotation
Item 1
Take a capital F and rotate it 90° clockwise in the plane of the page. What does it look like?
Answer: a horizontal bar along the top, with two prongs hanging down from it — a long one at the right-hand end and a shorter one in the middle.
The principle. The spine and the arms keep their relationship to each other. Rotation moves everything together; nothing detaches or reverses.
Item 2
Can a shape drawn on paper be turned into its own mirror image by rotating it within the plane of the page?
Answer: no, never. Rotation preserves handedness. A left-handed shape stays left-handed however far you turn it.
Why this matters more than any other rule here. Most rotation items include at least one option that is the correct shape mirrored. If you only check whether the parts match, that option looks right.
Item 3
Object A is a chain of cubes: from the base, three up, then two to the right, then two toward you. Object B: three up, then two to the left, then two toward you.
Same object or mirror images? Mirror images. Rotating A by 180° about its vertical axis would send the second leg to the left, but it would also send the third leg away from you rather than toward you.
The method. Walk both chains in the same order and compare the turns. If one turns left where the other turns right while everything else matches, no rotation will reconcile them.
Item 4
A cube has a red dot on its front face and a blue dot on its top face. It is turned 90° clockwise as seen from above.
Where are the dots now? Red on the left face, blue still on top.
Why. Viewed from above, clockwise sends back to right, right to front, front to left. The rotation axis is vertical, so the top face never moves.
Item 5
A die shows 1 on top, 2 facing you, 3 on the right. It is tipped 90° forward, so the top face rolls toward you and becomes the front. Opposite faces of a die sum to seven.
What is on top now? 5. The old back face rotates up, and the back is opposite the front — opposite the 2, which makes it 5.
The trap. Tracking only the face you can see. The answer lives on the face that was hidden, and the sum-to-seven rule is the only way to name it.
Family 2: Nets and Folding
Item 6
A cube net is a vertical column of four squares — call them A, B, C, D from the top — with two more squares attached to the left and right of B.
Which face ends up opposite A? C. Fold B into the front: A becomes the top, C becomes the bottom, D becomes the back.
Item 7: the rule that item 6 demonstrates
In any straight run of squares on a net, faces two apart are opposite each other. Adjacent squares are never opposite; they share an edge on the folded cube.
Why to memorise it. Most net items are solvable by this rule alone, without folding anything mentally. It converts a visualisation problem into a counting problem.
Item 8
Two squares share an edge on the net. Can they be opposite faces on the finished cube?
No — never. Sharing an edge on the net guarantees sharing an edge on the cube, and opposite faces share nothing.
How to use it. As an elimination tool. It kills wrong options faster than confirming the right one.
Item 9
How many genuinely different nets does a cube have? Eleven, counting nets that differ only by rotation or reflection as the same one.
Why it is worth knowing. Eleven is a small number. Unusual-looking nets on a test are not exotic — they are one of eleven arrangements, and most are variations on the cross and the staircase.
Item 10
Which net folds into a square-based pyramid? A square with one triangle attached to each of its four sides.
The check that always works. Count faces before folding anything. A square-based pyramid has five faces: one square base and four triangles. A net with the wrong count is wrong regardless of arrangement.
Family 3: Reading Solids From Flat Views
Item 11
An object's top view is a circle. Its front view and its side view are both squares.
What is it? A cylinder standing on its circular base, with its height equal to its diameter. The square profiles fix the proportions.
Item 12
All three views — front, side and top — are circles of the same size.
What is it? A sphere. It is the only solid that presents an identical circular profile from every direction.
The trap. A cylinder also gives a circle, but from one direction only. Two circular views are not enough; three settle it.
Item 13
A solid 4 × 4 × 4 block is built from unit cubes.
How many of them have no face on the outside surface? Eight. Strip one layer from every side and a 2 × 2 × 2 core remains.
Item 14
A 3 × 3 × 3 cube is painted on every outer surface, then separated into its 27 unit cubes.
How many have exactly two painted faces? Twelve. Two painted faces means an edge position but not a corner. A cube has twelve edges, and each holds exactly one non-corner cube.
The systematic way. Corners have three painted faces (8), edge-middles have two (12), face-centres have one (6), and the core has none (1). Those sum to 27.
Item 15
A stepped stack: the bottom layer is 3 × 3, the middle layer is 2 × 2, the top layer is a single cube.
How many cubes in total? Fourteen — nine, four and one.
The trap this format is built on. Counting the cubes you can see. In a real diagram several of the bottom layer are hidden behind the ones in front, and the visible count is always lower than the true one.
Family 4: Orientation and Position
Item 16
You are facing north. You turn 90° right, then 180°, then 90° left.
Which way are you facing? South. North to east, east to west, west to south.
The discipline. Resolve one turn at a time and name the direction out loud before applying the next. Compressing three turns into one mental step is where these go wrong.
Item 17
You are holding a standard map upside down — rotated 180° from its printed orientation. You need to travel north.
Which way do you move across the paper? Toward the bottom of the sheet as you are holding it.
Why this is genuinely hard. The task requires holding two frames of reference at once: the map's and your own. That conflict is the whole content of spatial orientation items.
Item 18
You face a mirror and raise your right hand.
Which hand does the reflection raise? The raised hand in the reflection is the one directly opposite your own — and if the reflection were a person, it would be their left.
The precise version. A mirror does not swap left and right. It reverses front and back, and we describe that reversal in left–right language because we imagine turning round to face ourselves.
Item 19
Five crates are stacked, one per position, from the bottom up.
- The red crate is directly below the blue crate.
- The green crate is at the bottom.
- The yellow crate is above the blue crate, but not at the top.
What is the order? Green, red, blue, yellow, white, from the bottom up.
Green takes position 1, leaving 2 to 5. The red–blue pair must be adjacent, and if red were at 3 or 4 then yellow would have to be at the top, which is ruled out. So red is 2, blue is 3, yellow is 4, and white takes 5.
Item 20
You walk three blocks north, four blocks east, then three blocks south.
Where are you relative to the start? Four blocks east. The north and south legs cancel exactly.
The habit. Resolve each axis separately and add. Trying to trace the whole route as a shape is slower and more error-prone than treating it as two independent sums.
Are These the Same as the Real Test?
No. These are teaching items chosen because they can be stated in words. A real spatial test is graphical throughout, and the figures do a lot of work these descriptions have to do laboriously.
The principles transfer completely. The mirror-image trap, the two-apart rule for nets, the hidden-cube undercount and the one-axis-at-a-time discipline are the same on any paper you sit.
What if You Got Most of These Wrong?
Check which ones before drawing any conclusion, because the four families fail for different reasons and only some of them are about ability.
- Rotation errors are usually handedness. Learning to check mirroring first fixes a large share of them immediately.
- Net errors are usually attempts to fold mentally instead of applying the two-apart rule.
- Counting errors are usually the visible-cubes undercount rather than a visualisation failure at all.
- Orientation errors are usually frame confusion, which is a discipline problem with a known fix.
Spatial skills also respond to training better than most cognitive abilities, and rotation responds best of all. A poor first attempt at this format is weak evidence about anything except how familiar the format is.