Everything the adaptive question bank can teach and test in Spatial Reasoning, from foundations through advanced practice. Work through it in order, or start practicing and let the questions find your level.
A whole figure is hard to turn in your head; one feature is easy. Pick the part that makes the shape lopsided, such as the short bar on a letter F, and ask only where it ends up. Then check each option for that feature in that place. Most wrong options fail this single check, so you rarely need to compare whole shapes.
Think of a clock hand. A feature pointing up, at 12, points right, at 3, after a 90° clockwise turn. A feature pointing right ends up pointing down. Say the new direction aloud for the feature you are tracking, then look for an option where it points that way.
A 180° turn moves every feature to the opposite side in both directions at once. A feature at the top left ends at the bottom right. That makes a half turn easy to spot: whatever was on top is now on the bottom, and the left side has also swapped. If only one of those swaps happened, it was not a half turn.
Three quarter turns clockwise land where one quarter turn anticlockwise does, so treat 270° clockwise as "a quarter turn the other way". A feature pointing up ends up pointing left. Working with the shorter turn is faster and leaves less room for losing count.
Comparing whole figures invites the eye to settle on whichever looks closest. Instead, take the feature you are tracking and cross out every option where it sits in the wrong place. Then check a second feature on the options that are left. Two checks usually leave exactly one option.
B. Mirror images
Picture the figure next to a mirror standing on its right edge. Whatever was on the left is now on the right, but nothing moves up or down. A letter F mirrored this way has its arms pointing left, while its upright stays on the same level. Check one feature for each axis: it should have swapped sides but kept its height.
Rotations keep a shape's handedness, the way a right glove stays a right glove however you turn it. A mirror image swaps the handedness, like a left glove. So if no amount of turning makes a figure match the original, it is a mirror image. Test with two features: in a rotation they keep the same arrangement relative to each other, while in a mirror the arrangement reverses.
Flipping a figure upside down, as in a lake reflection, reverses top and bottom but keeps left and right. You can get the same result by mirroring left to right and then turning 180°. Knowing this lets you check a combined move against a single flip you can picture more easily.
Some features look the same after a flip or a turn, such as a straight bar or a plain circle. Tracking one of those tells you nothing. Choose the part that breaks the symmetry, such as the foot on one side of a letter or a hook at one end. If the figure seems unchanged after a move, check whether you were watching a symmetric part.
C. Chains of moves
When an item applies two or three moves in order, do them one after another on a single feature, noting where it points after each step. Jumping straight to the final position is where errors come from, because two moves are hard to combine mentally. A quick note, such as "up, then left, then right", keeps your place.
A flip followed by a quarter turn usually lands somewhere different from the same quarter turn followed by the flip. Only half turns combine freely with a left-to-right flip in either order. Read the chain carefully and keep its order, because a wrong option is often the same moves done in the other order.
Two left-to-right flips cancel each other out. A flip, then a quarter turn clockwise, then another flip adds up to a quarter turn anticlockwise, because the flips reverse the direction of the turn. Reducing a chain to one move before you look at the options turns a long check into a short one.
Options are often built from an intermediate stage: the figure after only the first move, or after two of three moves. If an option matches where your tracked feature was midway through, it is a trap. Finish every step, then choose the option that matches the final stage only.
D. Figure analogies and sequences
Before you look at the third figure, say what changed between the first two: a quarter turn clockwise, a half turn, a quarter turn anticlockwise, a mirror flip, or a flip and a turn together. Naming the move in words makes it something you can apply, rather than an impression you have to match by eye.
The third figure is usually a different shape, so the answer will not look like the second figure. What carries over is the move, not the appearance. Track one feature of the third figure through the move you named, then find the option where that feature sits in the new place.
A sequence of figures that turns by the same amount each time hides a constant step, usually a quarter turn one way or the other. Compare the first two figures to find the step, confirm it between the second and third, then apply it once more to the last figure.
Turning by a quarter four times is a full circle. In a sequence that turns a quarter each step, the fifth figure matches the first and the sixth matches the second. When a sequence is long, or when you lose count, use that cycle to find the next figure.
E. The odd figure out
In an odd-one-out set, three figures share one orientation and one does not. Find the shared one first by checking a single feature across all four, such as which way an arm points. The figure where it points differently is the answer, and you do not need to work out exactly how it was moved.
Sometimes the exception has been flipped rather than turned. Try turning it in your head to match the others. If a feature has moved to the opposite side in a way no rotation can produce, it is a mirror image. Both kinds of exception count as the odd one out.
F. Counting
In a scattered figure the eye jumps around and loses its place. Sweep left to right along the top row, then the next row, and so on, the way you read a page. A steady route means each shape is passed exactly once, which removes both the missed shape and the double count.
When a figure mixes squares, circles and triangles, count only the kind the question asks for. Keep a running tally as you go, and do not count the other shapes "for later". The wrong options usually sit one or two away from the true count, so a single slip is enough to land on one.
After counting the target shapes, count the others too, and check that the two totals add up to the number of shapes in the figure. If they do not, one of the counts slipped. This takes a few seconds and catches the one-off errors the options are built to exploit.
"Any size" means every square the grid lines form, not just the small cells. Count each size separately: in a grid w cells wide and h tall, a k × k square fits (w − k + 1) × (h − k + 1) ways. A 2 × 8 grid has 16 one-by-one squares and 7 two-by-two squares, so 23 in all.
Every rectangle is fixed by its left and right edges and its top and bottom edges. In a grid 2 cells wide and 6 tall there are 3 vertical lines and 7 horizontal ones. Choosing 2 of 3 can be done 3 ways and 2 of 7 can be done 21 ways, so the grid holds 3 × 21 = 63 rectangles.
The tempting answer to an "any size" question is the number of small cells, because those are the squares you see first. Every larger square or rectangle overlaps several cells, and there are many of them. If your count equals the number of cells, you have answered a different question.
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