spatial-reasoning-s01-q01
A 180° turn swaps top and bottom, so the blue half is now on top.
This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.
A 180° turn swaps top and bottom, so the blue half is now on top.
N has half-turn symmetry: rotating it 180° maps each vertical stroke onto the other and the diagonal onto itself, so it looks unchanged.
A quarter turn clockwise moves 'right' round to 'down': follow the arrowhead a quarter of the way round a clock face.
A left-to-right flip swaps left and right but leaves top and bottom alone, so a top-left dot appears at the top-right.
A half-turn flips a shape both top-to-bottom and left-to-right at once, which turns b into q (a mirror flip alone would give d).
A half-turn reverses a shape's direction, so an upward point swings round to point downward.
Rotating the photo 90° anticlockwise carries its top edge round to the left, so the person's head, originally at the top, ends up on the left.
Each corner moves one position round in a quarter turn: bottom-left goes to top-left and top-right goes to bottom-right, so the stripe now lies along the other diagonal.
A full turn is 360°, so three-quarters of it is 360 × 3/4 = 270°.
A half-turn flips the figure top-to-bottom and left-to-right together, turning the tail-up loop of a 6 into the tail-down loop of a 9.
Two 90° clockwise turns total 180°, which points you directly opposite North: South.
Anticlockwise runs against the compass order N-E-S-W, so one quarter turn from East goes back to North.
Step through the quarter turns: South to West (90°), West to North (180°), North to East (270°). A 270° clockwise turn is also just 90° anticlockwise.
Rotate each half of the direction a quarter turn: North becomes East and East becomes South, so North-East becomes South-East.
The 180° turn takes West to East; a further quarter turn clockwise takes East to South.
Facing North puts the compass order N-E-S-W running clockwise from ahead of you, so East sits at your right hand.
Subtract full turns first: 450° − 360° leaves 90° clockwise, which takes North to East.
A half-turn gives the exact opposite direction: reverse both parts, so South-West becomes North-East.
Four quarter turns add up to 360°: one complete revolution back to the start.
Add the turns: 90° + 180° + 90° = 360°, a full revolution, so you finish facing East just as you began.
The 3 blocks north and 3 blocks south cancel out, leaving only the 4 blocks east.
Opposite directions partly cancel: 5 east minus 2 west leaves a net 3 blocks east.
North cancels south and east cancels west: the four equal legs trace a closed square back to the start.
The two legs are at right angles, so the straight-line distance is the hypotenuse: √(6² + 8²) = √100 = 10 metres.
Only the north-south legs count toward northward distance: 4 + 1 = 5 blocks north. The eastward block shifts her sideways, not north.
The 3 west and 3 east cancel, while the two northward legs add: 2 + 2 = 4 blocks north.
The first loop takes it 2 north and 1 east, leaving it facing south; the second loop repeats the same moves in the opposite direction, 2 south and 1 west, returning it to the start.
The east and west legs cancel, leaving her 3 km north of camp, so the way home is 3 km due south.
Tally each axis separately: east 2 − west 2 = 0, and north 3 − south (1 + 1) = 1 km north.
Clockwise from the south-west corner visits north-west (one quarter), north-east (half-way), then south-east at the three-quarter mark.
A letter survives a vertical-mirror reflection only if its left and right halves already mirror each other: true of A, but not of F, J, or N.
A vertical mirror swaps left and right, so arms that normally extend to the right now extend to the left.
A mirror swaps left and right from the viewer's perspective, so the raised hand appears on the reflection's left side.
Reflecting b across a vertical line gives d. The pairs m/w and n/u are related by flipping upside down, not by mirroring.
Seen from behind, the letters appear in reverse order and each one is mirrored; X and O are symmetric so they look unchanged, but B shows its reversed form.
A mirror reflects the face across its vertical axis: the 12 position stays put while the 3 position swaps with the 9, so the clock appears to read 9:00.
H, O, and T are symmetric about a vertical centre line, so they survive the reflection; G is not, so its mirror image looks reversed.
Reflection reverses handedness: no rotation can turn a left glove into a right one, but a mirror does exactly that.
The mirror reverses the letter order, but M-U-M reads the same backwards, and each of M and U is itself symmetric about a vertical line, so nothing visibly changes.
A horizontal mirror swaps top and bottom while keeping left and right, turning the descending stem of p into the ascending stem of b (a vertical mirror would give q instead).
Two folds create 4 layers of paper at that corner, so punching through all of them leaves 4 holes once unfolded.
One fold gives two layers; a punch through both layers pierces the paper in two places.
Each fold doubles the layers: 2, then 4, then 8. A punch through all 8 layers leaves 8 holes.
Unfolding reflects the punched hole across the crease, so a punch near the fold produces two mirror-image holes sitting close to the centre line.
The crease is the sheet's horizontal centre line, and the punch sits just below it on the right; unfolding mirrors that hole to just above the line, giving a close pair either side of the crease.
Only the layers actually pierced gain holes. Two layers punched means two holes, however many layers lie beneath.
The triangle's centre is away from the crease, so the punch marks two layers at points that unfold into mirror positions across the diagonal.
Four doublings give 2 × 2 × 2 × 2 = 16 layers, and every pierced layer becomes one hole.
The creased side is the sheet's vertical centre line, so a snip across the crease opens out into a single notch symmetric about the middle of the top edge.
The full-thickness punch marks all four layers (4 holes); the second punch pierces just one layer, adding a single extra hole for 5 in total.
The top face is unaffected by rotation around the vertical axis. A 90° clockwise turn (viewed from above) moves the right face into the front position, so C is now facing front.
Top and bottom are opposite faces, so they must sum to 7: the bottom shows 7 − 3 = 4.
Tilting a cube toward you rotates it about the left-right axis: the top face becomes the front face, carrying the star with it.
A half-turn about the vertical axis swaps front with back (and left with right) while leaving top and bottom in place, so the 1 moves to the back.
Rolling sideways rotates the cube about the axis running from front to back, so the faces toward you and away from you never move, the 3 still faces you.
Rolling away swings the near face upward: green rises to the top while red tips over to become the back face.
The face away from you is opposite the face toward you, so it must be 7 − 2 = 5.
Spinning about the vertical axis cycles the four side faces past you; the top and bottom faces can never come round to the front.
The vertical spin leaves the 4 on top (it only shuffles the side faces); the tilt then carries the top face round to face you, so you see the 4.
Each red face is bordered by four white faces, contributing four red-white edges, and the two red faces share no edge because they are opposite: 4 × 2 = 8.
A strip of four squares wraps into a ring around the cube, so squares two apart in the strip end up on opposite faces: 1 pairs with 3, and 2 pairs with 4.
The strip forms a ring of four faces, and the two side flaps close the remaining openings on either side, so the flaps 5 and 6 become the cube's two opposite end faces.
Folding a 1×6 strip wraps a band of four faces; the last two squares land on faces already covered, and the two end faces of the cube are never closed.
The column of four squares (C, C1, C2, C3) wraps into a ring, and the two flaps L and R close its opposite openings, opposite faces never share an edge.
Folding never separates squares that are joined: an edge shared in the flat net remains the shared edge of two adjacent faces on the cube.
A valid net must reach all six directions when folded; a solid 2×3 block doubles squares onto the same faces, so the cube can never be closed.
The four squares around the centre fold up to become the cube's sides; the sixth square, attached beyond one of them, swings over the top to close the cube directly opposite the centre.
Squares attached to opposite sides of the same centre square fold up into opposite walls of the cube, so E pairs with W (and N with S).
In a 2×2×2 block every small cube sits at a corner, exposing exactly three mutually adjacent faces while the other three are glued inside.
The corner diagonally opposite any corner is formed by the three faces opposite the original trio: here the opposites of 1, 2, and 3, which are 6, 5, and 4.
Two-face-painted cubes sit on the middle of each edge (not the corners). A cube has 12 edges, each contributing exactly one such piece.
Three painted faces only occur at the corners of the large cube, and a cube has exactly 8 corners.
Two-face cubes lie along the edges between the corners: each of the 12 edges holds 4 − 2 = 2 of them, giving 12 × 2 = 24.
One-face cubes sit at the centre of each face of the large cube: one per face, and a cube has 6 faces.
Add the layers from bottom to top: 3 + 2 + 1 = 6 cubes.
From directly above only the topmost cube in each floor position is visible, and the staircase occupies just three floor positions in a row.
Side-on you see one column per floor position, with heights 1, 2, and 3, a stepped silhouette of 1 + 2 + 3 = 6 squares.
Every small cube in a 2×2×2 block is a corner cube, so all 8 of them show exactly three painted faces.
With the base unpainted, the centre cube of the bottom layer joins the true centre cube as paint-free, the hidden centre column below the top layer.
The base layer shows 12 side faces around its perimeter and 8 top faces (9 minus the one covered); the single top cube adds 4 sides and 1 top: 12 + 8 + 5 = 25.
Looking straight down the cylinder's axis you see only its circular top. The plan view of an upright cylinder is a circle.
From the side, the straight vertical walls and flat top and bottom of an upright cylinder project a rectangular outline.
From the front, the sloping sides converge to the apex, projecting a triangular outline. The square shows only in the view from above.
Cutting parallel to the base slices straight across the cone's circular cross-section, giving a smaller circle.
The cut is as tall as the cube but as wide as a face diagonal, which is about 1.41 times the side length, so it is a rectangle, not a square.
A sphere looks the same from every direction, so every flat cut produces a circle. Largest when the cut passes through the centre.
A cone has a circular footprint seen from above and sloping sides that project a triangle from the front. A cylinder would give a rectangle, a sphere a circle.
Only a cube presents a square face in all three principal directions; a pyramid's front view is a triangle and a cylinder's plan view is a circle.
The three cut edges are all diagonals of identical square faces, so all three sides are equal. The section is an equilateral triangle.
From above, the outer edge and the central hole both project as circles, giving a ring-shaped (annulus) outline.
Each roll away lifts the near face to the top: the first roll brings the 2 up and swings the old bottom face (6, opposite the 1) round to face you; the second roll lifts that 6 to the top.
Turning the sheet anticlockwise carries its right-hand edge up to the top, and the right edge of a north-up map is east.
Unfold two adjacent faces flat and the route becomes a straight line across a 1 × 2 rectangle: √(1² + 2²) = √5 ≈ 2.24 metres.
A half-turn about the vertical axis sends the front face to the hidden back and the right face to the hidden left, while the top face stays on top and remains visible.
A half-turn moves each hand to the position directly opposite: the minute hand at 12 appears at 6 (half past) and the hour hand at 3 appears at 9.
Combine the moves: a left-right flip followed by a half-turn undoes the sideways reversal but leaves the up-down reversal, which equals a single top-to-bottom flip.
The three legs go north, east, then south: the north and south legs cancel, leaving you 10 m east, and after two clockwise quarter turns you face south.
Count each group: 8 corner cubes (3 faces), 12 edge cubes (2 faces), 6 face-centre cubes (1 face), 1 centre cube (none), the edge cubes form the largest group.
Three quarter-turns clockwise total 270°, and turning 270° one way lands in exactly the same position as turning 90° the other way.
Rolling east tips the cube over its eastern bottom edge, lifting the west face (4) to the top while the north and south faces stay put; rolling north then lifts the south face (5) to the top.