RAF Airman/Airwoman Selection Test (AST) Spatial Reasoning Syllabus

A cube is rotated $90^{\circ}$ about a vertical axis. What happens to the top and bottom faces?

The top and bottom faces stay in place (still top and bottom); the four side faces cycle around to the next position.

How many degrees of rotation about an axis through the centres of opposite faces returns a cube to an identical appearance?

Every $90^{\circ}$, because a cube has 4-fold rotational symmetry about a face-to-face axis.

For a solid cube with no hidden internal cavities, how many faces does it have in total and how many are hidden when resting on a table and viewed from one corner?

It has $6$ faces; resting and viewed from a corner you see $3$, and $3$ are hidden (the bottom and the two far side faces).

In a stack of cubes, how do you count the total number of small cube faces that are hidden (not visible)?

Count faces glued between touching cubes (each contact hides 2 faces) plus any faces pressed against the ground or facing away. Total faces $= 6 \times (\text{number of cubes})$; subtract visible faces to get hidden ones.

A $2\times2\times2$ block is built from 8 unit cubes. How many unit-cube faces are hidden internally where cubes touch?

There are 12 internal contacts between adjacent unit cubes, and each contact hides 2 unit faces, giving $12 \times 2 = 24$ hidden internal faces.

What is a cross-section of a 3D solid?

The 2D shape revealed on the flat surface produced when the solid is cut straight through by a plane.

What cross-section do you get by slicing a cube parallel to one of its faces?

A square identical in size to the face it is parallel to.

What cross-section results from slicing a cube with a plane through three vertices around one corner?

An equilateral triangle.

What shape is the horizontal cross-section of a cone taken parallel to its base?

A circle (smaller than the base), because the cone narrows uniformly toward the apex.

What cross-section is produced by slicing a sphere with any flat plane?

A circle; a plane through the centre gives the largest circle (a great circle) of radius equal to the sphere's radius.

What is a 'net' of a 3D solid?

A 2D arrangement of all the solid's faces, joined along edges, that can be folded along those edges to form the closed 3D shape with no overlaps and no gaps.

How many faces, and therefore how many squares, does the net of a cube contain?

Six squares, one for each of the cube's 6 faces.

How many distinct (non-congruent) nets can fold into a cube?

There are 11 distinct nets of a cube.

When folding a cube net, how can you identify which two squares end up as opposite faces?

Squares separated by exactly one square in a straight row, or that are two steps apart around the net, become opposite faces; adjacent squares in the net become adjacent (touching) faces.

What test rejects a candidate cube net immediately?

If it does not have exactly 6 squares, or if any square would have to overlap another when folded (e.g. an arrangement that wraps two faces onto the same position), it cannot form a cube.

What is 'unfolding' a solid into its net?

The reverse of folding: cutting the solid along enough edges so that all its faces can be laid flat in one connected piece without tearing any face.

How many faces does the net of a square-based pyramid contain, and what are they?

Five faces: one square base plus four congruent triangular faces.

How many faces does the net of a triangular prism contain?

Five faces: two triangular ends and three rectangular sides.

When checking 'which net forms a given shape', what is the role of the markings/symbols on faces?

They fix orientation: after folding you must confirm each symbol points the correct way and that symbols intended for adjacent or opposite faces actually land in those positions on the target solid.

On a folded cube, if three faces meet at one corner, what is true about their arrangement in the net?

In the net those three squares must form an L-shape or be mutually adjacent so that folding brings their shared edges together at a single vertex.

What does 'assembling component pieces into a whole' test, and how do you approach it?

It tests visualising how separate parts combine into one figure. Match each piece's unique edges/notches to where they fit, ensure orientations are allowed (rotation only, unless flips are permitted), and confirm the assembled outline matches the target.

In a 'complete the visual sequence' question, what must you identify before choosing the next figure?

The transformation rule linking each figure to the next, e.g. a fixed rotation step, a steady increase in number of sides or dots, shading that alternates, or an element moving a set amount each step.

A sequence rotates a shape $45^{\circ}$ clockwise each step. After 4 steps, what is the total rotation?

$4 \times 45^{\circ} = 180^{\circ}$ clockwise, so the shape is upside-down relative to the start.

How do you handle a sequence where two rules act at once (e.g. rotation plus shading change)?

Track each property in its own separate sequence (one for orientation, one for shading/count), predict each independently, then combine both predictions to pick the answer that satisfies all rules.

What is the method for 'spot the odd one out' among a set of shapes?

Find the property shared by all but one (number of sides, symmetry, shading, rotation vs reflection, count of elements). The figure that breaks that single common rule is the odd one out.

In odd-one-out questions, why are reflected (mirror-image) figures a common trap?

Several figures may be rotations of one shape while one is its mirror image. Since rotations preserve handedness and a reflection reverses it, the reflected figure is the odd one out.

What does 'identifying the rule behind a shape series' require you to articulate?

A precise, repeatable transformation that takes each term to the next, such as 'add one side', 'rotate $90^{\circ}$ clockwise', 'shade the next segment clockwise', so it can be applied to predict the missing or following term.

When a shape series changes the number of elements, what arithmetic patterns should you check first?

Check for a constant difference (arithmetic, e.g. $+1, +2$ each step) or a constant ratio (geometric, e.g. doubling), and whether counts of sides, dots or lines follow that pattern.

Why is comparing the cyclic order of features the single most useful skill across rotation, reflection and odd-one-out tasks?

Because rotation always preserves the clockwise cycle of features while reflection reverses it; checking this order instantly distinguishes identical (rotated) shapes from mirror images, which is the core decision in most AST spatial questions.

What general working method should you apply to every AST spatial reasoning item under time pressure?

Identify one or two invariant cues (a unique feature, edge length, count, or clockwise order), test each option against those cues to eliminate quickly, and confirm orientation/handedness before committing, rather than mentally rebuilding the whole figure.