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

Spatial Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Spatial Reasoning in RAF Airman/Airwoman Selection Test (AST), not a summary of it.

1. 1

   2D Shape Manipulation

   4 topics

   • Rotating flat shapes
     • Identifying the rotated version of a figure
   • Reflecting and mirroring shapes
   • Matching identical shapes among rotations
   • Combining shapes to form a target figure
2. 2

   3D Visualisation

   4 topics

   • Interpreting 3D objects from 2D drawings
   • Rotating cubes and blocks mentally
     • Tracking faces during rotation
   • Counting hidden and visible faces
     • Counting cubes in a stacked figure
   • Cross-sections and views from different angles
3. 3

   Nets, Folding and Assembly

   4 topics

   • Folding 2D nets into 3D solids
     • Matching opposite faces on a cube net
   • Unfolding a solid into its net
   • Identifying which net forms a given shape
   • Assembling component pieces into a whole
4. 4

   Pattern and Sequence Recognition

   3 topics

   • Completing a visual sequence
   • Spotting the odd shape out
   • Identifying the rule behind a shape series

Spatial Reasoning flashcards for RAF Airman/Airwoman Selection Test (AST)

24 of 50 cards from the Spatial Reasoning deck — real questions with worked answers.

1. In the AST Spatial Reasoning test, what does it mean to mentally 'rotate' a flat (2D) shape?

   To turn the whole shape clockwise or anticlockwise about a fixed point while keeping its size, proportions and handedness unchanged. Only its orientation changes, not the shape itself.

2. What stays the same and what changes when a 2D shape is rotated?

   Side lengths, angles, area and overall form stay the same (it is congruent); only the orientation/direction the shape faces changes.

3. A square is rotated by $90^{\circ}$. By how many degrees of rotation does a square look identical to its starting position?

   Every $90^{\circ}$. A square has rotational symmetry of order 4, so $\frac{360^{\circ}}{4} = 90^{\circ}$ between identical-looking positions.

4. How do you tell a rotation apart from a reflection of the same shape?

   A rotation preserves the shape's 'handedness' (you can spin it to match), while a reflection produces a mirror image with reversed handedness that cannot be matched by rotation alone.

5. What is a reflection (mirror image) of a 2D shape?

   A flip across a mirror line that reverses the shape left-to-right (or top-to-bottom), so the image is the same distance from the line but on the opposite side, with reversed orientation.

6. In a mirror reflection across a vertical line, how does a point at distance $d$ to the left of the line map?

   It maps to a point at the same distance $d$ to the right of the line, on a horizontal line perpendicular to the mirror. The line is the perpendicular bisector of the segment joining a point and its image.

7. What is the key visual giveaway that two shapes are reflections rather than rotations of each other?

   Their chirality is reversed: features that curve or point left in one curve or point right in the other (like a left and right hand). No amount of rotation in the plane can make them coincide.

8. Which letters of the alphabet look the same after reflection in a vertical mirror line?

   Symmetric letters such as A, H, I, M, O, T, U, V, W, X, Y. They have a vertical line of symmetry, so the reflection is identical to the original.

9. When 'matching identical shapes among rotations', what test confirms two figures are the same shape?

   One can be rotated (without flipping) so that every feature, length and angle lines up exactly with the other. If a flip is needed, they are reflections, not identical rotations.

10. What is a reliable strategy for spotting which option is just a rotation of a given shape?

    Pick a distinctive feature (an arrow, notch or asymmetric mark), track its position relative to the rest of the shape, and check that the clockwise/anticlockwise order of features is preserved (not reversed).

11. Why is feature order (clockwise sequence of marks) useful when matching rotated shapes?

    Rotation keeps the cyclic clockwise order of features identical; reflection reverses it. So a preserved cyclic order means rotation, a reversed order means a mirror image.

12. When combining several flat pieces to form a target figure, what two quantities must be conserved?

    The total area of the pieces must equal the area of the target, and the pieces must tile it with no overlaps and no gaps.

13. What is the first check to rule out a set of pieces that cannot form a target figure?

    Compare total area: if the combined area of the pieces does not equal the target's area, they cannot form it. Then check that edges and angles can fit together along the boundary.

14. In combining-shapes questions, how do matching edge lengths help?

    Pieces can only join cleanly where edge lengths and the angles at corners are compatible, so matching a unique long or short edge to the target's boundary quickly fixes a piece's position.

15. What does a 2D drawing (orthographic view) of a 3D object represent?

    A flat projection of the solid seen straight-on from one direction, typically the front (elevation), side (end elevation) or top (plan) view, with depth removed.

16. Name the three standard orthographic views used to interpret a 3D object.

    Plan (view from directly above), front elevation (view from the front) and side/end elevation (view from the side).

17. If a 3D object's plan, front and side views are all squares of equal size, what is the solid?

    A cube. Equal square projections in all three orthogonal directions are the signature of a cube.

18. How do you mentally reconstruct a 3D shape from its three orthographic views?

    Treat the plan as the footprint, then 'extrude' upward using the front and side elevations to set heights and depths, reconciling all three so every view matches the same solid.

19. When mentally rotating a cube, how many faces can you see at once from a general corner viewpoint?

    At most 3 of the 6 faces are visible simultaneously; the other 3 are hidden on the far side.

20. On a standard die, what is true of the numbers on opposite faces?

    Opposite faces always sum to $7$: $1$ opposite $6$, $2$ opposite $5$, and $3$ opposite $4$.

21. 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.

22. 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.

23. 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).

24. 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.

See more Spatial Reasoning flashcards →

Planning Spatial Reasoning for RAF Airman/Airwoman Selection Test (AST)

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