Spatial Aptitude

Syllabus: Spatial Aptitude: Transformation of shapes - translation, rotation, scaling, mirroring, assembling, and grouping; paper folding, cutting, and patterns in 2 and 3 dimensions.

Rotation, mirroring and scaling

A rotation preserves handedness; a mirror reverses it. So the fastest test for 'rotated or reflected' is to pick an asymmetric feature and check whether going clockwise around the shape still passes the same features in the same order.

$\text{rotation vs mirror}$
A rotation preserves the order of features going round; a mirror reverses it. The single most useful check.
$\text{mirror axes}$
A vertical mirror swaps left and right; a horizontal one swaps top and bottom.
$\text{mirror }\times\text{ mirror}=\text{rotation}$
two reflections compose into a rotation
$90^\circ\ \text{clockwise}=270^\circ\ \text{anticlockwise}$
check the sense given in the question

Paper folding and cutting

Work backwards: unfold one crease at a time, and at each unfold mirror every existing hole across that crease line. The number of holes doubles per fold that the cut passes through, so a cut through two folds gives four holes.

$n\ \text{folds through the cut}\Rightarrow2^n\ \text{holes}$
a quick sanity check on the options
$\text{holes are symmetric about every crease}$

Cubes, nets and assembly

On a cube net, faces two apart in a straight strip are opposite; faces that share an edge or a corner in the net are adjacent. That one rule settles most net questions without any mental rotation.

$1^{st}\ \text{and}\ 3^{rd}\ \text{are opposite}$
In a straight row of a cube net.
$\text{opposite faces of a die: }1\!-\!6,\ 2\!-\!5,\ 3\!-\!4\ (\text{sum }7)$

← Analytical Aptitude

Loading revision…