Rotation Sequences

Rotation is the single most common change in Type 2 AR questions. A shape turns by a consistent angle from one box to the next, and you must identify the angle and direction to predict the next position. This lesson drills the mechanics of rotation so you can identify it instantly.

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The Mechanics of Rotation

Direction

Direction	Also called	Visual
Clockwise (CW)	Right-turning	Follows the movement of clock hands
Anticlockwise (ACW)	Counter-clockwise, left-turning	Opposite to clock hands

Angle

Common rotation angles in UCAT:

Angle	Fraction of full turn	Steps to complete cycle
30°	1/12	12 steps
45°	1/8	8 steps
60°	1/6	6 steps
90°	1/4	4 steps
120°	1/3	3 steps
180°	1/2	2 steps

The most common angles in UCAT are 45° and 90°. If you suspect rotation, try these first.

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How to Determine the Rotation Angle

Method 1: Use an Asymmetric Feature as a Marker

Find a distinctive part of the shape — the point of an arrow, the right angle of a triangle, a notch or protrusion — and track where it moves from one box to the next.

Example: An arrow pointing up in Box 1 points right in Box 2. The tip moved from 12 o'clock to 3 o'clock — that is 90° clockwise.

Method 2: Use the Clock Analogy

Imagine the shape is at the centre of a clock face. The distinctive feature points to a "time":

Position	Clock equivalent
Up	12 o'clock
Upper-right	1:30
Right	3 o'clock
Lower-right	4:30
Down	6 o'clock
Lower-left	7:30
Left	9 o'clock
Upper-left	10:30

A move from 12 to 3 o'clock is 90° CW. A move from 12 to 1:30 is 45° CW. A move from 12 to 10:30 is 45° ACW.

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Rotation of Different Shape Types

Arrows

Arrows are the easiest shapes for identifying rotation because they have a clear "pointing direction."

Sequence: ↑ → → → ↓ → ← → ↑

This is a 90° CW rotation. Each arrow turns a quarter-turn clockwise.

Asymmetric Polygons (L-shapes, right-angled triangles)

These shapes look different at every angle (until the rotation completes a full cycle), making rotation easy to track.

Sequence of a right-angled triangle:

• Box 1: Right angle at bottom-left (like ⌐)
• Box 2: Right angle at bottom-right (like ¬)
• Box 3: Right angle at top-right (like ⌐ flipped vertically)
• Box 4: Right angle at top-left (like ¬ flipped vertically)

This is 90° CW rotation.

Symmetric Shapes

Regular shapes (squares, equilateral triangles, regular hexagons) are harder to assess because they look the same at certain rotation intervals:

Shape	Looks the same every...
Equilateral triangle	120°
Square	90°
Regular pentagon	72°
Regular hexagon	60°
Circle	Any angle (rotation invisible)

If the sequence uses highly symmetric shapes, look for a marker — a dot, a different colour on one side, a notch, or a line — that breaks the symmetry and allows you to track rotation.

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Worked Example: 45° Clockwise Rotation

Sequence:

• Box 1: An L-shaped figure oriented with the long arm pointing right and the short arm pointing up (imagine an "L" rotated so the base goes right)
• Box 2: The L-shape has rotated 45° CW — the long arm now points to the lower-right, the short arm to the upper-right
• Box 3: Another 45° CW — long arm points down, short arm points right
• Box 4: Another 45° CW — long arm points to the lower-left, short arm points down

Prediction for Box 5: Another 45° CW — long arm points left, short arm points to the lower-left.