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UAT-UK SPEC: M5MODULE: MATHEMATICS 1TOPIC ID: ARCH-M1-13

Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations

Master Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations on the ESAT Mathematics 1 paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 35s, saving +100s per question.

Standard Classroom Time
135s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
35s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+100s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Exterior Angle Identity): n=360∘e=360∘24∘n = \frac{360^\circ}{e} = \frac{360^\circ}{24^\circ}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Cancel 1212): 302=15\frac{30}{2} = 15 sides (15s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1fence_post_or_domain_trap

Adding/subtracting interior polygon angle (n-2)*180/n instead of exterior turn angle 360/n when updating a 3-figure bearing

At each vertex of a polygon track, the runner's bearing changes by the exterior turn angle 360/n, not the interior angle.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2subsystem_isolation_trap

Assuming the hour hand stays stationary on the hour mark while the minute hand moves (forgetting hour hand moves 0.5° per minute)

At H:M, the minute hand is at 6M° and the hour hand advances by 30H° + 0.5M°.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3sign_or_direction_flip

Swapping clockwise (x, y) -> (y, -x) with anticlockwise (x, y) -> (-y, x) or forgetting to add/subtract 180° for reverse bearings

Sign flip on coordinate rotation or back-bearing calculation.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations

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Full Lesson All 15 Questions (ARCH-M1-13)
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ARCH-M1-13: Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations (Sample)Mathematics 1
00:00.0
SUB-90 ZONE (<30S)
0.0s30s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-M1-13 (6-Card Lesson)Format: Standard 5-Option
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Question 1 of 1 • 90s Target

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