UAT-UK SPEC CODE: M5 (Geometry)ASSUMED MATHS 1 PREREQUISITE: M5.4FREQUENCY: VERY HIGH
Regular Polygon Exterior Angles (360°/n), 3-Figure Bearings, Clock Angles & 2D Vectors/Transformations
Deconstructed from 21 past UAT-UK questions (9.33% of all historical Mathematics 1 papers). Students using standard A-Level classroom methods spend an average of 135s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 35s (saving 100s per question).
Historical Frequency
21 Past Qs
9.33% of Mathematics 1
Classroom Trap Time
135s
+45s over 90s budget
Sub-90 Target Time
35s
Banks +100s on the clock
Dominant UI Format
5-Option A–E
Maths 1 Skill: M5.4
Card 1 & Card 2 Preview: The Classroom Time Trap vs. Sub-90 2-Line Rule
Excerpted from our interactive 6-Step Topic Lesson for ARCH-M1-13.
CARD 1 OF 6 • THE CLASSROOM TIME TRAP (135s)
Why Students Bleed Time:
Step 1: Recall the exterior angle theorem for any convex polygon.
The sum of the exterior angles of any convex polygon is . For a regular -gon, each exterior angle equals .
**Step 2: Solve for .**
The sum of the exterior angles of any convex polygon is . For a regular -gon, each exterior angle equals .
**Step 2: Solve for .**
In 21 past UAT-UK questions (9.33% of Mathematics 1), candidates lose 100s by at each vertex of a polygon track, the runner's bearing changes by the exterior turn angle 360/n, not the interior angle. Instead, apply M5 with Maths 1 skill M5.4.
CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<35s)
Line 1 (Exterior Angle Identity): .
**Line 2 (Cancel ):** sides (15s).
Sanity & Limit Check: Verify units/signs against
fence_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) and subsystem_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)).Examiner Distractor Blueprint for ARCH-M1-13
FOIL #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.
FOIL #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°.
FOIL #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.
FOIL #4intermediate_stop_trap
Solving column vector x- and y-equations for parameter p and forgetting to substitute into the second parameter q
Stopping after solving the first component of the 2D vector equation.
Try 1 Live Sample Question Under the 90-Second Stopwatch
Press W to open the 2-line dry-wipe scratchpad, select A–E, and lock in to reveal the Dual-View solution.
sub90 ESATARCH-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 (<35S)
0.0s35s Sub-9090s ESAT Budget150s Classroom
Right-click any option to cross out • Keys
A–E + EnterQuestion 1 of 1 • 90s Target
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The question stem, diagram, and answer options are hidden behind this pre-start gate. When you click below, the question will reveal and your 90-second split stopwatch will immediately begin ticking.
Mathematics 1•ARCH-M1-13•Standard 5-Option
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