75-Archetype SyllabusMathematics 1 • ARCH-M1-11 • Spec M6

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: M6 (Statistics)ASSUMED MATHS 1 PREREQUISITE: M6.5FREQUENCY: MEDIUM

Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms

Deconstructed from 9 past UAT-UK questions (4% 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 40s (saving 95s per question).

Historical Frequency

9 Past Qs

4% of Mathematics 1

Classroom Trap Time

135s

+45s over 90s budget

Sub-90 Target Time

40s

Banks +95s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M6.5

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-M1-11.

Launch All 6 Active-Recall Cards

CARD 1 OF 6 • THE CLASSROOM TIME TRAP (135s)

Why Students Bleed Time:

Original total mass

= 18 \times 72 = 1296\text{ kg}

. New mean

= 72 + 1.5 = 73.5\text{ kg}

, so new total mass

= 20 \times 73.5 = 1470\text{ kg}

. The

2

new rowers have combined mass

1470 - 1296 = 174\text{ kg}

, giving a mean of

\frac{174}{2} = 87\text{ kg}

(~115s).

In 9 past UAT-UK questions (4% of Mathematics 1), candidates lose 95s by ignoring sample size weights when combining subgroup means. Instead, apply M6 with Maths 1 skill M6.5.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<40s)

Line 1 (Deviation Balance): New mean is

73.5\text{ kg}

; the

18

original rowers need

+1.5\text{ kg}

each (

+27\text{ kg}

total).

Line 2 (Split Surplus Across 2):

73.5 + \frac{27}{2} = 73.5 + 13.5 = 87\text{ kg}

(20s).

Sanity & Limit Check: Verify units/signs against subsystem_isolation_trap (Taking unweighted average (mean_A + mean_B)/2 when group sizes n_A != n_B) and unit_or_prefix_mismatch (Reading histogram bar height (frequency density) as frequency without multiplying by class width).

Examiner Distractor Blueprint for ARCH-M1-11

FOIL #1subsystem_isolation_trap

Taking unweighted average (mean_A + mean_B)/2 when group sizes n_A != n_B

Ignoring sample size weights when combining subgroup means.

Open Subsystem Isolation Trap Clinic

FOIL #2unit_or_prefix_mismatch

Reading histogram bar height (frequency density) as frequency without multiplying by class width

Confusing y-axis frequency density with raw count across unequal class intervals.

Open Unit / Prefix Mismatch Clinic

FOIL #3fence_post_or_domain_trap

Using class midpoint instead of linear interpolation across the median class width

Assuming the median sits at the midpoint of the interval regardless of cumulative frequency position.

Open Fence-Post / Domain Trap Clinic

FOIL #4intermediate_stop_trap

Finding total sum S_new without subtracting S_old to isolate the added/removed item

Stopping at the new total sum.

Open Intermediate Stop Trap Clinic

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.

Full 6-Card Lesson Launch All 15 Questions (ARCH-M1-11)

ARCH-M1-11: Mean Deviation Balancing, Grouped Median Interpolation & Unequal-Width Histograms (Sample)Mathematics 1

00:00.0

SUB-90 ZONE (<40S)

0.0s40s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-M1-11 (6-Card Lesson)Format: Standard 5-Option

Right-click any option to cross out • Keys A–E + Enter

Question 1 of 1 • 90s Target

Ready to Start Question 1?

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-M1-11•Standard 5-Option

or press Enter to start