75-Archetype SyllabusMathematics 1 • ARCH-M1-05 • Spec M3

Full 6-Card Lesson 15-Question Timed Drill

UAT-UK SPEC CODE: M3 (Ratio and proportion)ASSUMED MATHS 1 PREREQUISITE: M3.5FREQUENCY: MEDIUM

Two-Component Mixing, Dilution Alligation & Combined Work Rates

Deconstructed from 8 past UAT-UK questions (3.56% of all historical Mathematics 1 papers). Students using standard A-Level classroom methods spend an average of 150s on this archetype—blowing past the 90s ESAT budget. Using the 2-line Sub-90 heuristic below compresses solve time to 45s (saving 105s per question).

Historical Frequency

8 Past Qs

3.56% of Mathematics 1

Classroom Trap Time

150s

+60s over 90s budget

Sub-90 Target Time

45s

Banks +105s on the clock

Dominant UI Format

5-Option A–E

Maths 1 Skill: M3.5

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-M1-05.

Launch All 6 Active-Recall Cards

CARD 1 OF 6 • THE CLASSROOM TIME TRAP (150s)

Why Students Bleed Time:

Scale

P : Q = 5 : 3

2

so that the middle term

Q

equals

6

, giving

P : Q = 10 : 6

. Combining with

Q : R = 6 : 7

gives

P : Q : R = 10 : 6 : 7

, so

P : R = 10 : 7

(~90s).

In 8 past UAT-UK questions (3.56% of Mathematics 1), candidates lose 105s by forgetting that adding solute or solvent changes the total denominator of the mixture. Instead, apply M3 with Maths 1 skill M3.5.

CARD 2 OF 6 • THE 2-LINE SUB-90 HEURISTIC (<45s)

Line 1 (Fraction Product):

\frac{P}{R} = \frac{P}{Q} \times \frac{Q}{R} = \frac{5}{3} \times \frac{6}{7}

**Line 2 (Cancel

3

):**

\frac{10}{7} \implies 10 : 7

(20s).

Sanity & Limit Check: Verify units/signs against subsystem_isolation_trap (Dividing solute mass by added water volume V_added instead of final total volume V_initial + V_added) and intermediate_stop_trap (Adding times T₁ + T₂ instead of rates 1/T₁ + 1/T₂).

Examiner Distractor Blueprint for ARCH-M1-05

FOIL #1subsystem_isolation_trap

Dividing solute mass by added water volume V_added instead of final total volume V_initial + V_added

Forgetting that adding solute or solvent changes the total denominator of the mixture.

Open Subsystem Isolation Trap Clinic

FOIL #2intermediate_stop_trap

Adding times T₁ + T₂ instead of rates 1/T₁ + 1/T₂

Combining work times additively rather than inverting the sum of individual rates.

Open Intermediate Stop Trap Clinic

FOIL #3factor_of_two_or_stoichiometry_trap

Chain ratio Q:R = a:b and R:S = c:d combined as a*d : b*c instead of a*c : b*d

Cross-multiplying the wrong terms when bridging the shared middle variable R.

Open Factor-of-2 / Stoichiometry Clinic

FOIL #4sign_or_direction_flip

Inverting the alligation ratio |C₂ - C_target| : |C_target - C₁|

Assigning the larger weight to the component further from the target concentration.

Open Sign / Direction Flip 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-M1-05)

ARCH-M1-05: Two-Component Mixing, Dilution Alligation & Combined Work Rates (Sample)Mathematics 1

00:00.0

SUB-90 ZONE (<45S)

0.0s45s Sub-9090s ESAT Budget150s Classroom

Question 1 of 1ARCH-M1-05 (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-M1-05•Standard 5-Option

or press Enter to start