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OFFICIAL UAT-UK SPEC: M3MODULE: MATHEMATICS 13 Tested Topics

M3: Ratio, Proportion, Mixing and Rates

Official Cambridge & Imperial ESAT specification requirements for Ratio, Proportion, Mixing and Rates on the Mathematics 1 paper. Understand the syllabus boundaries, spot distractor traps engineered by examiners, and master the 2-step Sub-90 shortcuts that compress solve time well below the 88.8-second cutoff.

Start 40-Min Timed Mock Explore 3 Tested Topics

Official Syllabus Subtopics

Requirements specified in the UAT-UK framework

  • 1Non-linear direct and inverse proportionality: y ∝ xⁿ and y ∝ 1/xⁿ
  • 2Two-component mixing and dilution alligation
  • 3Reverse percentage compounding and multi-period multiplier equations
  • 4Combined work rates: 1/Tₜₒₜ = 1/t₁ + 1/t₂
  • 5Geometric similarity scaling: linear factor k, area factor k², volume factor k³
  • 6Cone frustums and proportional volume slicing

Sub-90 Exam Speed Tips

How top candidates solve this spec under the 88.8s clock

Speed Invariant #1

For combined work rates, invert individual times to find work completed per hour and sum the rates directly.

Speed Invariant #2

When scaling geometric solids, verify whether the question asks for linear, surface area, or volume ratios.

Examiner Trap Alert

Examiners engineer distractor options using common algebraic expansions and sign slips. Always test structural ratios or invariants before calculating arithmetic values.

Tested Topics in Specification M3

Master the individual question patterns and Sub-90 shortcuts for this specification.

3 Topics Catalogued
ARCH-M1-0429 Past Qs (12.89%)

Non-Linear Proportionality (y ∝ xⁿ) & Reverse Percentage Compounding

Never solve for proportionality constant k: write y2/y1 = (x2/x1)ⁿ directly using fractional multipliers (e.g. +20% = 6/5, -25% = 3/4). For reverse percentages, divide by the multiplier.

Classroom: 120s→Sub-90: 35s
+85s Saved per Question
Topic Shortcut Guide →Shortcut Lesson →Practice Free Questions →
ARCH-M1-058 Past Qs (3.56%)

Two-Component Mixing, Dilution Alligation & Combined Work Rates

Lock onto the invariant quantity (pure solute or pure metal) that does not change during dilution: C1*V1 = C2*V2. For two mixtures C1 and C2 making Cₘ, the volume ratio is |C2 - Cₘ| : |Cₘ - C1|.

Classroom: 150s→Sub-90: 45s
+105s Saved per Question
Topic Shortcut Guide →Shortcut Lesson →Practice Free Questions →
ARCH-M1-069 Past Qs (4%)

2D/3D Geometric Similarity Scaling (k, k², k³) & Frustums

Write the scaling triad L : A : V = k : k² : k³ immediately. For a frustum cut at fraction k of height from apex, V(frustum) = (1 - k³) * V(whole).

Classroom: 145s→Sub-90: 35s
+110s Saved per Question
Topic Shortcut Guide →Shortcut Lesson →Practice Free Questions →
UAT-UK ESAT SPEED REVOLUTION

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