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UAT-UK SPEC: B11MODULE: BIOLOGYTOPIC ID: ARCH-B-12

Photosynthesis Inverse-Square Law (I ∝ 1/d²), Limiting Factors & Capillary Potometers (πr²ʰ/t)

Master Photosynthesis Inverse-Square Law (I ∝ 1/d²), Limiting Factors & Capillary Potometers (πr²ʰ/t) on the ESAT Biology paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 40s, saving +105s per question.

Standard Classroom Time
145s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
40s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+105s
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
Distance doubles (20→40 cm20 \to 40\text{ cm})   ⟹  I\implies I drops by 22=4  ⟹  R2=644=16 bubbles min−12^2 = 4 \implies R_2 = \frac{64}{4} = \mathbf{16\text{ bubbles min}^{-1}}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Distance doubles (20→40 cm20 \to 40\text{ cm})   ⟹  I\implies I drops by 22=4  ⟹  R2=644=16 bubbles min−12^2 = 4 \implies R_2 = \frac{64}{4} = \mathbf{16\text{ bubbles min}^{-1}}.

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 #1factor_of_two_or_stoichiometry_trap

Substituting capillary tube diameter d directly as radius r into V = pi * r² * h (causing a 4x volume error)

Classic potometer trap: failing to halve capillary internal diameter d to radius r = d/2 before squaring.

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

Scaling light intensity linearly (1/d) instead of by the inverse-square law (1/d²) when lamp distance changes

Halving lamp distance quadruples light intensity (×4); tripling distance reduces intensity to 1/9.

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

Claiming light intensity is still the limiting factor on the flat horizontal plateau of a rate-vs-light graph

On the horizontal plateau, increasing light intensity has zero effect—CO2 concentration or temperature is now the limiting factor.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Photosynthesis Inverse-Square Law (I ∝ 1/d²), Limiting Factors & Capillary Potometers (πr²ʰ/t)

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Full Lesson All 15 Questions (ARCH-B-12)
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ARCH-B-12: Photosynthesis Inverse-Square Law (I ∝ 1/d²), Limiting Factors & Capillary Potometers (πr²ʰ/t) (Sample)Biology
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SUB-90 ZONE (<35S)
0.0s35s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-B-12 (6-Card Lesson)Format: Standard 5-Option
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Question 1 of 1 • 90s Target

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