Ratio, Proportion and Change
Model scaling, percentages, direct and inverse proportion, growth, decay and iterative processes.
How to prepare for the current ESAT
Confirm your course combination, build no-calculator fluency from Mathematics 1 upward, and use official Pearson materials for authentic timing and interface rehearsal.
Core concepts
Concept 1
Translate ratios into common multipliers or fractions of a whole.
Exam cue: Identify whether the comparison is part-to-part or part-to-whole.
Concept 2
Represent direct and inverse proportion algebraically and graphically.
Exam cue: Test how one variable changes when the other doubles.
Concept 3
Apply multiplicative percentage change repeatedly in growth and decay.
Exam cue: Use a multiplier such as 1.08 rather than repeatedly adding percentage points.
Risk pitfalls and guardrails
Reversing the direction of a ratio.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Assuming every increasing relationship is direct proportion.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Using the original base for repeated percentage changes.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Memory anchors
Ratio order
Match each number to the stated order of quantities.
Direct
y = kx and a straight line through the origin.
Inverse
y = k/x and xy is constant.
Scale effects
Lengths scale by k, areas by k² and volumes by k³.
Percentage multiplier
Increase by r uses 1 + r; decrease uses 1 − r.
Iteration
Each output becomes the next input.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Divide £84 in the ratio 3:4.
Red:blue=5:2 and there are 35 red. Blue?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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