IP EMaths Notes (Upper Sec, Year 3-4): 13) Variation and Rate of Change

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08 Nov 2025, 00:00 Z

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Marcus Pang·Managing Director (Maths)

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Q: What does IP EMaths Notes (Upper Sec, Year 3-4): 13) Variation and Rate of Change cover?
A: Model direct, inverse, and joint variation, and interpret gradient as rate of change in real contexts.

Variation equations compress word problems into algebra. Identify whether quantities move together or in opposition, then encode that with proportionality constants and a positive constant $k$ that captures the context (units, efficiency, scaling).

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These notes align with SEAB GCE O-Level Mathematics (4048) content used in IP programmes (exams from 2026).

Status: SEAB O-Level Mathematics 4048 syllabus (exams from 2026) checked 2025-11-30 - scope unchanged; remains the reference for these notes.

Quick reference

Direct variation: $y \propto x \Rightarrow y = kx$

Time $t / \pu{s}$	Volume $V / \pu{L}$
0	120
10	147
20	171
30	195

IP EMaths Notes (Upper Sec, Year 3-4): 13) Variation and Rate of Change

Quick reference

Spotting variation language

Workflow for variation questions

Worked example 1 - Fuel consumption model

Worked example 2 - Inverse variation (product stays constant)

Worked example 3 - Joint variation with rate of change

Rate of change on graphs and tables

Worked example 4 - Average rate from a data table

Practice Quiz

Try this

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