NumberStudy Notes

Worked Example 1: Direct Proportion

Part of Proportion — GCSE Mathematics

This study notes covers Worked Example 1: Direct Proportion within Proportion for GCSE Mathematics. Revise Proportion in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 7 of 15 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 15

Practice

12 questions

Recall

22 flashcards

Worked Example 1: Direct Proportion

y is directly proportional to x. When x = 5, y = 20. Find the value of y when x = 8.

Solution

y ∝ x, so y = kx

When x = 5, y = 20: 20 = k × 5

k = 20 ÷ 5 = 4

So y = 4x

When x = 8: y = 4 × 8 = 32

Answer: y = 32

Keep building this topic

Read this section alongside the surrounding pages in Proportion. That gives you the full topic sequence instead of a single isolated revision point.

Visual Understanding Worked Example 2: Inverse Proportion The Language of Relationships What is Proportion?

Practice Questions for Proportion

y is directly proportional to x. Which equation could represent this relationship?

A. y = k/x
B. y = kx
C. y = k − x
D. y = x²

1 markfoundation

Explain how you can tell from a graph whether two quantities are in direct or inverse proportion.

2 marksstandard

Quick Recall Flashcards

Proportion Symbol

∝ means 'proportional to' Examples: y ∝ x (y is proportional to x) y ∝ 1/x (y is inversely proportional to x)

Recipe Application

Recipe for 4 people uses 300g flour How much for 10 people? Flour ∝ People (direct) F = kP 300 = k × 4, so k = 75 For 10 people: F = 75 × 10 = 750g

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Visual Understanding

Worked Example 2: Inverse Proportion