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The symbol y∝xy \propto xy∝x means yyy is proportional to xxx. In GCSE questions, you usually replace ∝\propto∝ with an equation using a constant kkk.
For direct proportion, y=kxy = kxy=kx, so both variables scale by the same factor. For inverse proportion, y=kxy = \frac{k}{x}y=xk, so when one variable gets bigger, the other gets smaller.
Watch the wording carefully. If AAA is directly proportional to the square of BBB, write A=kB2A = kB^2A=kB2, but if PPP is inversely proportional to the cube of QQQ, write P=kQ3P = \frac{k}{Q^3}P=Q3k.
Question 1
3 marksp p\,p is directly proportional to the cube of q q\,q
When p=108p = 108p=108, q=3q = 3q=3
Find the value of q q\,q when p=500p = 500p=500
What does the symbol ∝\propto∝ represent in a formula?
Revision notes for WJEC GCSE Maths Direct and Inverse Proportion: explanations and worked examples.
1 of 5
ppp is directly proportional to qqq. When p=15p=15p=15 and q=5q=5q=5, find ppp when q=12q=12q=12.