Write the stated relationship before inserting values. The constant multiplies the whole power or root: y x means y=k x; inverse cube-root proportion means y= k [3]x. **Relationship** | **Model** | **Effect of multiplying positive x by 8** Direct cube | y=kx3 | Multiply y by 512 Direct cube root | y=k [3]x | Multiply y by 2 Inverse cube root | y= k [3]x | Divide y by 2 Example If y x and y=12 at x=9, then 12=3k, so y=4 x. At x=25, y=20. If y=28, then x=7 and x=49. Use the positive physical range when quantities are lengths, times or masses. A fixed added charge changes a pure proportional model.

Write the stated relationship before inserting values. The constant multiplies the whole power or root: \(y\propto\sqrt x\) means \(y=k\sqrt x\); inverse cube-root proportion means \(y=\dfrac{k}{\sqrt[3]x}\).

If \(y\propto\sqrt x\) and \(y=12\) at \(x=9\), then \(12=3k\), so \(y=4\sqrt x\). At \(x=25\), \(y=20\). If \(y=28\), then \(\sqrt x=7\) and \(x=49\).

Use the positive physical range when quantities are lengths, times or masses. A fixed added charge changes a pure proportional model.

Direct and Inverse Proportion

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Relationship	Model	Effect of multiplying positive x by 8
Direct cube	\(y=kx^3\)	Multiply y by \(512\)
Direct cube root	\(y=k\sqrt[3]x\)	Multiply y by \(2\)
Inverse cube root	\(y=\dfrac{k}{\sqrt[3]x}\)	Divide y by \(2\)

Proportion involving powers and roots

Proportion involving powers and roots