Variation describes how one quantity changes when another changes. This section has four lessons and a practice set, and belongs to the wider SPM Mathematics guide.
What does this section cover?
Start with solving direct variation problems, where both quantities rise together. Then learn inverse variation, where one rises as the other falls.
Next is working with joint variation, where one quantity depends on a product of two others. The final lesson is translating combined variation into equations. The practice set mixes all four.
One situation, three equations
Here is an illustrative example. A cleaning team paints a hall. Let T be the time taken, n the number of painters and A the area painted.
| Statement | Type | Equation |
|---|---|---|
| Area painted grows with time (fixed team) | Direct | A = kT |
| Time to paint a fixed area falls as painters join | Inverse | T = k/n |
| Area depends on both painters and time | Joint | A = knT |
The hall is the same in every row. The wording tells you which form to write, and the form tells you where k goes.
Who should start where?
If you are unsure whether to write k over x or times x, start with direct and inverse variation. If two letters appear in a sentence, begin with joint variation.
If the question mixes words like directly, inversely and square of, begin with combined variation. If your setup is correct but your arithmetic slips, use the practice set and the algebra step repair trainer.
For a teacher to go through your setup step by step, see online one-to-one Mathematics tuition.