Variation · 1.2.1
Inverse variation
This standard asks you to understand what it means when one quantity varies inversely as another: as x increases, y decreases in the same proportion (and vice versa), so the product xy stays constant. You should be able to recognise inverse variation from a table, a graph, a real situation, or the equation y = k/x.
The official learning standard (1.2.1)
“Explain the meaning of inverse variation.”
What it means
This standard asks you to understand what it means when one quantity varies inversely as another: as x increases, y decreases in the same proportion (and vice versa), so the product xy stays constant. You should be able to recognise inverse variation from a table, a graph, a real situation, or the equation y = k/x.
How it is examined
In Paper 1, expect short objective items asking you to identify a table, graph or statement that shows inverse variation, or to choose the correct equation y = k/x. In Paper 2, this idea usually opens a longer structured question on variation, before further parts ask you to find k or an unknown value.
Worked example
The time, T (hours), taken to fill a tank varies inversely as the number of identical pipes used, n. Using 2 pipes takes 6 hours.
Explain what this means, and state what happens to T if n is doubled.
- Inverse variation means T = k/n for a constant k, so the product nT is always the same.
- Substitute n = 2, T = 6: k = nT = 2 × 6 = 12.
- So the relation is T = 12/n.
- If n is doubled to 2n: T = 12/(2n) = 6/n, which is half the original T.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How is inverse variation different from direct variation?
In direct variation, both quantities increase or decrease together, so the ratio y/x is constant, giving y = kx. In inverse variation, one quantity increases as the other decreases, so the product xy is constant instead, giving y = k/x.
What does the graph of an inverse variation look like?
It is a smooth curve, sometimes called a hyperbola, that gets closer and closer to both axes but never actually touches them. This is very different from direct variation, whose graph is always a straight line passing through the origin.
Can x be equal to zero in an inverse variation?
No. Since y = k/x involves dividing by x, x can never be zero, because division by zero is undefined.
In real situations this makes sense too, for example, you cannot have zero pipes filling a tank in a finite time.