Variation
Inverse variation
A relationship where one quantity decreases as another increases so their product is constant, y = k/x.
| English | Inverse variation |
|---|---|
| Bahasa Melayu | Variasi songsang |
| 中文 | 反比 |
How it is used
A journey of 240 km takes 4 hours at 60 km/h. Speed is inversely proportional to time, so k = 60 × 4 = 240.
At 80 km/h the time is 240 ÷ 80 = 3 hours.
Where it shows up in SPM
Inverse proportion is the everyday wording of inverse variation in the Form 5 Variation chapter. Both papers use word problems where one quantity falls as another rises: workers against time, speed against time, or pressure against volume.
Don't confuse it with
Frequently asked questions
How do I know a problem is inverse proportion?
Look for one quantity going down as the other goes up while their product stays fixed. More workers means less time; faster speed means shorter time.
If x rises and y falls so that xy is constant, model it as y = k/x.
Why do I multiply to find k here?
Because in inverse proportion xy = k. At 60 km/h for 4 hours, k = 60 × 4 = 240 km, the fixed distance.
In direct proportion you would divide instead, so identifying the type first stops you using the wrong step.
If x is halved, what happens to y?
y doubles. Since y = k/x, replacing x with x/2 gives k ÷ (x/2) = 2k/x = 2y.
So halving one quantity doubles the other, the opposite of direct proportion.