Variation

Constant of variation

The fixed number k linking the quantities in a variation relationship.

EnglishConstant of variation
Bahasa MelayuPemalar variasi
中文变化常数

How it is used

In y = kx with y = 20 when x = 4, the constant of variation is k = 20 ÷ 4 = 5, so y = 5x. In y = k/x with y = 20 when x = 4, k = 20 × 4 = 80.

Where it shows up in SPM

The constant of variation k appears in every question of the Form 5 Variation chapter. In Paper 1 you find k directly; in Paper 2 finding k is the first step, then you reuse the same k to predict later values.

Don't confuse it with

GradientIn direct variation y = kx, k equals the gradient of the line; but in inverse or joint variation k is just a multiplier, not a gradient.
VariableA variable such as x or y changes throughout a problem; the constant of variation k is fixed once found and stays the same for every part.

Open the chapter: Variation →

Frequently asked questions

Is k always found the same way?

No. It depends on the model.

For direct variation y = kx you divide (k = y ÷ x); for inverse variation y = k/x you multiply (k = xy); for joint variation you substitute all values and solve. Always write the model first.

Does k change between parts of the same question?

No. Once you find k from the first set of values, it is fixed for the whole question.

You reuse the same k with the new numbers in every later part. A changing k usually means an arithmetic slip.

Can k be a fraction or decimal?

Yes. If y = 6 when x = 8 in direct variation, k = 6 ÷ 8 = 0.75, so y = 0.75x.

Keep it as an exact fraction like 3/4 where possible to avoid rounding errors in later parts.

Related terms

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