Variation · Form 5
Variation: Common Mistakes
The mistakes that quietly cost marks in Variation, and how to avoid each one in the SPM exam.
In our experience teaching Variation, most lost marks come from a small set of repeated slips, not from a lack of understanding. Here they are, with the fix for each.
Mistakes to avoid
- Confusing direct with inverse variation
- Forgetting to square or root when the variation involves a power
- Solving for the answer without finding k first
Six more slips that quietly cost variation marks
- What students write: for y = k/x they compute k = y ÷ x → Why it loses marks: that is the constant for DIRECT variation; inverse variation keeps the product constant → Correct working: k = x × y, e.g. y = 6 when x = 4 gives k = 24, not 1.5.
- What students write: for joint variation they write y = k(x + z) → Why it loses marks: 'varies jointly as x and z' means a product, not a sum → Correct working: y = kxz.
- What students write: for inverse variation they say 'when x doubles, y doubles' → Why it loses marks: in y = k/x, doubling x halves y → Correct working: x → 2x gives y → y/2.
- What students write: they jump from the values straight to the final number → Why it loses marks: no equation and no k are shown, so the method marks are gone → Correct working: state y = kx, show k, then substitute.
- What students write: for combined variation y = kx/z they find k using k = y/x only → Why it loses marks: the z in the denominator is ignored → Correct working: k = yz/x, using every given value.
- What students write: they stop at k = 3 and offer it as the answer → Why it loses marks: the question asked for the variable (e.g. y or R), not the constant → Correct working: substitute k back and solve for the quantity requested.
The single costliest slip
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
I reached the right final number but still lost marks, how?
Almost always because you showed no equation and no value of k. Paper 2 pays method marks for stating y = kx in the correct form and for finding k; the final number alone earns just the answer mark.
Always write the equation and k, even when the arithmetic feels obvious.
For inverse variation, what happens to y when x is doubled?
It halves. In y = k/x, replacing x with 2x gives k/(2x), which is half of k/x.
A common slip is to say y also doubles, copying the behaviour of direct variation. Doubling x doubles y only when the relationship is direct, y = kx.
How do I stop mixing up multiply and divide in combined variation?
Translate each word before you calculate: 'directly as' or 'jointly' puts the variable on top, 'inversely as' puts it underneath. Write y = kx/z in full first, then substitute every given value to find k.
Deciding multiply-or-divide on the page, not in your head, removes the guesswork.