Variation · Form 5
Variation: Paper 2 Answering Guide
How Variation appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Paper 2 gives a relationship in words (“y varies directly with the square of x”), a pair of values to find k, and then asks you to predict another value. The single most common slip is misreading the type of variation, so the first sentence deserves care.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
A fully worked Paper 2 variation question
The electrical resistance R (in ohms) of a wire varies directly as its length L (in metres) and inversely as the square of its diameter d (in mm). When L = 8 m and d = 2 mm, the resistance is R = 6 ohms.
(a) Form an equation connecting R, L and d. (b) Find R when L = 15 m and d = 3 mm.
(c) Find L when R = 12 ohms and d = 2 mm.
- State the relationship: R ∝ L/d², so R = kL/d².
- Substitute the given values to find k: 6 = k(8)/(2)².
- Simplify: 6 = 8k/4 = 2k, so k = 3.
- Write the full equation: R = 3L/d².
- (b) Substitute L = 15, d = 3: R = 3(15)/(3)² = 45/9 = 5 ohms.
- (c) Substitute R = 12, d = 2: 12 = 3L/(2)² → 12 = 3L/4 → L = 48/3 = 16 m.
Where the method marks are won or lost
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How are the marks usually split between the equation and the final answer?
Usually the first marks go to forming the equation and finding k, and the remaining marks to each value you compute. That is why skipping to the answer is expensive: even a correct final number leaves the method marks on the table.
Show the relationship, the substitution and k every time.
Does a variation answer need units?
If the quantity has units, yes. When R is a resistance in ohms or L a length in metres, the final answer must carry them, R = 5 ohms, L = 16 m.
The constant k usually has no simple unit and is left as a number, but the quantity you solve for should always be stated with its unit.
For parts (b) and (c) do I find k again each time?
No. You find k once from the complete pair given, then reuse the same k for every later part.
Re-deriving k from an incomplete later set is a common error that produces a wrong constant. Box your k after part (a) and substitute it into the same equation for (b) and (c).