Operations on Sets · Form 4
Operations on Sets: Paper 2 Answering Guide
How Operations on Sets 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 usually gives a Venn diagram to shade or a worded scenario to translate into set notation, sometimes with numbers in each region to work out. The skill being tested is careful translation between words, symbols and diagrams.
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 worked Paper 2 set question, laid out for marks
In a survey of 80 residents, 45 read newspaper A, 38 read newspaper B, and 12 read neither newspaper. By drawing a Venn diagram, find (a) the number of residents who read both newspapers, (b) the number who read newspaper A only, and (c) the number who read newspaper B only.
- State what is given: n(ξ) = 80, n(A) = 45, n(B) = 38, n(A ∪ B)' = 12.
- Find the union first: n(A ∪ B) = n(ξ) − n(A ∪ B)' = 80 − 12 = 68 residents.
- State the rule: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- Substitute: 68 = 45 + 38 − n(A ∩ B).
- Simplify: n(A ∩ B) = 83 − 68 = 15, so (a) 15 residents read both newspapers.
- Newspaper A only = n(A) − n(A ∩ B) = 45 − 15 = 30, so (b) 30 residents.
- Newspaper B only = n(B) − n(A ∩ B) = 38 − 15 = 23, so (c) 23 residents.
- Check on the diagram: 30 + 15 + 23 + 12 = 80 = n(ξ). ✓
Where the marks sit in a question like this
A structured question like this spreads its marks across the working, not just the three final numbers. Drawing and labelling the Venn diagram, writing the union formula, substituting the given values correctly, and each of the answers 15, 30 and 23 are separately credited.
That is exactly why a single arithmetic slip in one part rarely drags down the others, provided every line of working is shown. Skip straight to a bare answer and one wrong number can wipe out everything, because the marker has nothing else to reward.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I have to draw the Venn diagram if the question doesn't ask for one?
Draw it anyway. Even when the diagram earns no mark of its own, it organises the 'only', 'both' and 'neither' counts so you place them correctly and can check they total n(ξ).
The few seconds it takes prevents the double-counting error that quietly loses the answer marks in this topic.
The question lists elements instead of counts, does the same method work?
Yes. List the elements into the correct Venn regions first, then count each region to get n(A ∩ B), n(A) and so on.
Once you have the counts, the formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B) is applied in exactly the same way. Elements just add one sorting step before the counting.
If my final number is wrong but my method is right, how much do I lose?
Usually only the accuracy mark for that part, not the method marks. Marks are split, so a stated formula, a correct substitution and a clearly labelled diagram each stand on their own.
That is exactly why you write every line out: one arithmetic slip costs one mark, not the whole question.