Direct and inverse proportion: tables and relationships
3 exam-style questions. Answers and the mark for each step are on the last page.
- Question 1
Answer each part without a calculator.
(a) 6 cinema tickets cost £45. Work out the cost of 10 tickets.
(b) A recipe for 4 people uses g of flour. How much flour is needed for 10 people?
- Question 2
(a) Positive quantities x and y satisfy y = 72/x. Find the change in y when x increases from 6 to 9. Give the amount by which y decreases.
- Question 3
(a) A job is planned to take 12 workers 15 days. Each worker works at the same constant rate. After 6 days, the deadline changes: the whole job must be finished by the end of day 12. How many additional workers are needed for the remaining days? You must show your working.
Answers and marks
Question 1
(a) £75
- M1 Finding the cost of one ticket, £7.50 (or of 2 tickets, £15).
- A1 The correct answer, £75.
(b) g
- M1 Scaling correctly, such as g per person or .
- A1 The correct answer, g.
Question 2
(a)
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer:
Question 3
(a)
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- P1 Establishing or an equivalent valid method.
- A1 Correct answer: