R10 Direct and inverse proportion problems Quiz: AQA Maths, Unit 3

The 20 questions

1. y is directly proportional to x. When x = 4, y = 20. What is y when x = 7?

   • 28
   • 32
   • 35
   • 140

2. y is inversely proportional to x. When x = 3, y = 8. What is y when x = 6?

   • 2
   • 4
   • 11
   • 16

3. In inverse proportion, what happens to y when x doubles?

   • It halves
   • It stays constant
   • It doubles
   • It quadruples

4. What line represents a direct proportion graph y = kx?

   • Curved through origin
   • Straight through origin
   • Vertical straight line
   • Horizontal straight line

5. What shape is the graph of y = k/x in the first quadrant?

   • Circle
   • Parabola
   • Straight line
   • Reciprocal curve

6. 5 workers take 12 days to build a wall. At the same rate, how many days would 8 workers take?

   • 7.5 days
   • 8.5 days
   • 19.2 days
   • 7.2 days

7. 6 pens cost £4.50. At the same price per pen, what would 10 pens cost?

   • £7.50
   • £45.00
   • £7.20
   • £6.75

8. If y is directly proportional to x and y = 12 when x = 3, what is the constant of proportionality k?

   • 9
   • 0.25
   • 4
   • 36

9. p is inversely proportional to q. p = 20 when q = 0.5. What is p when q = 2?

   • 40
   • 1.25
   • 5
   • 10

10. 4 identical machines fill a tank in 9 hours. How many hours would 6 of the same machines take to fill it?

    • 4 hours
    • 6 hours
    • 13.5 hours
    • 3 hours

11. y is directly proportional to x. y = 3.6 when x = 0.8. What is y when x = 2.5?

    • 2.25
    • 9.0
    • 12.5
    • 11.25

12. In direct proportion, which quantity stays constant as the values change?

    • The sum y + x
    • The difference y − x
    • The product y × x
    • The ratio y ÷ x

13. Which relationship is an example of inverse proportion?

    • Distance and time
    • Hours worked
    • Cost and weight
    • Speed and time

14. (H) y is directly proportional to x². When x = 2, y = 20. What is y when x = 5?

    • 100
    • 125
    • 50
    • 25

15. The time t for a job is inversely proportional to the number of workers n. 10 workers take 15 days. How many workers finish the job in 12 days?

    • 18.75 workers
    • 15 workers
    • 12.5 workers
    • 8 workers

16. P is directly proportional to Q, and Q is inversely proportional to R. If R doubles, what happens to P?

    • P halves
    • P quarters
    • P stays the same
    • P doubles

17. x = 2 gives y = 30 and x = 5 gives y = 12 in an inverse relationship. What is y when x = 10?

    • 24
    • 3
    • 12
    • 6

18. A tank fills in 40 minutes with 3 equal pipes. How long would 5 of the same pipes take?

    • 66.7 minutes
    • 15 minutes
    • 24 minutes
    • 32 minutes

19. A bag of rice is directly proportional to its price: 2 kg costs £3.40. What does 500 g cost?

    • £0.85
    • £0.34
    • £6.80
    • £1.70

20. For y = k/x, y = 0.25 when x = 8. What is the value of k?

    • 0.03125
    • 32
    • 6.25
    • 2

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