Chapter 5 Practice Paper: Direct and Inverse Proportion — question paper

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1. 1

   y is proportional to x, and y = 9 when x = 3. The equation linking them is

   1. Ay = 3x
   2. By = 9x
   3. Cy = x + 3
   4. Dy = 3/x
   ( )
2. 2

   The graph of y = kx, where k is positive, is

   1. Aa curve approaching the y-axis
   2. Ba horizontal line at height k
   3. Ca straight line through the origin
   4. Da curve approaching the x-axis
   ( )
3. 3

   Five identical books cost $35. What do eight books cost?

   1. A$49
   2. B$40
   3. C$63
   4. D$56
   ( )
4. 4

   y ∝ 1/x with constant k = 60. When x = 12, y equals

   1. Ay = 720
   2. By = 5
   3. Cy = 12
   4. Dy = 0.2
   ( )
5. 5

   If y ∝ x and x is tripled, then y is

   1. Adivided by 3
   2. Bunchanged
   3. Ctripled
   4. Dsquared
   ( )
6. 6

   For a fixed journey, speed and travelling time vary

   1. Ainversely
   2. Bdirectly
   3. Cnot at all
   4. Das squares
   ( )
7. 7

   The line through the origin passes through (2, 10). Which other point lies on it?

   1. A(3, 16)
   2. B(4, 30)
   3. C(5, 20)
   4. D(3, 15)
   ( )
8. 8

   Six taps fill a tank in 40 minutes. How long do eight taps take, working at the same rate?

   1. A53 minutes
   2. B30 minutes
   3. C45 minutes
   4. D80 minutes
   ( )
9. 9

   In which table does x × y stay the same in every row?

   1. A(1, 5), (2, 10), (3, 15)
   2. B(1, 5), (2, 6), (3, 7)
   3. C(1, 5), (2, 2.5), (4, 1.25)
   4. D(1, 5), (2, 4), (3, 3)
   ( )
10. 10

    m ∝ n², and m = 32 when n = 4. What is m when n = 6?

    1. A72
    2. B48
    3. C18
    4. D128
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly.

1. 1

   A car uses 24 litres of fuel to travel 300 km.

   1. (a)

      How much fuel does the car use for 100 km?

      fuel =[1]
   2. (b)

      How much fuel does the car use for 500 km?

      [2]
   3. (c)

      How far can the car travel on 30 litres?

      [2]
2. 2

   In this question y varies as the reciprocal of x (that is, y = k/x). When x = 8, y equals 3.

   1. (a)

      State the value of the constant k.

      k =[1]
   2. (b)

      Give the equation connecting y and x.

      equation =[1]
   3. (c)

      Find y when x = 4.

      y =[1]
   4. (d)

      Given y = 12, work out x.

      [2]
3. 3

   A paddling pool fills at a steady rate. The table shows three recordings.

   Filling record

   Time (minutes)	1	2	4
   Depth (cm)	3	6	12

   1. (a)

      Show that depth and time are in direct proportion.

      [2]
   2. (b)

      Find the depth after 7 minutes.

      depth =[1]
   3. (c)

      How long does the pool take to reach a depth of 30 cm?

      [2]
4. 4

   A stone dropped from a cliff falls a distance s metres in t seconds, where s ∝ t². The stone falls 45 m in 3 seconds.

   1. (a)

      Find the number k in s = kt².

      [2]
   2. (b)

      How far does the stone fall in 5 seconds?

      distance =[1]
   3. (c)

      After how many seconds has the stone fallen 20 m?

      [2]