Direct and Inverse Proportion: Higher Tier Practice - Worksheets, Questions and Revision

8 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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5.2H Direct and Inverse Proportion: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 80 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A recipe for 6 portions uses 300 g of flour. Work out how much flour is needed for 15 portions, assuming the amount of flour is directly proportional to the number of portions.
(Total for Question 1 is 2 marks)
2
A car uses fuel at a rate directly proportional to its speed. At 40 mph the car uses 7 litres of fuel per hour. Work out the fuel used per hour at 70 mph.
(Total for Question 2 is 3 marks)
3
The time t (in hours) taken to fill a tank with a pump is inversely proportional to the pump's flow rate r (in litres per hour). A pump with flow rate 500 l/h fills the tank in 4 hours.
(a) Find an expression for t in terms of r. (2 marks)
(b) Using your expression, show that a pump with flow rate 750 l/h fills the tank in 8/3 hours. (2 marks)
(a)Find an expression for t in terms of r.(2)
(b)Using your expression, show that a pump with flow rate 750 l/h fills the tank in 8/3 hours.(2)
(Total for Question 3 is 4 marks)
4
The brightness B of a lamp varies directly as the square of the current I through it. A particular lamp has brightness 400 units when the current is 2 A.
(a) Find the constant of proportionality k in B = k I2. (2 marks)
(b) Use your k to find the current when the brightness is 225 units. Give your answer as a simplified surd if necessary. (2 marks)
(a)Find the constant of proportionality k in B = k I2.(2)
(b)Find the current when the brightness is 225 units. Give your answer as a simplified surd if necessary.(2)
(Total for Question 4 is 4 marks)
5
Two quantities x and y are related by x = k / y2. When y = 2, x = 9.
(a) Find k. (1 mark)
(b) Write y in terms of x and k, giving y in simplest form. (3 marks)
(c) Hence or otherwise, find y when x = 1, giving an exact value. (1 mark)
(a)Find k.(1)
(b)Write y in terms of x and k, giving y in simplest form.(3)
(c)Hence or otherwise, find y when x = 1, giving an exact value.(1)
(Total for Question 5 is 5 marks)
6
A scientist measures that the pressure P of a gas varies directly as the temperature T and inversely as the volume V. This can be modelled as P = k T / V. For a sample, when T = 300 K and V = 0.2 m3 the pressure is 120 kPa.
(a) Find k. (2 marks)
(b) Using this k, calculate the pressure when T = 450 K and V = 0.15 m3. Give your answer to 3 significant figures. (4 marks)
(a)Find k.(2)
(b)Using this k, calculate the pressure when T = 450 K and V = 0.15 m3. Give your answer to 3 significant figures.(4)
(Total for Question 6 is 6 marks)
7
A cyclist rides so that the time t (hours) to travel a fixed route is inversely proportional to her speed v (mph), since the route length is fixed. Last week she rode at speed v and completed the route in t hours. This week her speed decreases by 4 mph and she takes 15 minutes longer.
(a) Express the new speed in terms of v. (1 mark)
(b) Write an equation linking t, v and the 15 minute increase and show that 16t = v - 4. (3 marks)
(c) Hence find v in terms of t, simplifying fully, and find the value of v when t = 1.5 hours. (4 marks)
Note: 15 minutes = 1/4 hour.
(a)Express the new speed in terms of v.(1)
(b)Write an equation linking t, v and the 15 minute increase and show that 16t = v - 4.(3)
(c)Hence find v in terms of t, simplifying fully, and find the value of v when t = 1.5 hours.(4)
(Total for Question 7 is 8 marks)
8
A factory produces items at a rate directly proportional to the number of machines m and inversely proportional to the time h taken per shift. The production per shift P is modelled by P = c m / h. When the factory runs 12 machines and each shift lasts 8 hours, production is 480 items.
(a) Find c. (2 marks)
(b) The factory increases the number of machines by 50% and reduces shift length by 20%. Calculate the new production per shift. (3 marks)
(c) The manager wants production per shift to be 900 items while keeping h = 8 hours. Find the required number of machines, giving an integer result and explaining any rounding. (3 marks)
(a)Find c.(2)
(b)The factory increases machines by 50% and reduces shift length by 20%. Calculate the new production per shift.(3)
(c)Find the required number of machines to get P = 900 items per shift when h = 8 hours. Give an integer result and explain any rounding.(3)
(Total for Question 8 is 8 marks)
Mark scheme · 5.2H Direct and Inverse Proportion: Higher Tier Practice

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8