Inverse Proportion - Worksheets, Questions and Revision

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KS3 · Ratio, Proportion and Rates of Change

KS3.M-R8 Inverse Proportion

Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
State whether each pair of quantities is directly proportional, inversely proportional, or neither.
(a)The time taken to fill a bath and the number of taps open (all taps are identical).(1)
(b)The cost of 1 kg of apples and the number of kilograms bought when there is a fixed total budget of 6 pounds.(1)
2
Two quantities x and y are inversely proportional. When x = 5, y = 12. Find y when x = 15.
(2)
3
In an inverse proportion y = k/x. Find the constant k for each case.
(a)When x = 2, y = 9.(1)
(b)When x = 7, y = 3/7.(1)
4
A job takes 6 workers 10 hours to finish. Assuming work completed is fixed and workers are equally efficient, how long would it take 15 workers?
(3)
5
The brightness of a lamp varies inversely with the square of the distance from the lamp. If brightness is 100 units at 2 m, find the brightness at 5 m. Give your answer as a fraction or a decimal.
(3)
6
If y is inversely proportional to x and y = 8 when x = 1.5, find x when y = 12.
(2)
7
A cyclist takes 2 hours to travel 30 miles at a steady speed. Assuming speed is inversely proportional to time for a fixed distance, find how long it takes to travel the same distance at 9 mph.
(3)
8
The pressure P of a gas varies inversely with its volume V at constant temperature, P = k/V. If pressure is 2.5 kPa when volume is 8 litres, find the pressure when volume is 5 litres.
(3)
9
Two machines working together complete a task in 4 hours. If one machine alone would take 6 hours, find how long the second machine would take alone. Assume each machine works at constant rate and rates add.
(2)
10
An electrical heating element gives a fixed amount of heat energy per second. The temperature rise per minute is inversely proportional to the mass of water heated. If 500 g of water heats up by 6 degrees in one minute, how many degrees does 750 g of water rise in one minute?
(3)
11
Solve the equation 7 = k/x given that x = 0.5. Find k, then state k/x when x = 2.5.
(3)
12
A photographer says the exposure is inversely proportional to shutter speed. If an exposure of 1/60 s gives correct exposure at f-number fixed, what exposure corresponds to shutter speed 1/240 s? State whether exposure increases or decreases.
(2)
13
Two variables a and b are inversely proportional. When a = 10, b = 1.5. When a = 25, what is b? Show your working.
(3)
14
A pump fills a tank at a rate that is inversely proportional to the time taken. If the pump fills the tank in 2 hours at 90 litres per hour, what rate (in litres per hour) will fill the same tank in 6 hours?
(2)
15
A simple inverse proportion problem: The time t (in minutes) to boil water varies inversely with the power p (in units) of the kettle. When p = 4, t = 9. Calculate t when p = 6.
(3)
16
Stretch: The intensity I of light from a point source varies inversely with the square of the distance d. Two lamps give intensities I1 and I2 at distances d1 and d2 respectively. Lamp A at 3 m gives intensity 80 units. Lamp B at 6 m gives intensity 30 units. Are these two lamps likely to be identical point sources? Justify your answer with calculation.
(3)
17
Stretch: A recipe requires an amount of spice s that varies inversely with the number of servings n. A recipe uses 2 teaspoons for 8 servings. How many teaspoons are needed for 30 servings? Give your answer as a fraction and as a decimal to two decimal places.
(3)
18
Extension problem: A wind turbine's power output P varies approximately inversely with the cube of the time t taken for one revolution (so P = k/t3). If a turbine produces 200 kW when t = 2 s, find the power when t = 3 s. Give your answer to 1 decimal place.
(3)
Mark scheme · KS3.M-R8 Inverse Proportion

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18