Higher Mathematics GCSE
– Direct and Inverse Proportion Homework
1.
y is proportional to x where x > 0 and y > 0.
When x = 5, y = 12.5.
(a)
Find an equation expressing y in terms of x.
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Answer y = ..............................................
(3)
(b)
Calculate x when y = 0.72.
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Answer x = ..............................................
(2)
2.
The resistance, R, to the motion of a sailing boat is directly proportional to the square of its speed, V.
If R = 300 when V = 12, find the value of V when R = 150.
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(5)
Howden School
1
3.
The area, A square metres, of a new logo is directly proportional to the square of its width, w metres.
The area of the logo is 12 square metres when its width is 4 metres.
(a)
Find an equation connecting A and w.
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Answer ..........................................................................
(3)
(b)
Find the area of a logo with a width of 5 metres.
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Answer ................................................................... m2
(1)
4.
W and P are both positive quantities.
W is directly proportional to the square root of P.
When W = 12, P = 16.
(a)
Express W in terms of P.
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Answer ..........................................................
(3)
(b)
What is the value of W when P = 25?
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Answer ..........................................................
(1)
(c)
What is the value of P when W = 21?
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Answer ..........................................................
(2)
Howden School
2
5.
Salt is sold in different sized blocks.
The weight of each block, B kilograms, is directly proportional to the cube of its height, h metres.
A block of weight 54 kg has height 3m.
(a)
Find an equation connecting h and B.
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B  .......... .......... .......... .......... ..........
Answer ..........
(3)
(b)
Find the weight of a block with a height of 1m.
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Answer ................................................ kg
(1)
(c)
Another block has a weight of 128 kg.
Find its height.
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Answer ................................................
(3)
Howden School
3
6.
The table shows values of the variables x and y, where y is inversely proportional to x.
(a)
x
0.4
y
5.0
2.5
0.02
Find an equation expressing y in terms of x.
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Answer y = ...................................................
(3)
(b)
Complete the table.
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(2)
7.
In a circuit, the resistance, R ohms, is inversely proportional to the current, I amps.
When the resistance is 12 ohms, the current in the circuit is 8 amps.
(a)
Find an equation connecting R and I.
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Answer ....................................................................
(3)
(b)
Find the current when the resistance in the circuit is 6.4 ohms.
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Answer ............................................................ amps
(2)
Howden School
4
8.
y is inversely proportional to x2
When x = 2, y = 5
(a)
Find the value of y when x = 4
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(3)
(b)
Find the values of x when y = 0.2
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(2)
9.
y is inversely proportional to the square root of x.
When y = 6 then x = 4.
(a)
What is the value of y when x = 9?
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(3)
(b)
What is the value of x when y = 10?
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(2)
Howden School
5
10.
y is proportional to x3
(a)
When x = 4, y = 80.
Find the value of y when x = 8.
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(3)
Also, x is inversely proportional to the square root of z.
(b)
When y = 10, z = 16.
Find the value of z when x = 4.
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(4)
Howden School
6