Direct and Inverse Proportion worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 64 marks Sheet 1

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6 marks
\(P\) is directly proportional to \(Q\).

When \(Q = 6\), \(P = 36\).

(a)
Find a formula for \(P\) in terms of \(Q\).

(b)
Work out the value of \(P\) when \(Q = 7\).

(c)
Work out the value of \(Q\) when \(P = 120\).
7 marks
\(A\) is directly proportional to \(r^2\).

When \(r = 3\), \(A = 45\).

(a)
Find a formula for \(A\) in terms of \(r\).

(b)
Find the value of \(A\) when \(r = 6\).

(c)
Find the positive value of \(r\) when \(A = 605\).
6 marks
\(y\) is inversely proportional to \(x\).

When \(x = 2\), \(y = 60\).

(a)
Find a formula for \(y\) in terms of \(x\).

(b)
Calculate the value of \(y\) when \(x = 5\).

(c)
Calculate the value of \(x\) when \(y = 30\).
6 marks The table shows four pairs of values of \(x\) and \(y\).

x 1 2 3 4

y 9 36 81 144

(a)
Write down how \(y\) is related to \(x\).

(b)
Find a formula for \(y\) in terms of \(x\).

(c)
Calculate the value of \(y\) when \(x = 6\).
4 marks
\(y\) is directly proportional to \(x^2\).

When \(x = 8\), \(y = 45\).

(a)
Complete this sentence.

When \(x\) is multiplied by 3, \(y\) is …

(b)
Hence work out the value of \(y\) when \(x = 24\).
8 marks
\(y\) is inversely proportional to \(\sqrt{x}\).

When \(x = 16\), \(y = 11\).

(a)
Find a formula for \(y\) in terms of \(x\).

(b)
Work out the value of \(y\) when \(x = 4\).

(c)
Work out the value of \(x\) when \(y = 4\).
8 marks
The loudness of a sound, \(L\), is inversely proportional to the square of the distance from the speaker, \(d\).

When \(d = 12\) m, \(L = 7\).

(a)
Find a formula for \(L\) in terms of \(d\).

(b)
Find the value of \(L\) when \(d = 4\) m.

(c)
Find the value of \(d\) when \(L = 28\).
6 marks
\(P\) is directly proportional to \(Q\).

When \(Q = 10\), \(P = 90\).

(a)
Find a formula for \(P\) in terms of \(Q\).

(b)
Work out the value of \(P\) when \(Q = 15\).

(c)
Work out the value of \(Q\) when \(P = 108\).
7 marks
\(E\) is directly proportional to \(v^2\).

When \(v = 4\), \(E = 64\).

(a)
Find a formula for \(E\) in terms of \(v\).

(b)
Find the value of \(E\) when \(v = 9\).

(c)
Find the positive value of \(v\) when \(E = 36\).
6 marks
\(y\) is inversely proportional to \(x\).

When \(x = 3\), \(y = 48\).

(a)
Find a formula for \(y\) in terms of \(x\).

(b)
Work out the value of \(y\) when \(x = 9\).

(c)
Work out the value of \(x\) when \(y = 72\).

x	1	2	3	4
y	9	36	81	144

Answers

(a) \(P = 6Q\)
(b) \(42\)
(c) \(20\)
(a) \(A = 5r^2\)
(b) \(180\)
(c) \(11\)
(a) \(y = \dfrac{ 120 }{ x }\)
(b) \(24\)
(c) \(4\)
(a) \(y\) is directly proportional to \(x^2\)
(b) \(y = 9x^2\)
(c) \(324\)
(a) multiplied by 9
(b) \(405\)
(a) \(y = \dfrac{ 44 }{ \sqrt{x} }\)
(b) \(22\)
(c) \(121\)
(a) \(L = \dfrac{ 1,008 }{ d^2 }\)
(b) \(63\)
(c) \(6\ \text{m}\)
(a) \(P = 9Q\)
(b) \(135\)
(c) \(12\)
(a) \(E = 4v^2\)
(b) \(324\)
(c) \(3\)
(a) \(y = \dfrac{ 144 }{ x }\)
(b) \(16\)
(c) \(2\)

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