Rearranging Harder Formulae 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.
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6 marks
(a)
Make \(x\) the subject of \(5x + y = x + 12\)
(b)Make \(x\) the subject of \(y\left(x + 3\right) = 5x - 6\)
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4 marks
Make \(x\) the subject of \(y = \frac{ 3x + 7 }{x - 5 }\)
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6 marks
(a)
Make \(x\) the subject of \(y = \sqrt{ 7x + 15 }\)
(b)Make \(x\) the subject of \(y = 6\sqrt{x} - 7\)
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6 marks
(a)
Rearrange \(y = \frac{ 11 }{ x } + 12\) to make \(x\) the subject.
(b)Rearrange \(y = \frac{ 9 }{x - 2 }\) to make \(x\) the subject.
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5 marks
A car moving in a straight line starts at a speed of \(u\) metres per second and finishes at a speed of \(v\) metres per second. Its acceleration is \(a\) metres per second squared and it travels a distance of \(s\) metres.
Those four are connected by the formula
\(v^2 = u^2 + 2as\)
(a)Rearrange the formula to make \(u\) the subject.
(b)Work out \(u\) when \(v = 11\), \(a = 8\) and \(s = 7\).
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6 marks
(a)
Make \(x\) the subject of \(7x + y = x - 13\)
(b)Make \(x\) the subject of \(y\left(x + 1\right) = 6x + 3\)
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4 marks
Make \(x\) the subject of \(y = \frac{ x - 9 }{x - 5 }\)
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6 marks
(a)
Rearrange \(y = \sqrt{ 9x + 13 }\) to make \(x\) the subject.
(b)Rearrange \(y = 5\sqrt{x} + 2\) to make \(x\) the subject.
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6 marks
(a)
Make \(x\) the subject of \(y = \frac{ 15 }{ x } - 2\)
(b)Make \(x\) the subject of \(y = \frac{ 15 }{x + 2 }\)
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5 marks
A car moving in a straight line starts at a speed of \(u\) metres per second and finishes at a speed of \(v\) metres per second. Its acceleration is \(a\) metres per second squared and it travels a distance of \(s\) metres.
Those four are connected by the formula
\(v^2 = u^2 + 2as\)
(a)Rearrange the formula to make \(u\) the subject.
(b)Work out \(u\) when \(v = 15\), \(a = 8\) and \(s = 11\).
Answers
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(a) \(x = \frac{ 12 - y}{ 4 }\)
(b) \(x = \frac{ -6 - 3y }{y - 5 }\) - \(x = \frac{ 7 + 5y }{y - 3 }\)
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(a) \(x = \frac{y^2 - 15 }{ 7 }\)
(b) \(x = \frac{\left(y + 7\right)^2}{ 36 }\) -
(a) \(x = \frac{ 11 }{y - 12 }\)
(b) \(x = \frac{ 9 }{ y } + 2\) -
(a) \(u = \sqrt{v^2 - 2as}\)
(b) \(3\ \text{m/s}\) -
(a) \(x = \frac{ -13 - y}{ 6 }\)
(b) \(x = \frac{ 3 -y }{y - 6 }\) - \(x = \frac{ -9 + 5y }{y - 1 }\)
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(a) \(x = \frac{y^2 - 13 }{ 9 }\)
(b) \(x = \frac{\left(y - 2\right)^2}{ 25 }\) -
(a) \(x = \frac{ 15 }{y + 2 }\)
(b) \(x = \frac{ 15 }{ y } - 2\) -
(a) \(u = \sqrt{v^2 - 2as}\)
(b) \(7\ \text{m/s}\)