[discia] GCSE Maths › Algebra › Changing the Subject of a Formula

Changing the Subject of a Formula

discia.org 10 questions · 23 marks
Name Date
  1. Either paper 3 marks
    (a)

    Make \(x\) the subject of \(y = x - 13\)

    (b)

    Make \(t\) the subject of \(w = 5t\)

    (c)

    Make \(k\) the subject of \(p = \frac{k}{ 4 }\)

    Show answer
    (a) \(x = y + 13\)
    (b) \(t = \frac{w}{ 5 }\)
    (c) \(k = 4p\)
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  2. Either paper 1 mark
    \(ab^{3} = c\) Circle the correct expression for \(a\).
    \(cb^{3}\)\(3bc\)\(\frac{ c }{ b^{3} }\)\(\frac{ c }{ 3b }\)
    Show answer
    \(\frac{ c }{ b^{3} }\)
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  3. Either paper 2 marks

    Make \(x\) the subject of the formula \(y = 3x + 2\)

    Show answer
    \(x = \frac{y - 2 }{ 3 }\)
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  4. Either paper 2 marks

    Rearrange the formula \(y = \frac{x}{ 3 } + 5\) to make \(x\) the subject.

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    \(x = 3(y - 5)\)
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  5. Either paper 4 marks

    A hire shop uses the formula

    \(C = 4d + 15\)

    to work out the cost, \(C\) pounds, of hiring a carpet cleaner for \(d\) days.

    (a)

    Make \(d\) the subject of the formula.

    (b)

    Priya pays £43 to hire the carpet cleaner.

    Find the number of days she hires it for.

    Show answer
    (a) \(d = \frac{C - 15 }{ 4 }\)
    (b) \(7\ \text{days}\)
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  6. Either paper 2 marks

    Make \(x\) the subject of the formula \(y = \frac{ x - 17 }{ 6 }\)

    Show answer
    \(x = 6y + 17\)
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  7. Either paper 2 marks

    Rearrange the formula \(y = 5(x + 8)\) to make \(x\) the subject.

    Show answer
    \(x = \frac{ y }{ 5 } - 8\)
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  8. Either paper 2 marks

    Make \(x\) the subject of the formula \(y = 40 - 2x\)

    Show answer
    \(x = \frac{ 40 - y }{ 2 }\)
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  9. Either paper 3 marks

    Make \(x\) the subject of the formula \(y = \frac{ 3x }{ 8 } + 20\)

    Show answer
    \(x = \frac{ 8(y - 20) }{ 3 }\)
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  10. Either paper 2 marks

    Rearrange the formula \(y = 82 - \frac{x}{ 4 }\) to make \(x\) the subject.

    Show answer
    \(x = 4(82 - y)\)
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discia.org Changing the Subject of a Formula · sheet 1
Answers Changing the Subject of a Formula · sheet 1
  1. (a) \(x = y + 13\)
    (b) \(t = \frac{w}{ 5 }\)
    (c) \(k = 4p\)
  2. \(\frac{ c }{ b^{3} }\)
  3. \(x = \frac{y - 2 }{ 3 }\)
  4. \(x = 3(y - 5)\)
  5. (a) \(d = \frac{C - 15 }{ 4 }\)
    (b) \(7\ \text{days}\)
  6. \(x = 6y + 17\)
  7. \(x = \frac{ y }{ 5 } - 8\)
  8. \(x = \frac{ 40 - y }{ 2 }\)
  9. \(x = \frac{ 8(y - 20) }{ 3 }\)
  10. \(x = 4(82 - y)\)
discia.org Changing the Subject of a Formula · sheet 1