[discia] GCSE Maths › Algebra › Solving Quadratics

Solving Quadratics

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 2 marks

    Here is the graph of \(y = 0.5x^2 + 3x - 2\)

    -8-7-6-5-4-3-212-8-7-6-5-4-3-2-112340xy

    Use the graph to estimate the solutions of \(0.5x^2 + 3x - 2 = 0\)

    Show answer
    \(x \approx -6.6\) and \(x \approx 0.6\)
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  2. Either paper 2 marks

    Solve \(x^2 + 6x + 5 = 0\)

    Show answer
    \(x = -5\) or \(x = -1\)
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  3. Either paper 2 marks

    \(x = 3\) is a solution of the equation

    \(x^2 +x + c = 0\)

    Work out the value of \(c\).

    Show answer
    \(-12\)
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  4. Either paper 3 marks

    The solutions of the equation

    \(x^2 + bx + c = 0\)

    are \(x = -6\) and \(x = -9\).

    Work out the value of \(b\) and the value of \(c\).

    Show answer
    \(b = 15\) and \(c = 54\)
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  5. Either paper 5 marks

    The diagram shows the plan of the floor of an L-shaped room. All lengths are in metres.

    (x + 4) mx m(x + 1) m4 mDiagram NOT accurately drawn

    The area of the floor is 244 m².

    (a)

    Show that \(x^2 + 8x - 240 = 0\)

    (b)

    By factorising \(x^2 + 8x - 240\), work out the value of \(x\). You must show your working.

    Show answer
    (a) \(x(x + 4) + 4(x + 1) = 244\), so \(x^2 + 8x - 240 = 0\)
    (b) \(12\ \text{m}\)
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  6. Either paper 2 marks

    Leila is asked to solve \(4t^2 - 17t + 15 = 0\)

    Here is her working and answer.

    \((t - 3)(4t - 5) = 0\)

    \(t = -3\) or \(t = \frac{5}{4}\)

    (a)

    What mistake has Leila made?

    (b)

    Work out the correct solutions of the equation.

    Show answer
    (a) Leila got the sign of the root wrong in the bracket with just t. The bracket that Leila solved to get \(t = -3\) gives \(t = 3\).
    (b) \(t = \frac{5}{4}\) or \(t = 3\)
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  7. Either paper 2 marks

    Here is the graph of \(y = x^2 + 7x + 9\)

    -7-6-5-4-3-2-11-5-4-3-2-112340xy

    Use the graph to estimate the solutions of \(x^2 + 7x + 9 = 0\)

    Show answer
    \(x \approx -5.3\) and \(x \approx -1.7\)
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  8. Either paper 2 marks

    \(x^2 - 11x + 18 = 0\)

    Work out the values of \(x\).

    Show answer
    \(x = 2\) or \(x = 9\)
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  9. Either paper 2 marks

    \(x = 1\) is a solution of the equation

    \(x^2 - 6x + c = 0\)

    Calculate the value of \(c\).

    Show answer
    \(5\)
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  10. Either paper 3 marks

    The solutions of the equation

    \(x^2 + bx + c = 0\)

    are \(x = -2\) and \(x = 9\).

    Work out the value of \(b\) and the value of \(c\).

    Show answer
    \(b = -7\) and \(c = -18\)
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discia.org Solving Quadratics · sheet 1
Answers Solving Quadratics · sheet 1
  1. \(x \approx -6.6\) and \(x \approx 0.6\)
  2. \(x = -5\) or \(x = -1\)
  3. \(-12\)
  4. \(b = 15\) and \(c = 54\)
  5. (a) \(x(x + 4) + 4(x + 1) = 244\), so \(x^2 + 8x - 240 = 0\)
    (b) \(12\ \text{m}\)
  6. (a) Leila got the sign of the root wrong in the bracket with just t. The bracket that Leila solved to get \(t = -3\) gives \(t = 3\).
    (b) \(t = \frac{5}{4}\) or \(t = 3\)
  7. \(x \approx -5.3\) and \(x \approx -1.7\)
  8. \(x = 2\) or \(x = 9\)
  9. \(5\)
  10. \(b = -7\) and \(c = -18\)
discia.org Solving Quadratics · sheet 1