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Quadratic Formula

discia.org 10 questions · 36 marks
Name Date
  1. Calculator 3 marks

    Solve \(2x^2 + 9x - 9 = 0\)

    Give your solutions correct to 2 decimal places.

    You may use the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\)

    Show answer
    \(x = -5.34\) or \(x = 0.84\)
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  2. Calculator 4 marks

    The length of a rectangle is 1 cm more than its width.

    The area of the rectangle is 47 cm².

    The width of the rectangle is \(x\) cm, where

    \(x^2 +x - 47 = 0\)

    Work out the width of the rectangle.

    Give your answer correct to 2 decimal places.

    Show answer
    \(6.37\ \text{cm}\)
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  3. Either paper 3 marks

    The equation

    \(x^2 + 4x + c = 0\)

    has exactly one solution.

    Find the value of \(c\).

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

    \(2x^2 + kx + 162 = 0\)

    This equation has a repeated root.

    Work out the two possible values of \(k\).

    Show answer
    \(k = 36\) or \(k = -36\)
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  5. Either paper 3 marks

    Solve the equation \(x^2 - 3x - 1 = 0\)

    Give your answers in surd form.

    Show answer
    \(x = \frac{ 3 \pm \sqrt{ 13 } }{2}\)
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  6. Either paper 3 marks

    An equation is given as \(x^2 - 9x - 2 = 0\)

    (a)

    Work out the value of \(b^2 - 4ac\) for this equation.

    (b)

    Write down how many real solutions the equation has.

    Show answer
    (a) \(89\)
    (b) Two real solutions
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  7. Calculator 4 marks

    Solve \(3x^2 - 4x = 16\)

    Give your solutions correct to 2 decimal places.

    You may use the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\)

    Show answer
    \(x = -1.74\) or \(x = 3.07\)
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  8. Calculator 4 marks

    A ball is thrown straight up into the air.

    Its height, \(h\) metres, at a time \(t\) seconds after it is thrown, is given by

    \(h = 22t - 5t^2\)

    Work out the two times at which the ball is \(18\) m above the ground.

    Give your answers correct to 2 decimal places.

    Show answer
    After \(1.09\) seconds and again after \(3.31\) seconds.
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  9. Calculator 4 marks

    Solve

    \(x - 1 = \frac{ 27 }{ x }\)

    Give your solutions correct to 2 decimal places.

    Show answer
    \(x = -4.72\) or \(x = 5.72\)
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  10. Calculator 5 marks

    A rectangular photograph measures \(21\) cm by \(11\) cm.

    It is mounted with a border of the same width all the way round it. The border is \(x\) cm wide.

    The photograph and the border together cover \(362\) cm².

    Work out the width of the border.

    Give your answer correct to 2 decimal places.

    Show answer
    \(1.84\ \text{cm}\)
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discia.org Quadratic Formula · sheet 1
Answers Quadratic Formula · sheet 1
  1. \(x = -5.34\) or \(x = 0.84\)
  2. \(6.37\ \text{cm}\)
  3. \(4\)
  4. \(k = 36\) or \(k = -36\)
  5. \(x = \frac{ 3 \pm \sqrt{ 13 } }{2}\)
  6. (a) \(89\)
    (b) Two real solutions
  7. \(x = -1.74\) or \(x = 3.07\)
  8. After \(1.09\) seconds and again after \(3.31\) seconds.
  9. \(x = -4.72\) or \(x = 5.72\)
  10. \(1.84\ \text{cm}\)
discia.org Quadratic Formula · sheet 1