Quadratic Formula worksheet
9 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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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.
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3 marks
The equation
\(x^2 + 4x + c = 0\)
has exactly one solution.
Find the value of \(c\).
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3 marks
\(2x^2 + kx + 162 = 0\)
This equation has a repeated root.
Work out the two possible values of \(k\).
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3 marks
Solve the equation \(x^2 - 3x - 1 = 0\)
Give your answers in surd form.
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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.
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4 marks
Solve \(3x^2 - 4x = 16\)
Give your solutions correct to 2 decimal places.
You may use the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\)
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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.
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4 marks
Solve
\(x - 1 = \frac{ 27 }{ x }\)
Give your solutions correct to 2 decimal places.
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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.
Answers
- \(6.37\ \text{cm}\)
- \(4\)
- \(k = 36\) or \(k = -36\)
- \(x = \frac{ 3 \pm \sqrt{ 13 } }{2}\)
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(a) \(89\)
(b) Two real solutions - \(x = -1.74\) or \(x = 3.07\)
- After \(1.09\) seconds and again after \(3.31\) seconds.
- \(x = -4.72\) or \(x = 5.72\)
- \(1.84\ \text{cm}\)