Printable · GCSE Higher · ages 14-16

Solving quadratic equations worksheet — GCSE Higher

Fifteen questions on "solving quadratic equations" — DfE statement A18. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Solving quadratic equations worksheet — GCSE Higher

Maths · GCSE Higher · A18 · Solving quadratic equations · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
2.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
3.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?
(a)It has two whole-number solutions
(b)It has one repeated real solution
(c)It has two different real solutions
(d)It has no real solutions at all
4.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
5.Solve 5x² − 15x = 0.
(a)x = 0 or x = 15
(b)x = 3
(c)x = 0 or x = 3
(d)x = 5 or x = 3
6.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
7.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.
y = x² − 2x − 8
(a)x = −2
(b)x = −1 or x = 3
(c)x = −2 or x = 4
(d)x = 0 or x = −8
8.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.
(a)t = 0 or t = 4
(b)t = 2
(c)t = 0
(d)t = 1 or t = 3
9.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.
(a)x = 4 ± √13
(b)x = −4 ± √13
(c)x = 8 ± √13
(d)x = 4 ± √19
10.Solve x² − 6x = 0.
(a)x = 0
(b)x = 3
(c)x = 6
(d)x = 0 or x = 6
11.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
12.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.
(a)k = −9
(b)k = 9
(c)k = 3
(d)k = 36
13.Solve x² − x − 12 = 0.
(a)x = 4 or x = −3
(b)x = −4 or x = 3
(c)x = 12 or x = −1
(d)x = 4 or x = 3
14.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.
(a)13
(b)−7
(c)25
(d)22
15.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.
(a)k < 16
(b)k ≤ 4
(c)k > 4
(d)k < 4

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