Robinson Tuition
AS Pure Mathematics · Edexcel 8MA0 · free A-level maths worksheet

Quadratic and simultaneous equations

Solving by factorising, formula and completing the square; one linear and one quadratic; equations in a function of x.

12 original questions, 53 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Solve the equation 2x2 − 7x − 15 = 0

2 marks
Show answer
x = 5 or x = -32
2

By completing the square, solve x2 + 6x − 4 = 0, giving your answers in the form a ± √b, where a and b are integers.

3 marks
Show answer
x = -3 ± √13
3

Solve 3x2 − 5x − 1 = 0, giving your answers to 3 significant figures.

3 marks
Show answer
x = 1.85 or x = -0.180
4

Solve the simultaneous equations

y = x + 3

x2 + y2 = 29

5 marks
Show answer
x = 2, y = 5 or x = -5, y = -2
5

Solve the simultaneous equations

x + 2y = 7

x2 − xy + y2 = 7

You must show all stages of your working.

6 marks
Show answer
x = 3, y = 2 or x = 1, y = 3
6

Using the substitution u = √x, or otherwise, solve x − 7√x + 10 = 0

4 marks
Show answer
x = 4 or x = 25
7

Solve the equation 22x − 9(2x) + 8 = 0

4 marks
Show answer
x = 0 or x = 3
8

The line l has equation y = 2x + k, where k is a constant. The curve C has equation y = x2 − 4x + 7

  1. Show that the x coordinates of any points where l meets C satisfy x2 − 6x + (7 − k) = 0
  2. Given that l is a tangent to C, find the value of k and the coordinates of the point where l touches C.
5 marks
Show answer
a) shown b) k = -2, (3, 4)
9

Solve 2x − 1 + 3x + 2 = 1, giving your answers in simplest surd form.

4 marks
Show answer
x = 2 ± √7
10

A rectangular allotment plot in Leeds has a perimeter of 46 m. The diagonal of the plot is 17 m long. Find the length and the width of the plot.

5 marks
Show answer
15 m by 8 m
11

Find all the real solutions of the equation (x2 − 3x)2 − 2(x2 − 3x) − 8 = 0

5 marks
Show answer
x = -1, 1, 2, 4
12

Ayesha chips a golf ball up a straight hillside. Relative to the point where the ball is struck, the path of the ball is modelled by

y = 2 + 0.8x − 0.05x2

where y m is the height and x m is the horizontal distance. The hillside is modelled by the line y = 0.2x

  1. Find the horizontal distance travelled by the ball before it lands on the hillside. Give your answer to 3 significant figures.
  2. Show that the vertical height of the ball above the hillside is h = 2 + 0.6x − 0.05x2 metres, and hence find the greatest vertical height of the ball above the hillside.
  3. Give one limitation of the model.
7 marks
Show answer
a) 14.7 m b) 3.8 m c) for example: the ball is modelled as a particle, or air resistance and spin are ignored

Every question here is original and written by Robinson Tuition. It follows the Edexcel AS specification and suits AQA and OCR AS maths too; this is not an exam-board paper.

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