EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Solving Quadratic Equations 1
Solving quadratic equations 1 · Equations and inequalities · Lesson 2 of 7 · 17 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 NON-CALCULATOR (3 marks)
Solve x² + 5x + 6 = 0.
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(Total for Question 1 = 3 marks)
Question 2 NON-CALCULATOR (3 marks)
Solve x² − 2x − 15 = 0.
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(Total for Question 2 = 3 marks)
Question 3 NON-CALCULATOR (2 marks)
Solve x² − 49 = 0.
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(Total for Question 3 = 2 marks)
Question 4 NON-CALCULATOR (2 marks)
Solve x² − 7x = 0.
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(Total for Question 4 = 2 marks)
Question 5 NON-CALCULATOR (3 marks)
Solve x² = 3x + 10.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (4 marks)
The diagram shows a rectangle. The length is (x + 3) cm and the width is x cm. The area of the rectangle is 40 cm². Work out the value of x.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 17 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
(x + 2)(x + 3) = 0, so x = −2 or x = −3.
• Correct factorisation M1
• One solution A1
• Both solutions A1
Question 2 (3 marks)
(x − 5)(x + 3) = 0, so x = 5 or x = −3.
• Correct factorisation M1
• One solution A1
• Both solutions A1
Question 3 (2 marks)
(x − 7)(x + 7) = 0, so x = 7 or x = −7.
• Factorising or x² = 49 M1
• x = 7 and x = −7 A1
Question 4 (2 marks)
x(x − 7) = 0, so x = 0 or x = 7.
• x(x − 7) M1
• x = 0 and x = 7 A1
Question 5 (3 marks)
x² − 3x − 10 = 0, so (x − 5)(x + 2) = 0 and x = 5 or x = −2.
• Rearranging to zero M1
• Correct factorisation M1
• x = 5 and x = −2 A1
Question 6 (4 marks)
x(x + 3) = 40, so x² + 3x − 40 = 0 and (x + 8)(x − 5) = 0. x = 5, since a length cannot be negative.
• Forming the equation M1
• Rearranging to zero M1
• Factorising M1
• x = 5 A1