EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Quadratic equations
Quadratic equations · Equations and graphs · Lesson 3 of 6 · 16 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 SOLVE (2 marks)
Solve x² − 5x + 6 = 0.
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(Total for Question 1 = 2 marks)
Question 2 SOLVE (3 marks)
Solve 2x² + 5x − 3 = 0.
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(Total for Question 2 = 3 marks)
Question 3 SOLVE (3 marks)
Solve x² + 4x − 7 = 0. Give your solutions correct to 2 decimal places.
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(Total for Question 3 = 3 marks)
Question 4 SOLVE (4 marks)
(a) Write x² + 6x − 2 in the form (x + a)² + b. (b) Hence solve x² + 6x − 2 = 0. Give your answers correct to 2 decimal places.
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(Total for Question 4 = 4 marks)
Question 5 USE THE GRAPH (2 marks)
The graph of y = x² − 4x + 1 is shown. Use the graph to find estimates for the solutions of x² − 4x + 1 = 0.
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(Total for Question 5 = 2 marks)
Question 6 SOLVE (2 marks)
Solve x² = 7x.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (2 marks)
(x − 2)(x − 3) = 0, so x = 2 or x = 3.
• (x − 2)(x − 3) M1
• 2 and 3 A1
Question 2 (3 marks)
(2x − 1)(x + 3) = 0, so x = ½ or x = −3.
• Factorises M1
• One correct solution A1
• Both correct A1
Question 3 (3 marks)
x = (−4 ± √44)/2; x = 1.32 or x = −5.32.
• Substitutes into the formula M1
• (−4 ± √44)/2 A1
• 1.32 and −5.32 A1
Question 4 (4 marks)
(a) (x + 3)² − 11. (b) x + 3 = ± √11, so x = 0.32 or x = −6.32.
• a = 3 B1
• b = −11 B1
• x = −3 ± √11 M1
• 0.32 and −6.32 A1
Question 5 (2 marks)
x ≈ 0.3 and x ≈ 3.7. Accept 0.2 to 0.4 and 3.6 to 3.8.
• One correct estimate B1
• Both correct B1
Question 6 (2 marks)
x² − 7x = 0, x(x − 7) = 0, so x = 0 or x = 7.
• x(x − 7) = 0 M1
• 0 and 7 A1