EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Solving Quadratic Equations 2
Solving quadratic equations 2 · Equations and inequalities · Lesson 3 of 7 · 20 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 2x² + 7x + 3 = 0.
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(Total for Question 1 = 3 marks)
Question 2 NON-CALCULATOR (3 marks)
Solve 3x² − 10x + 8 = 0.
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(Total for Question 2 = 3 marks)
Question 3 NON-CALCULATOR (4 marks)
Solve 2x² − 5x − 12 = 0.
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(Total for Question 3 = 4 marks)
Question 4 CALCULATOR (3 marks)
Solve x² + 3x − 5 = 0. Give your solutions correct to 2 decimal places.
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(Total for Question 4 = 3 marks)
Question 5 CALCULATOR (3 marks)
Solve 3x² − 4x − 2 = 0. Give your solutions correct to 2 decimal places.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (4 marks)
Solve x² − 6x + 2 = 0. Give your answers in the form p ± √q, where p and q are integers.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 20 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
(2x + 1)(x + 3) = 0, so x = −½ or x = −3.
• Correct factorisation M1
• One solution A1
• Both solutions A1
Question 2 (3 marks)
(3x − 4)(x − 2) = 0, so x = 4/3 or x = 2.
• Correct factorisation M1
• One solution A1
• Both solutions A1
Question 3 (4 marks)
(2x + 3)(x − 4) = 0, so x = −3/2 or x = 4.
• 2x² − 8x + 3x − 12 M1
• (2x + 3)(x − 4) M1
• One solution A1
• Both solutions A1
Question 4 (3 marks)
x = (−3 ± √(9 + 20))/2 = (−3 ± √29)/2, so x = 1.19 or x = −4.19.
• Correct substitution into the formula M1
• (−3 ± √29)/2 A1
• 1.19 and −4.19 A1
Question 5 (3 marks)
x = (4 ± √(16 + 24))/6 = (4 ± √40)/6, so x = 1.72 or x = −0.39.
• Correct substitution M1
• (4 ± √40)/6 A1
• 1.72 and −0.39 A1
Question 6 (4 marks)
x = (6 ± √(36 − 8))/2 = (6 ± √28)/2 = (6 ± 2√7)/2 = 3 ± √7.
• Correct substitution M1
• √28 A1
• 2√7 M1
• 3 ± √7 A1