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1. Prior Knowledge
2 questions
2. Worked Example
Worked example
3. Fluency
3 questions
4. Standard Practice
3 questions
5. Problem Solving
2 questions
GCSE • Year 10 • Edexcel • Mixed
Algebra • Quadratics • Completing the Square
Prior Knowledge
[2 marks]
- 1.
Expand (x + 2)(x + 3).
(1)Answer: x² + 5x + 6 - 2.
Expand (x - 4)(x + 1).
(1)Answer: x² - 3x - 4
Fluency
[3 marks]
- 3.
Rewrite x² + 6x + 5 in completed square form.
(1)Answer: (x + 3)² - 4 - 4.
Rewrite x² - 8x + 3 in completed square form.
(1)Answer: (x - 4)² - 13
- 5.
Rewrite x² + 10x + 7 in completed square form.
(1)Answer: (x + 5)² - 18
Standard Practice
[6 marks]
- 6.
Solve x² + 6x + 2 = 0 by completing the square.
(2)Answer: x = -3 ± √7 - 7.
Solve x² - 4x - 1 = 0 by completing the square.
(2)Answer: x = 2 ± √5
- 8.
Find the turning point of y = x² + 4x + 1.
(2)Answer: (-2, -3)
Problem Solving
[6 marks]
- 9.
Find the minimum value of y = x² - 6x + 11 by completing the square.
(3)Answer: Minimum value is 2
- 10.
A quadratic is given by y = x² + 8x + 10. Find its turning point.
(3)Answer: (-4, -6)