Lemmara logoLemmaraWorked solution

WMA11/01 Oct 2020, Question 2: The Quadratic Formula and Completing the Square

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

For f(x) = 3 + 12x − 2x², complete the square and then find the area of triangle PQR formed by the curve y = f(x) − 7 crossing the axes.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Rewrite f(x) = 3 + 12x − 2x² as a − b(x + c)², finding integer values of a, b and c.

  1. 1f(x) = 3 − 2(x² − 6x)
  2. 2= 3 − 2[(x − 3)² − 9]
  3. 3= 3 + 18 − 2(x − 3)²
  4. 4= 21 − 2(x − 3)²

Answerf(x) = 21 − 2(x − 3)², so a = 21, b = 2, c = −3

Part (b) · 4 marks

For y = f(x) − 7, find where it meets the x-axis at P and Q and the y-axis at R, then find the area of triangle PQR as m√n.

  1. 1y = f(x) − 7 = −4 + 12x − 2x², so R = (0, −4)
  2. 2Solve 14 − 2(x − 3)² = 0: (x − 3)² = 7
  3. 3x = 3 ± √7, so PQ = 2√7
  4. 4Area = (1/2) × 2√7 × 4 = 4√7

Answer4√7

Stuck on a step? Read the free lesson: The Quadratic Formula and Completing the Square

Practise more the quadratic formula and completing the square questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on the quadratic formula and completing the square

Also searched as: WMA11 October 2020 · WMA11/01 · wma11 oct20 · IAS Maths Pure Mathematics 1 October 2020 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.