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WMA11/01 Oct 2021, Question 3: Harder Inequalities and Curved Regions

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Solve the inequality 3/x > 4, then use the given line gradient 3 and curve y = 2x² − 50, intersecting on the negative x-axis, to define shaded region R with inequalities.

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Part (i) · 3 marks

Solve 3/x > 4 for x.

  1. 1Multiply by x² (positive): 3x > 4x²
  2. 24x² − 3x < 0, so x(4x − 3) < 0
  3. 3Critical values x = 0 and x = 3/4
  4. 4Inside region: 0 < x < 3/4

Answer0 < x < 3/4

Part (ii) · 3 marks

Find the line equation, then give inequalities defining the infinite region R bounded by C and l.

  1. 1C meets the negative x-axis where 2x² − 50 = 0, so x = −5
  2. 2l has gradient 3 through (−5, 0): y = 3(x + 5) = 3x + 15
  3. 3R is above l: y > 3x + 15
  4. 4R is outside (left of) the curve: y < 2x² − 50, with x < −5

Answery < 2x² − 50, y > 3x + 15, x < −5

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Also searched as: WMA11 October 2021 · WMA11/01 · wma11 oct21 · IAS Maths Pure Mathematics 1 October 2021 · question 3.
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