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WMA11/01 Oct 2022, Question 7: Harder Inequalities and Curved Regions

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Use the graph of y = f(x) with marked points P(−4, 6), Q(−1, 6), R(2, 6), S(3, 6) to solve inequality and transformation questions.

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

Part (a) · 3 marks

From Figure 1, find the x-values where the curve lies below y = 6.

  1. 1The curve is below y = 6 to the left of P, between Q and R, and to the right of S
  2. 2x < −4, −1 < x < 2, x > 3

Answerx < −4, −1 < x < 2, x > 3

Part (b) · 1 mark

Give the largest x satisfying f(2x) = 6.

  1. 1Largest solution of f(u) = 6 is u = 3
  2. 22x = 3 ⇒ x = 3/2

Answerx = 3/2

Part (ci) · 3 marks

Sketch y = f(−x) and state the images of P, Q, R and S.

  1. 1y = f(−x) is a reflection in the y-axis: (x, y) → (−x, y)
  2. 2P(−4, 6) → (4, 6), Q(−1, 6) → (1, 6)
  3. 3R(2, 6) → (−2, 6), S(3, 6) → (−3, 6)

AnswerReflection of y = f(x) in the y-axis, with P → (4, 6), Q → (1, 6), R → (−2, 6), S → (−3, 6); the small maximum is now on the left between −3 and −2, the high maximum on the right between 1 and 4

Part (cii) · 1 mark

Using your sketch, find x < 0 where f(−x) ≥ 6.

  1. 1f(−x) ≥ 6 on the reflected curve where −3 ≤ x ≤ −2 or 1 ≤ x ≤ 4
  2. 2With x < 0: −3 ≤ x ≤ −2

Answer−3 ≤ x ≤ −2

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