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2 marksFunctions

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 2(a)(ii)

This section covers Module 1.1. Answer both questions. The function, f, is given by f(x) = 2x² + 11x + 3.

Sketch the graph of f(x).

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 2(a)(i)Express f(x) in the form p(x-q)² + r, where p, q, r ∈ R.[3 marks]
  2. 2(a)(iii)Hence, or otherwise, find the turning point of the graph and determine whether it is a maximum or a minimum.[3 marks]
  3. 2(b)Given that δ is an acute angle such that cos δ = (1/4)x, find the expression for sin 2δ in terms of x.[4 marks]
  4. 2(c)(i)Express cot θ and cosec θ in terms of x and y.[3 marks]
  5. 2(c)(ii)Find an equation connecting x and y.[2 marks]
  6. 2(d)(i)Sketch, in separate diagrams, the graphs of y = sin x and y = cos x for -2π ≤ x ≤ 2π.[6 marks]
  7. 2(d)(ii)State clearly the transformation which maps y = cos x onto y = sin x.[2 marks]

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