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2 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 2 · Question 4(a)(ii)b)

Two diagrams are shown. The first is a sector OABC of a circle with centre O and radius 7 cm, where angle AOC measures π/3 radians. The second is a right circular cone with vertex O and circular base of radius r cm, formed when the sector OABC is folded so that OA coincides with OC.

If h cm is the height of the cone, then the exact value of h is (7√35)/6.

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Other parts of this question

  1. 4(a)(i)Express the arc length ABC in terms of π.[1 mark]
  2. 4(a)(ii)a)Hence, show that r = 7/6.[3 marks]
  3. 4(b)(i)Show that cos 3θ = 4cos³θ - 3cosθ.[5 marks]
  4. 4(b)(ii)By using the identity in (b)(i) above, find the value of θ, 0 ≤ θ ≤ π/2, such that a and b are perpendicular.[5 marks]
  5. 4(c)Find the modulus of the complex number z = (25(2+3i))/(4+3i).[4 marks]

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