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3 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 3(a)(i)

This section covers Module 1.2. Answer both questions. A pair of simultaneous equations is given by 2x + py = 13 and px + 32y = 52, where p ∈ R. Find the value(s) of p for which the system of equations above has a unique solution.

Find the value(s) of p for which the system of equations above has a unique solution.

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Other parts of this question

  1. 3(a)(ii)Find the value(s) of p for which the system of equations above has an infinite number of solutions.[3 marks]
  2. 3(a)(iii)Find the value(s) of p for which the system of equations above has no solution.[3 marks]
  3. 3(b)(i)Solve the following equations for 0 ≤ x ≤ π/2: 6 sin²x - cos x - 4 = 0.[5 marks]
  4. 3(b)(ii)Solve the following equations for 0 ≤ x ≤ π/2: √3 sin x + cos x = 2.[5 marks]
  5. 3(c)Show that, for A ≠ π/2, sec A – tan A = tan (π/4 - A/2).[6 marks]

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