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3 marksNumbers

CAPE Integrated Mathematics · 2017 · Paper 2 · Question 1(a)

A complex number is given by Z = \frac{\sqrt{3}}{4} - \frac{1}{4}i. Find the modulus of Z.

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  1. 1(b)(i)Determine the equation of the straight line which passes through the point (1, 5) and is perpendicular to the line 3x + y = 4.[4 marks]
  2. 1(b)(ii)The line y = x + 6 meets the curve y = x^2 + x + 2 at the points P and Q. Determine the coordinates of points P and Q.[5 marks]
  3. 1(c)Obtain the binomial expansion of (1 + 2x)^3.[5 marks]
  4. 1(d)Determine the range of values of x for which |2x + 5| \le 3.[4 marks]
  5. 1(e)Solve the equation tan(\theta + \frac{\pi}{3}) = 1, for 0 < \theta < \pi.[4 marks]

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