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CAPE Pure Mathematics Unit 1 · 2022 · Paper 2 · Question 4(b)(ii)

Determine the angle between the vector 3\mathbf{i} - 2\mathbf{j} and the x-axis.

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  1. 4(a)(i)A circle has equation x^2 + y^2 - 10x + 4y - 5 = 0. Determine the centre and radius of the circle.[4 marks]
  2. 4(a)(ii)Determine the equation of the tangent to the circle at the point (2, 3).[4 marks]
  3. 4(b)(i)Determine the equation of the plane that passes through the point (0, 2, -2) and which is perpendicular to the vector…[3 marks]
  4. 4(c)The parametric equations of a line are given as x = 2 + 5\lambda, y = -3 + 4\lambda, z = 4 - 2\lambda. Determine the coordinates of the point where the…[5 marks]
  5. 4(d)A point P(x, y) moves in the xy plane such that it is the same distance from the point A(1, 2) as it is from the line x = 3. Determine the equation of…[6 marks]

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