A curve is defined by the parametric equations x = t2, y = 2t - t3, for t ≠ 0.
(a) Find dy/dx in terms of t.
(b) Find the exact coordinates of the points where the tangent to the curve is horizontal.
From Paper 1: Pure Mathematics
149 marks
A circle C has centre (2, -1) and passes through the point (5, 3).
(a) Find an equation for C.
(b) Show that the point (1, 6) lies outside C.
(c) The line y = x + k is a tangent to C. Find the two possible exact values of k.
From Paper 3: Pure and Statistics
911 marks
(a) Find the exact value of ∫0π/2 sin2 x dx.
(b) Find ∫ 6x/(3x2 + 1) dx.
(c) A curve is given parametrically by x = t2, y = t3 for t ≥ 0. Find the area of the region bounded by the curve, the x-axis and the line x = 4.
Score 0 / 26 · 0 of 3 marked
This paper is written by Plasmo in the style of the AQA A-Level Maths exam. It is not a past paper and is not produced or endorsed by the exam board.