y = x(x + 4)(x – 2)
The curve C crosses the x-axis at the origin O and at the points A and B.
(a) Write down the x-coordinates of the points A and B.
The finite region, shown shaded in Figure 3, is bounded by the curve C and the x-axis.
(b) Use integration to find the total area of the finite region shown shaded in Figure 3.
(ii) Given that loga y + 3loga 2 = 5
express y in terms of a.
Give your answer in its simplest form.
tan(x – 40°) = 1.5, giving your answers to 1 decimal place.
(ii) (a) Show that the equation
sinθtanθ = 3cosθ + 2
can be written in the form
4cos2θ + 2cosθ – 1 = 0
(b) Hence solve, for 0° < x < 360°,
sinθtanθ = 3cosθ + 2
showing each stage of your working.
Use calculus
(a) to find the coordinates of P,
(b) to determine the nature of the stationary point P.
(a) Write down an equation for the circle C, that is shown in Figure 4.
A line through the point P(8, – 7) is a tangent to the circle C at the point T.
(b) Find the length of PT.
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