1)
3)
2)
4) Given that 𝑦 = 𝑥 3 − 3𝑥 − 2, determine
i.
ii.
the co-ordinates of the stationary points
the nature of the stationary points
(5 marks)
5) The point P(1, 8) lies on the curve with equation 𝑦 = 2𝑥(𝑥 + 1)2 . Determine the equation of the normal
to the curve at the point P.
(5 marks)
6) Obtain the equation for EACH of the two tangents drawn to the curve 𝑦 = 𝑥 2 at the points where 𝑦 = 16.
(5 marks)
7) Differentiate the following expression with respect to x, simplifying your answer.
(4 marks)
3𝑥 + 4
𝑥−2
8) Prove the following identities
sin 2𝜃
a) tan 𝜃 ≡ 1+cos 2𝜃
b)
c)
sin 2𝐴+sin 𝐴
1+cos 2𝐴+cos 𝐴
1+sin 𝑥
cos 𝑥
+
(4 marks)
≡ tan 𝐴
cos 𝑥
2
≡ cos 𝑥
1+sin 𝑥
(4 marks)
(4 marks)