Q1
Answer
The diagram shows triangle $ABC$ with $AC = 8x-3$, $BC = 4x-1$, $\angle ABC = 120^{\circ}$ and $\angle ACB = 15^{\circ}$.
  1. Show that the exact value of $x$ is $\dfrac{9+\sqrt{6}}{20}$.
  2. Find the area of triangle $ABC$, giving your answer to 2 decimal places.
  1. Sine rule: $\dfrac{8x-3}{\sin 120} = \dfrac{4x-1}{\sin 45}$ and simplify
  2. $0.26$
Q2
Answer
A curve $C$ has equation $y = x^3 - x^2 - x + 2$ The point $P$ has $x$ coordinate 2.
  1. Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$.
  2. The normal to $C$ at $P$ intersects the $x$ axis at $A$. Find the coordinates of $A$.
  1. $3x^2 - 2x - 1$
  2. $(30,0)$
Q3
Answer
  1. Find the first four terms, in ascending powers of $x$, of the binomial expansion of $$(2+px)^9$$
  2. Given that the coefficient of the $x^3$ term is $-84$, find the value of $p$.
  1. $512 + 2304px + 4608p^2x^2 + 5376p^3x^3$
  2. $-\dfrac{1}{4}$
Q4
Answer
Find the set of values of $x$ for which $x^3-4x^2-35x+20$ is increasing.
$x < -\dfrac{8}{3}$ or $x > 5$