Q1
Answer
Relative to a fixed origin, the points $A$, $B$ and $C$ have position vectors $3\mathbf{i} + \mathbf{j}$, $\mathbf{i} - 2\mathbf{j}$ and $2\mathbf{i} - 5\mathbf{j}$ respectively.
  1. Find the area of triangle $ABC$.
  2. $D$ is a point such that $ABCD$ is a parallelogram. Find the position vector of $D$.
  1. $4.5$
  2. $4\mathbf{i} - 2\mathbf{j}$
Q2
Answer
The first three terms of a geometric sequence are $k - 2$, $2k+2$, and $2k^2 - 2$. Find the first term and the common ratio of the sequence.
$a = 3$ and $r = 4$
Q3
Answer
Find the first three terms, in ascending powers of $x$, in the expansion of:
  1. $(2 + x)^6$
  2. $(2 + x)^{-6}$
  1. $64 + 192x + 240x^2$
  2. $\dfrac{1}{64} - \dfrac{3}{64}x + \dfrac{21}{256}x^2$