Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
Find the equation of the line parallel to $x + 2y = 4$ which passes through the point $(6,5)$. Give your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers.
$x + 2y - 16 = 0$
Q2
Answer
The points $A, B, C$ have coordinates $(-2,0), (0,-1), (2,3)$ respectively.
  1. Find the equation of the line through $C$ which is parallel to $AB$, giving your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers.
  2. Show that $ABC$ is a right angled triangle.
  3. Find the equation of the circle which passes through the points $A$, $B$ and $C$.
  1. $x + 2y - 8 = 0$
  2. Gradient of $BC$ is $2$
  3. $x^2 + y^2 - 3y - 4 = 0$
Q3
Answer
  1. Find the first four terms in ascending powers of $x$ in the expansion of $(2-x)^7$
  2. Hence find the coefficient of $y^6$ in the expansion of $\left(2 - \dfrac{y^2}{4}\right)^7$
  1. $128 - 448x + 672x^2 - 560x^3$
  2. $-\dfrac{35}{4}$
Q4
Answer
Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ for the following
  1. $y = \frac{1}{2}x^4 - 3x$
  2. $y = (2x^2 + 3)(x+1)$
  3. $y = \sqrt[5]{x}$
  1. $2x^3 - 3$
  2. $6x^2 + 4x + 3$
  3. $\dfrac{1}{5}x^{-\frac{4}{5}}$