Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
The point $A$ has coordinates $(a,2)$ and the point $B$ has coordinates $(6, b)$. The line $y + 4x = 11$ is the perpendicular bisector of $AB$. Find $a$ and $b$.
$a = -2$ and $b = 4$
Q2
Answer
Find the coordinates of the minimum point of the graph $$y = (x+2)(x^2 - 3x + 5)$$ justifying that it is a minimum.
$(1, 9)$
Q3
Answer
  1. Express $4x^2 + 12x - 3$ in the form $a(x+p)^2 + q$.
  2. Hence solve $4x^2 + 12x - 3 = 0$ giving your answers in surd form.
  3. The equation $4x^2 + 12x - k = 0$ has equal roots. Find $k$.
  1. $4\left(x+\frac{3}{2}\right)^2 - 12$
  2. $-\dfrac{3}{2} \pm \sqrt{3}$
  3. $-9$
Q4
Answer
Express the following in the form $8^p$
  1. $\sqrt{8}$
  2. $\dfrac{1}{64}$
  3. $2^6 \times 4$
  1. $8^{\frac{1}{2}}$
  2. $8^{-2}$
  3. $8^{\frac{8}{3}}$
Q5
Answer
Prove by exhaustion that if $n$ is a prime number greater than 5, then $n^4$ ends in a $1$.
All primes larger than 5 end in $1, 3, 7, 9$. All end in $1$ when raised to power of $4$.