Q1
Answer
  1. Express $11^{-2}$ as a fraction.
  2. Evaluate $100^{\frac{3}{2}}$.
  3. Express $\sqrt{50} + \dfrac{6}{\sqrt{3}}$ in the form $a\sqrt{2} + b\sqrt{3}$ where $a$ and $b$ are integers.
  1. $\dfrac{1}{121}$
  2. $1000$
  3. $5\sqrt{2} + 2\sqrt{3}$
Q2
Answer
Amy claims that the product of a rational number and an irrational number is irrational.
  1. Write down a rational number for which this is not the case.
  2. Prove that Amy is correct in all other cases
  1. $0$
  2. Use proof by contradiction $\dfrac{a}{b}n = \dfrac{c}{d}$ and $n$ is rational.
Q3
Answer
  1. Solve $x^2 - 8x + 11 = 0$ giving your answers in exact form
  2. Sketch the curve $y = x^2 - 8x + 11$ labelling the coordinates of the points where it crosses the axes
  3. Solve $y - 8\sqrt{y} + 11 = 0$, giving your answers in the form $a \pm b\sqrt{5}$
  1. $4\pm\sqrt{5}$
  2. Correct sketch
  3. $y = 21 \pm 8\sqrt{5}$
Q4
Answer
Solve the inequality $x^2 + 8x + 10 \geq 0$
$x \leq -4 - \sqrt{6}$, $x\geq -4 + \sqrt{6}$