Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
  1. Express $x^2 + 3x$ in the form $(x+a)^2 + b$
  2. Express $y^2 - 4y - \dfrac{11}{4}$ in the form $(y + p)^2 + q$
  1. $\left(x+\frac{3}{2}\right)^2 - \frac{9}{4}$
  2. $(y - 2)^2 - \frac{27}{4}$
Q2
Answer
  1. Solve the simultaneous equations $$y = x^2 - 5x + 15$$ $$5x - y = 10$$
  2. What can you deduce about the line $5x - y = 10$ and the curve $y = x^2 - 5x + 15$
  3. Hence find the equation of the normal to the curve $y = x^2 - 5x + 15$ at the point $(5,15)$ giving your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers
  1. $x = 5$ and $y = 15$
  2. The line is tangent to the curve
  3. $x + 5y = 80$
Q3
Answer
Solve the inequalities
  1. $3(x-5) \leq 24$
  2. $5x^2 - 2 > 78$
  1. $x \leq 13$
  2. $x > 4$, $x < -4$
Q4
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. $5\sqrt{2} + 2\sqrt{3}$
Q5
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.