Express $y^2 - 4y - \dfrac{11}{4}$ in the form $(y + p)^2 + q$
$\left(x+\frac{3}{2}\right)^2 - \frac{9}{4}$
$(y - 2)^2 - \frac{27}{4}$
Q2
Answer
Solve the simultaneous equations $$y = x^2 - 5x + 15$$ $$5x - y = 10$$
What can you deduce about the line $5x - y = 10$ and the curve $y = x^2 - 5x + 15$
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
$x = 5$ and $y = 15$
The line is tangent to the curve
$x + 5y = 80$
Q3
Answer
Solve the inequalities
$3(x-5) \leq 24$
$5x^2 - 2 > 78$
$x \leq 13$
$x > 4$, $x < -4$
Q4
Answer
Express $11^{-2}$ as a fraction.
Evaluate $100^{\frac{3}{2}}$.
Express $\sqrt{50} + \dfrac{6}{\sqrt{3}}$ in the form $a\sqrt{2} + b\sqrt{3}$ where $a$ and $b$ are integers.
$\dfrac{1}{121}$
$1000$
$5\sqrt{2} + 2\sqrt{3}$
Q5
Answer
Amy claims that the product of a rational number and an irrational number is irrational.
Write down a rational number for which this is not the case.
Prove that Amy is correct in all other cases
$0$
Use proof by contradiction $\dfrac{a}{b}n = \dfrac{c}{d}$ and $n$ is rational.