Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
Solve $3x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 = 0$
$x = \dfrac{8}{27}, -1$
Q2
Answer
The line with equation $3x + 4y - 10 = 0$ passes through the point $A(2,1)$ and $B(10, k)$.
  1. Find $k$.
  2. Calculate the length of $AB$.
  1. $k = -5$
  2. $10$
Q3
Answer
For the curve $y = x^3 + x^2 - x + 3$,
  1. Find the coordinates of the stationary points
  2. Determine whether each is a minimum or a maximum
  3. State the set of values of $x$ for which the curve is decreasing
  1. $\left(\frac{1}{3}, \frac{76}{27}\right)$ and $(-1,4)$
  2. min, max
  3. $-1 < x < \frac{1}{3}$
Q4
Answer
Prove that in a right angled triangle, it is not possible for all the side lengths to be odd.
Use Pythagoras with $2n + 1$ and $2m+1$ to get an even number