5.1 Homework Due Tue 15.9.15

To be done neatly in the front of your books
TOTAL 20 marks

1. The plots shows the curve $y=-\frac{1}{3}x^2+3x+1$

   

   1. Use the formula to solve the equation $-\frac{1}{3}x^2+3x+1=0$ giving your answers to 2 d.p.
   2. Use the formula to find the solutions to 2 significant figures $-\frac{1}{3}x^2+3x+1=3$
   3. $-\frac{1}{3}x^2+3x+1=k$ has no solutions, where k is an integer. Use the plot above to find the minimum value of k

   [6 marks]

2. By factorising only, solve: $12x^2+23x-24=0$

   [3 marks]

3. The volume of a balloon is directly proportional to the cube of its radius. A balloon of radius 5cm has volume $525cm^3$:
   1. Find a formula for v in terms of r
   2. Find the volume of the balloon when the radius is 15cm
   3. What is the radius of a balloon with volume $2560cm^3$?

   [4 marks]

4. Find the image of the point (4, -5) under the transformation represented by M $M = \begin{pmatrix} 3 & -2 \\ 1 & -1 \end{pmatrix}$

   [2 marks]

5. Find the 2x2 matrix which represents a rotation 90 degrees anticlockwise around the origin.

   [2 marks]

6. A line passes through the points A(-1,5) and B(4, -5). By first finding the gradient of AB, write down the equation of the line in the form y=mx+c

   [3 marks]