6.6 FM Progress Homework due 5.10.15

Total: 25 marks. Show all working out. Those not showing mathematical rigour will be penalised.

1. Factorise fully $6x^2-7x-20$

   [2 marks]

2. Complete the square: $y=5-2x-3x^2$ and use your answer to sketch y, indicating clearly any points where the curve crosses the axes

   [4 marks]

3. Sketch $y=(3-x)(2x+5)^2$ indicating any intersections with the axes

   [4 marks]

4. \[ y^2=x^2+x \\ y=2x+k \\ \]Find the values of k such that the hyperbola and the line do not meet.

   [4 marks]

5. Find the centre and radius of the circle that passes through A(9,3), B(13,-5) and C(-5,-11)

   [5 marks]

6. Solve: \[ \frac{3}{27^{5-x}}=\sqrt{81^{5-2x}} \]

   [3 marks]

7. Simplify as far as possible: \[ \frac{15}{\sqrt 5} - \frac{6}{\sqrt 7 - \sqrt 5} \]

   [3 marks]

   ANSWERS