5.3 Homework 20.11.14

To be done in books neatly showing all working out for Monday 24th Nov. 38 Marks

1. Evaluate:
   1. $4^{-2}$
   2. $\left(\dfrac{8}{27}\right)^{-\dfrac{2}{3}}$
   3. $\left(\dfrac{25}{16}\right)^{-\dfrac{3}{2}}$
   4. $\left(\dfrac{1}{4}\right)^{-\dfrac{1}{2}}$

   [9 marks]

2. Simplify
   1. $2x^3 \times 3x^{-2}$
   2. $8x^{-3} \div 2x^{-\frac{1}{2}}$

   [4 marks]

3. Solve by factorising:
   1. $x^2-9=0$
   2. $x^2+3x=0$
   3. $2x-7x^2=0$
   4. $x^2+3x+2=0$
   5. $x^2-x-12=0$
   6. $6x^2+11x-10=0$

   [12 marks]

4. Solve by using the formula \[ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \]
   1. $x^2-9x-2=0$
   2. $x^2+3x=14$
   3. $2x^2-7x=11$
   4. $4x-5x^2=-11$

   [8 marks]

5. Make y the subject and use the result to find the gradient and intercept \[3x+5y=12\]

   [3 marks]

6. Factorise $2x^2-5x-3$ Help here

   [2 marks]