4.2 Homework Answers Due 28 Sept 15

Complete neatly in the front of your books. Calculator allowed but working must be shown. Total: 21 marks

1. A teacher has a 3% pay increase to £18,200. What was his previous salary? \[18200 \div 1.03 = 17669.90\]

   [3 marks]

2. £3000 is deposited in a bank account with an interest rate of 3.1% p.a., what will the balance be after 8 years? \[3000 \times 1.031^8 = 3829.93 \]

   [2 marks]

3. Without a calculator, find the value of \[ \frac{5.6 \times 10^{-5}}{8 \times 10^{-8}} = 0.7 \times 10^3 = 7 \times 10^2 \] Give your answer in standard form.

   [2 marks]

4. Solve \[ \text{Start by multiplying both sides by 4} \\ \frac{3x-2}{2}=\frac{4-x}{4} \\ 2(3x-2)=4-x \\ 6x-4=4-x \\ 7x=8 \\ x = \frac{8}{7} \]

   [3 marks]

5. Solve \[ 3(2x+3)-4(5-3x)=1 \\ 6x+9-20+12x=1 \\ 18x-11=1 \\ 18x=12 \\ x=\frac{2}{3} \]

   [3 marks]

6. Find the gradient of the line between A(-1,4) and B(3,-8) and hence find the equation of the line \[ \text{Gradient is} -3 \\ y=-3x+c \\ 4=3 +c \\ c=1 \\ \therefore y=1-3x \]

   [4 marks]

7. Pete's son is a third of his age. 8 years ago, Pete was four times his son's age. How old is Pete today? Show your method clearly. Guesses get nothing!! \[ \begin{array}{|c|c|c|} \hline \ & Pete & Son \\ \hline \ \text{Now} & x & \frac{x}{3} \\ \hline \ \text{8 yrs ago} & x-8 & \frac{x}{3} - 8 \\ \hline \end{array} \\ \text{Let Pete's age be }x \\x-8=4(\frac{x}{3} - 8) \\ x-8 = \frac{4x}{3} - 32 \\ \frac{x}{3} = 24 \\ x=72 \text{ years old}\]

   [4 marks]