3rd Year Homework 3

Homework 3: To be done neatly in the front of your books for first lesson back after Easter
TOTAL 30 marks

1. Solve this equation \[\frac{2x+1}{3}-\frac{2(4-3x)}{7}=x\]

[4 marks]

2. Find
a. The length of AV
b. the angle between AV and the base ABCD

[5 marks]

3. Rob puts £200 in a bank account with interest rate r for 8 years? When he checks his balance it is £446.31. What was the interest rate (r)?

[4 marks]

4. By showing your working and not using a calculator, find the value of $ \left( \frac {9}{4} \right)^{-\frac{3}{2}}$

[2 marks]

5. Find the perimeter of a sector of a circle with radius 4cm and angle 52 degrees to 2 significant figures

[3 marks]

6. Find the gradient of this line: $5y+3x=2$ and use this value to find the equation of a line perpendicular to this line which passes through (0,5)

[4 marks]

7. Solve the simultaneous equations: \[3x+2y=-8\\-5x+4y=17\]

[3 marks]

8. HARD: A ship sails 9 km on a bearing of 092 degrees and then 10 km on a bearing of 115 degrees. Draw a diagram and work out how far it must travel to return to the starting position. (HINT: one way to do this would be take a look at the Cosine Rule)

[5 marks]