3rd Year Homework 4

Homework 4: To be done neatly in the front of your books for first lesson back after bank holiday
TOTAL 34 marks

1. Solve this equation \[\frac{3x-2}{5}-\frac{5(-4-2x)}{3}=2x\]

[4 marks]

2. A cuboid has a bottom face with sides 5 and 8 cm with a height of 12cm. Find the length of the longest line between 2 vertices. Also find the angle between this line and the lower face.

[5 marks]

3. A car bought for £9000 depreciates at rate r% per year. If it is worth £5300 after 3 years what is r?

[4 marks]

4. By showing your working and not using a calculator, find the value of $ \left( \frac {27}{64} \right)^{-\frac{2}{3}}$

[2 marks]

5. Find the area of a sector of a circle with radius 10cm and angle 272 degrees to 2 significant figures

[3 marks]

6. Find the gradient of this line: $4y+7x=3$ and use this value to find the equation of a line perpendicular to this line which passes through (0,-1)

[4 marks]

7. Solve the simultaneous equations: \[4x+y=-1\\-6x-3y=4.5\]

[3 marks]

8. HARD: A ship sails 7 km on a bearing of 011 degrees and then 17 km on a bearing of 177 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]

9. Find coordinates of the image of the point (-3,2) after:

1. A reflection in the line y=-x
2. A rotation 90 degrees clockwise about (0,-1)
3. A translation $\left(\begin{array} \left \\ 4 \\ -2 \end{array}\right)$
4. An enlargement scale factor 2, centre (0,1)

[4 marks]