3rd Year Homework 1

Homework 1: To be done neatly in the front of your books for Monday 24th March
TOTAL 28 marks

1. Solve this equation

$$\frac{x+1}{5}-\frac{2(3-x)}{4}=1$$

[4 marks]

2. A 3m ladder is leaning up a wall at an angle to the ground of $60^o$. How far up the wall can it reach?

[3 marks]

3. Pete decided to buy a new car. After 4 years depreciation at 20% from new, Pete decides to sell the car. It does not sell and so Pete reduces the price by 15%. The car still does not sell and he reduces it by a further 7% to £3,200. It sells after 3 days. What did the car cost new?

[5 marks]

4. Expand $(3x-2)(4x+3)$

[2 marks]

5. Factorise $6x^2-11x-35$

[3 marks]

6. Find the gradient of this line: $3x-2y=7$ and use this value to find the equation of a line parallel to this line which passes through (0,4)

[4 marks]

7. In a triangle ABC, AB=10cm, BC=6cm and angle C is a right angle. Find angle A.

[3 marks]

8. A ship sails 9.2km from a lighthouse on a bearing of $135^o$ and arrives due east of a pier which happens to be due south of the lighthouse. Draw a diagram and calculate how far east of the pier the boat is.

[4 marks]