4th Year Homework 1

Homework 1: To be done neatly in the front of your books for Thu 20th 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. Solve these simultaneous equations algebraically:\[3x+2y=1\]\[-2x-y=1\]

[4 marks]

4. If n(E)=20, n(A)=7 and n(B)=17, find n(AnB)

[2 marks]

5. Solve these simultaneous equations algebraically:\[2x+5y=4\]\[3x-5y=2\]

[4 marks]

6. Find the gradient of this line: $3x-2y=7$ and use this value to find the gradient of a line which is perpendicular (at right angles) to this line

[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]