Course Revision Set1

 

 

 

1.                   A car hire company has depots in Glasgow and Edinburgh.  The company has a total of 3000 cars.

Each week 80% of the cars hired from Glasgow are returned there, and the remainder are returned to the Edinburgh depot.  Of the cars hired from Edinburgh, 40% are returned to Glasgow and the rest to their place of hire.

 

In the long run, what is the optimum number of cars for the company to hold in each depot?

 

 

2.                   Show that the points A(-1,2,7), B(1,-2,1) and C(2,-4,4) are collinear, and find the ratio AB:BC

 

 

 

3                     A circle has centre (3,-3) and radius .

 

Prove that the line          y =        is a tangent, and find the point of contact.

 

 

 

4.         Sketch the graph of        y = x3 + x2 – x + 2          

 

            This graph crosses the x-axis at A, and crosses the y-axis at B.  Find the equation of the tangents to the graph at A and B.

Prove that the point of intersection of these two tangents is at the point P()

 

Find the size of the angle APB.

 

 

 

5.                   The points A(-4,-2), B(-4,4), C(6,4) and D(6,-2) form a rectangle.  Given that the four points lie on the circumference of a circle, find the equation of the circle. 

(hint: by making a sketch and drawing the diagonals – remember that the diagonals of a rectangle bisect one another – consider the angles in a semi circle)