PAPER 1

1. Diagram below shows a parallelogram ABCD with BED as a straight line.

Given that = 6p , = 4q and DE = 2EB, express, in terms of p and q

(a)

(b)

[4 marks]

2. Given that O(0,0), A(-3,4) and B(2, 16), find in terms of the unit vectors, i and j,(a)

(b) the unit vector in the direction of

[4 marks]

3. Given that A(-2, 6), B(4, 2) and C(m, p), find the value of m and of p such that

+ 2 = 10i – 12j.

[4 marks]

4. Diagram below shows vector drawn on a Cartesian plane.

(a) Express in the form

(b) Find the unit vector in the direction of

[3 marks]

5. Diagram below shows a parallelogram, OPQR, drawn on a Cartesian plane.

1

It is given that = 6i + 4j and = - 4i + 5j. Find .

[3 marks]6. Diagram below shows two vectors, and .

Express

(a) in the form

(b) in the form xi + yj

[2 marks]

7. The points P, Q and R are collinear. It is given that = 4a – 2b and

, where k is a constant. Find

(a) the value of k

(b) the unit vector in the direction of

[4 marks]8. Given that and find the possible value (or values) of p for following cases:-

a) are parallel

b)[5 marks]

PAPER 2

1. Give that and , find

(a) the coordinates of A, [2 marks]

2

(b) the unit vector in the direction of , [2 marks]

(c) the value of k, if is parallel to [2 marks]

2. Diagram below shows triangle OAB. The straight line AP intersects the straight line OQ at R. It is given that OP = 1/3 OB, AQ = ¼ AB, and

(a) Express in terms of x and/or y: (i)

(ii)

[4 marks] (b) (i) Given that state in terms of h, x and y.

(ii) Given that state in terms of k, x and y. [2 marks]

(c) Using and from (b), find the value of h and of k. [4 marks]

3. In diagram below, ABCD is a quadrilateral. AED and EFC are straight lines.

3

It is given that 20x, 8y, = 25x – 24y, AE = ¼AD and EF = EC.

(a) Express in terms of x and/or y:

(i)

(ii) [3 marks]

(b) Show that the points B, F and D are collinear. [3 marks]

(c) If | x | = 2 and | y | = 3, find | |. [2 marks]

4. Diagram below shows a trapezium ABCD.

It is given that =2y, = 6x, = and =

(a) Express in terms of x and y [2 marks]

(b) Point F lies inside the trapezium ABCD such that 2 = m , and m is a constant.

(i) Express in terms of m , x and y

(ii) Hence, if the points A, F and C are collinear, find the value of m. [5 marks]

ANSWERS (PAPER 1)

1 a) = −6p + 4q 1 b) = −

= 6p −4q1

=

1

1

2. a)

= 5i + 12j

11

4

b)u

1

1

3. 1

= (-2+2m)i + (-8+2p)j 1m = 6 1p = -2 1

4. a) 1

b) 1

1

5. 1

1

1

6. a)1

b) 1

7. a)

1

3 = m(4)1

1+ k = m(-2)

1

b)

1

8 a)1

1

1

b)1

1

1 (a) 1

A = (-3,-4)1

(b)

1

1

(c)

1

1

2 (a)(i)

1

(ii)

1

1

1

(b) (i) 1

1

(c)

1

1

1

3(a)(i) 1 (ii)

= 24y 1

1

(b)

1

1

1

5

(c)

1 = 104 1

4 (a)

= 5x 1

= 5x + 2y 1

(b) (i)

1

= 4x 1

= 4x + my 1

(ii)

1

Assume A, F, C collinear,

= 4x + my

1

6