Post on 05-Jan-2016
description
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