DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
ALI USAMA
19 OAB is a triangle.
→
→
OA = a
OB = b
The point C lies on OA such that OC : CA = 1 : 2
The point D lies on OB such that OD : DB = 1 : 2
Using a vector method, prove that ABDC is a trapezium.
(Total for Question 19 is 3 marks)
*P62657A02124*
ALI USAMA
21
Turn over
ALI USAMA
Finty takes at random 2 counters from the bag.
The probability that Finty takes 2 blue counters from the bag is
Work out the value of X.
Show clear algebraic working.
3
8
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
There are 4 more blue counters than red counters in the bag.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
There are only red counters and blue counters in the bag.
.......................................................
(Total for Question 20 is 5 marks)
22
*P62657A02224*
DO NOT WRITE IN THIS AREA
20 A bag contains X counters.
ALI USAMA
ALI USAMA
25
B
Diagram NOT
accurately drawn
M
P
N
A
O
OAN, OMB, APB and MPN are straight lines.
OA : AN = 1 : 4
OM : MB = 1 : 1
→
OA = 2a
→
OB = 2b
By using a vector method, find the ratio AP : PB
Give your answer in its simplest form.
24
*P64693A02428*
ALI USAMA
ALI USAMA
.......................................................
(Total for Question 25 is 5 marks)
Turn over for Question 26
*P64693A02528*
ALI USAMA
25
Turn over
ALI USAMA
21
P
A
Diagram NOT
accurately drawn
Q
4a
O
6b
B
OAB is a triangle.
Q is the point on AB such that OQP is a straight line.
→
→
→
OA = 4a OB = 6b AP = 2a + 8b
Using a vector method, find the ratio AQ : QB
AQ : QB = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question 21 is 5 marks)
*P68798RA02124*
ALI USAMA
21
Turn over
ALI USAMA
25 ABCD is a parallelogram and ADM is a straight line.
B
C
Diagram NOT
accurately drawn
K
L
A
M
D
→
→
→ 1
AB = a BC = b DM = b
2
K is the point on AB such that AK : AB = λ : 1
L is the point on CD such that CL : CD = μ : 1
KLM is a straight line.
Given that λ : μ = 1 : 2
use a vector method to find the value of λ and the value of μ
λ = .......................................................
μ = .......................................................
(Total for Question 25 is 5 marks)
TOTAL FOR PAPER IS 100 MARKS
28
*P68791A02828*
ALI USAMA
ALI USAMA
3a
C
P
2a − 2b
O
4b
B
OACB is a quadrilateral.
= 3a = 4b = 2a − 2b
(a) (i) Find the vector
in terms of a and b
Simplify your answer.
= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
(ii) Find the vector
in terms of a and b
= ......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
20
*P73469A02024*
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA
Diagram NOT
accurately drawn
A
ALI USAMA

DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA
22
ALI USAMA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREADO NOT WRITE IN THIS AREA
The point P lies on AB and on OC
(b) Using a vector method, find the ratio AP : PB
Show your working clearly.
......................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 22 is 5 marks)

*P73469A02124*
ALI USAMA
21
Turn over