Sec 4 Integrated Mathematics: Revision Worksheet (6) – Probability & Vectors
Name: __________________________ Sec 4 (
1
)
Date: ___________
 –ln 2 
The position vectors of the points A, B and C relative to an origin O are 
,
 2 
 ln128 
ln 4 
and


 −p 
 7 


respectively. Determine the value of p for which A, B and C are collinear.
2


ABCDEFGH is a regular octagon and AB = p and BC = q . Show that
   
AE + BH + CG + DF = 2 2 + 2 (q − 2p)
(
3
4
)



 



Given that=
OA a=
, OB b=
, OB 2 BC=
, AD 2OA and AB = 2 AX .
(i)
 

Express AB, OX and CD in terms of a and b ,
(ii)

Y is a point on CD such that CY : YD = 1: 2 . Express OY in terms of a and b ,
(ii)
Hence write down two facts about O, X and Y .

  −11

 8    6 
,
,
express
as
a
column
vector.
It
is
given
that
BC
=
CD
=
AC
 
 . Find the

 −4 
 4
 h 
Given that AB = 
two possible values of h which will make ABCD a trapezium.
5
A box contains 9 apples of which x are red and the rest are green. Two apples are taken one at a time
from the box.
(a)
Write down the probability, in terms of x , that the two apples are red.
(b)
Given the probability of choosing two apples which are of the same colour is
1
, form an
2
equation in x and show that it reduces to x 2 − 9 x + 18 =
0 . Hence find two possible values of x .
6
May either walks or cycles to school each morning. The probability that she walks is
walks, the probability that she is late is
1
4
. When she cycles, the probability that she is late is . Find
9
9
the probability that, on a particular morning.
(a)
Amy walks and is not late,
2
. When she
3
(b)
she is late.