19902010 CE A.Math Questions
S4 M2 Chapter 3: Binomial Theorem
[10 Q5]
The sum of the coefficients of x and x2 in the expansion of (1 + 4 x) n is 180, where n is a positive
integer.
Find the value of n and the coefficient of x3.
[09 Q11]
20
1
In the binom

1. Express each of the following as a single vector.
(a)
BC AB
(b)
AC AB
(a)
BC AB AB BC
AC
(b)
AC AB AC BA
BA AC
BC
2. Express each of the following as a single vector.
(a)
PQ QR RS
(b)
PR SR QR SQ
(a)
PQ QR RS PR RS
PS
PR SR QR SQ PR SR RQ QS
(b)
P

7
y
3 7 8
z
1. It is given that A =
2 x 5 a nd B = 2 2 x 1 5 . If A = B , find the values of x , y a nd z .
Consider the definition of equality of two matrices,
x = 2 x 1 . (1)
y = 8 . (2)
z = 3 . (3)
From (1), x = 2 x 1
x =1
x = 1, y = 8, z = 3
2. Eva

1. Find the value of a b for each of the following, where is the angle between a and b.
(a)
a 8, b 4 , 60
(b)
a 3, b 7 , 45
(a) a b 8 4 cos 60
16
(b)
a 3 7 cos 45
b
21 2
2
2. Find the value of a b for each of the following, where is the angle between a an

(
1. Find
1
) dx .
5
1
1
( 5 )dx 5 x C
2. Find
4 x
4 x
3
3
dx
.
1
dx 4 x 4 C
4
x 4 C
3. Find
( 2 x
( 2 x
4. Find
3
3
3
) dx
.
1
) dx 2 x 2 C
2
2
x C
3
x 2 dx .
x 2 dx 3( 1) x
1
C
3x 1 C
1
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5. Find
dx