t) 3 or 1
u) 3v) 2- 7
3.x2,81
4.x1,49
Exercise 2 – 4:- a) 512 x^3
b) 2 t^3
c) 55 x+y+3z
d) 1515 x
e) 7
f) 21 d^7
g) ^187 a^15 b^12
h)bk^2 +k
i) 4 c^6 m^2
j) 2
k) 7 a^110 b
l) ab^148
m) 25 p: 33 p
n) 27 mt
o) 31 x 5
p) 6251
q)^274
r) 271
s) 271
t) yx^25
u) 8
v) 8 x^6 ay^3 b
w) 4 x+3
x) 22
y) 27
z)^65- a)^13
b)^18
c) 14
d) 22 p 2 p+ 1
e)a^5 b^3
f) 3 x^4 y^2
g) 34
h) 320 z+^2
i) 11 b 4 p
j) 112 c ^2 214 c ^4
k) 21334 5
l)^8150
m) 109
n) 108 a^6 b^9
o) 22 p^10 q^6
p) (ab) ^1
q)x^6
r)(^23 )^2 y
s) 4- a) 3
b) 3
c) 1
d)
2
3
e) 9
f) 5
g)^12
h) 1
i) 16
j) 161
k) 1
l) 1 or 16
m) 2
n)k= 811
o)x= 81
p)^12
q)x= 3orx= 2
r) x= 2
s)x= 1orx= 1
t)x= 8
u)x= 1
v) x= 1
w) x= ^13 orx=
1
x) no solution
4.x2,73
5.x3,10- a)The sum of two pow-
ers of the same de-
gree is not the power
of the sum of the
bases
b)The sum of two pow-
ers of the same de-
gree is not the power
of the sum of the
bases
c)A negative sign is
missing, when a
power is moved
from the denomina-
tor to the numerator,
the sign of the expo-
nent changes.
d)We cannot multiply
bases unless they are
raised to the same
power
e)The sign of a base is
not changed when
an exponent is
moved from the
denominator to the
numerator in a frac-
tion
f)The power of a prod-
uct is the product of
all the bases raised to
the same power - 25 102013 2015 digits.
3 Number patterns
Exercise 3 – 1:2.Tn 1 = 1
3.Tn 4 =C- a)no common difference
b)d= 7
c)no common difference
d)d= 0,65 - a)35, 45 and 55
b)7, 12 and 17
c)21, 18 and 15
d)T 4 = 28,1;T 5 =
33,1;T 6 = 38,1
e)T 4 = 39 x;T 5 = 49 x;T 6 =
59 x
f)T 4 =44,2;T 5 =64,2;T 6 =
84,2
g)T 4 = 42b;T 5 = 46b;T 6 = 50b
6.T 6 = 28andT 9 = 43
7.T 5 =GandT 8 =J
8.T 5 = 23andT 8 = 35- a) 8
b) 1
c) 9 and 5
d) 28
e) 27 - a)13 triangles
b) 2 n+ 3
c) 53 - a)47 ; 55 ; 63
b) 8 n+ 7
c)= 23- a)76 ; 106 ; 136
b) 30 n 74
c)= 16 - a)No common difference
b)T 1 = 3 andT 2 = 3 - a)d= 2 n 3
b)T 1 = 2andT 3 = 0 - a) ^53
b) ^149 ;^439 and^1009 - a) ^12
b) 2 ; 3 and 4
18.E
Exercise 3 – 2:2.d= 3
3.no common difference
4.Tn 3 = 7- a)T 4 = 67,2 ; T 5 =
86,2;T 6 = 105,2
b)T 4 = 38r;T 5 = 34r;T 6 =
30 r
6.T 6 = 31andT 8 = 41
7.T 6 =FandT 10 =J - a)T 6 = 49
b)T 6 = 11
c)T 6 =18,9- a)Tn = 4 n 14 ; T 10 =
54 ; T 15 = 74 ; T 30 = 134
b)Tn = 7 n+ 8; T 10 =
62 ; T 15 = 97 ; T 30 = 202 - a)12 and 16
b) 10
c)23 and 53 - a)Tn= 4n 1
b)Tn= 3n 5
c)Tn= 4n+ 7
d)Tn=^13 n- a) 49 ; 63 ; 77
b)= 14 n+ 7
c)= 66
13.M
14.C
15.111 seats - a)17 boxes
Solutions 501