এই বইটি মূলত ভোকেশনাল ৯ম শ্রেণির ছাত্র-ছাত্রীদের জন্য। এখানে গনিতের যে প্রশ্নগুলো দেয়া আছে আশা করা যায় শুধু এগুলো পড়েই ভালো রেজাল্ট করা যাবে।

1. 5
3
2
3.89,2.178,5.89798
0.006+0.92+0.134
2.05+8.04+7.018
0.62 X 0.3
0.35 / 1.7
(0.3 X0.83)/(0.5 X0.1)+0.35/0.08
0.31 0.12
5.7 ,8.34,6.245
U={1,2,3,4,5,6,7}, A={1,3,5} B={2,4,6} C={3,4,5,6,7} (AUB)’ = (A’ Ո B’)
A B 35 45 (AUB) (A Ո B)
A={3,4,5} B={4,5,6} C={x,y} (A Ո B)xC
P={1,2,3}, Q={3,4} R={x,y} (PUQ) x R (P Ո Q) x R
P={3,5,7} Q={5,7} R=P/Q (P U Q)xR
Q={x,y} R={m,n,l} P(Q) P(R)
A={1,2,3} P(A)
(x-1,y+2)=(y-2,2x+1) x y
(6x-y,13)=(1,3x+ 2y) x y
A={3,4} B={2,4} xꜪA yꜪB A B x>y
  3
5
4
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f    
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2. a2
+b2
+c2
=9 ab+bc+ca=8 (a+b+c)2
a+b+c=2 ab+bc+ca=1 (a+b)2
+(b+c)2
+(c+a)2
x+y+z=10 xy+yz+zx=31 (x+y)2
+(y+z)2
+(z+x)2
(x + 7) (x - 9)
(2x + 3y) (4x – 5y)
2x -
x
2
= 3 x2
+ 2
1
x
x -
x
1
= 4 x4
- 4
1
x
= 322
7
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a 5

 b
a   24
8 2
2

 b
a
ab
a -
a
1
= 1 a3
- 3
1
a
= 4
2x -
x
2
= 3 8 x3
- 3
1
x
63
2
3 

a a3
+ 3
1
a
= 18 3
0
1
3
2
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 a
a a3
+ 3
1
a
a3
-b3
=513 a-b=3 ab
a+b=m, a2
+b2
=n a3
-b3
= p3
m3
+2p3
= 3mn
a+b+c=0 a3
+b3
+c3
=3abc
p-q=r p3
-q3
-r3
=3pqr
(i) ab + a –b -1
(ii) a2
+6a+8-y2
+2y
(iii) 16x2
-25y2
-8xy+10yz
(iv) 1
27 2
4

 a
a
(v) 4
2
2
4
6 y
y
x
x 

(vi) (a2
-b2
)(x2
-y2
)+4abxy
(vii) 20
2
4

 x
x
(viii)4x4
– 27x2
– 81
(ix) a
x
a
ax 

 )
1
( 2
2
(x) 3(a2
+2a) – 22(a2
+2a) + 40
(xi) (a-1)x2
+a2xy+(a+1)y2
(xii)
27
8
3
3 b
a 
(xiii)
8
1
3

a
(xiv)
8
1
3

a
(xv) 6
5
2 2
3


 x
x
x
(xvi) a3
– 6a2
+ 12a -9
(xvii) x3
– x -6
(xviii) 24
3

 x
x
7 650 6
4% 2 1
11 10%
36 72

3. y
x 1

. z
y 1

. x
z 1

(2a-1
+ 3b-1
)-1
2
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2
2
1
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l
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l
n
m
n
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l
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a
a
a
a
a
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)
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)
.(
)
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1
1
1

ca
a
c
bc
c
b
ab
b
a
x
x
x
x
x
x
ax
=b, by
=c cz
=a xyz=1
(x) logx324=4
(x) logx =-2
3log102+2log103+log105=log10360
3log102+log105 =log1040
log10 = log102 + 2log105 - log103- 2log107
loge + loge + loge - 3loge𝑏 𝑐
ᴧABC BC D AB+AC>2AD
ABC BA D BA=AD <BCD=
ᴧABC D AB+AC>BD+DC
ᴧABC <B <C O <BOC=900
+1/2<A
ABCD BC CD <B <C <D

4. 60 1200
20 4
2 3
6
10 48
512
160 6
5 500
363
125 5
4 5 360
2
8
21:16:12 87
2400
12 5