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1 	 / 	 1 2
C B S E 	 C l a s s 	 9 	 M a t h e m a t i c s
S a m p l e 	 P a p e r
G e n e r a l 	 I n s u t r u c t i o n s :
1 . 	 A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y .
2 . 	 T h e 	 q u e s t i o n 	 p a p e r 	 c o n s i s t s 	 o f 	 3 0 	 q u e s t i o n s 	 d i v i d e d 	 i n t o 	 f o u r 	 s e c t i o n 	 A , 	 B , 	 C , 	 a n d 	 D .
S e c t i o n - A 	 c o m p r o s e s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h ; 	 S e c t i o n - B 	 c o m p r i s e s 	 o f 	 6
q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h ; 	 S e c t i o n - C 	 c o m p r i s e s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h 	 a n d
s e c t i o n - D 	 c o m p r i s e s 	 o f 	 8 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
3 . 	 T h e r e 	 i s 	 n o 	 o v e r a l l 	 c h o i c e 	 i n 	 t h i s 	 q u e s t i o n 	 p a p e r .
4 . 	 U s e 	 o f 	 c a l c u l a t o r 	 i s 	 n o t 	 p e r m i t t e d .
S e c t i o n 	 - 	 A
1 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 ( 6 4 )
1 / 2
	 x 	 ( 1 2 5 )
1 / 3
.
2 . 	 I f 	 p ( x ) = x
3
- 3 x
2
	 + 	 2 x , 	 t h e n 	 f i n d 	 t h e 	 v a l u e 	 o f 	 p ( 1 ) .
3 . 	 P o i n t s 	 A 	 ( 8 , 	 4 ) 	 & 	 B 	 ( - 2 , 4 ) 	 l i e 	 o n 	 a 	 l i n e . 	 A B 	 i s 	 p a r a l l e l 	 t o 	 w h i c h 	 a x i s .
4 . 	 I f 	 t h e 	 g r a p h 	 o f 	 e q u a t i o n 	 2 x 	 + 	 k y 	 = 	 1 0 k , 	 i n t e r s e c t 	 x - a x i s 	 a t 	 p o i n t 	 ( 5 , 0 ) . 	 F i n d 	 v a l u e 	 o f 	 k .
5 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 x 	 f r o m 	 t h e 	 a d j a c e n t 	 f i g u r e .
6 . 	 F i n d 	 t h e 	 r a t i o 	 o f 	 t o t a l 	 s u r f a c e 	 a r e a 	 o f 	 a 	 s p h e r e 	 a n d 	 a 	 s o l i d 	 h e m i s p h e r e 	 o f 	 s a m e 	 r a d i u s .
S e c t i o n - B
7 . 	 F a c t o r i s e : 	
8 . 	 F i n d 	 t h e 	 c o o r d i n a t e s 	 o f 	 t h e 	 p o i n t 	 w h e r e 	 t h e 	 g r a p h 	 o f 	 t h e 	 e q u a t i o n 	 5 x 	 + 	 2 y 	 = 1 0 	 i n t e r s e c t
b o t h 	 a x e s .
9 . 	 T h e 	 s i d e s 	 o f 	 a 	 t r i a n g l e 	 a r e 	 2 2 c m , 	 2 0 c m 	 a n d 	 1 8 	 c m . 	 F i n d 	 i t s 	 a r e a .
Page 2


1 	 / 	 1 2
C B S E 	 C l a s s 	 9 	 M a t h e m a t i c s
S a m p l e 	 P a p e r
G e n e r a l 	 I n s u t r u c t i o n s :
1 . 	 A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y .
2 . 	 T h e 	 q u e s t i o n 	 p a p e r 	 c o n s i s t s 	 o f 	 3 0 	 q u e s t i o n s 	 d i v i d e d 	 i n t o 	 f o u r 	 s e c t i o n 	 A , 	 B , 	 C , 	 a n d 	 D .
S e c t i o n - A 	 c o m p r o s e s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h ; 	 S e c t i o n - B 	 c o m p r i s e s 	 o f 	 6
q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h ; 	 S e c t i o n - C 	 c o m p r i s e s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h 	 a n d
s e c t i o n - D 	 c o m p r i s e s 	 o f 	 8 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
3 . 	 T h e r e 	 i s 	 n o 	 o v e r a l l 	 c h o i c e 	 i n 	 t h i s 	 q u e s t i o n 	 p a p e r .
4 . 	 U s e 	 o f 	 c a l c u l a t o r 	 i s 	 n o t 	 p e r m i t t e d .
S e c t i o n 	 - 	 A
1 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 ( 6 4 )
1 / 2
	 x 	 ( 1 2 5 )
1 / 3
.
2 . 	 I f 	 p ( x ) = x
3
- 3 x
2
	 + 	 2 x , 	 t h e n 	 f i n d 	 t h e 	 v a l u e 	 o f 	 p ( 1 ) .
3 . 	 P o i n t s 	 A 	 ( 8 , 	 4 ) 	 & 	 B 	 ( - 2 , 4 ) 	 l i e 	 o n 	 a 	 l i n e . 	 A B 	 i s 	 p a r a l l e l 	 t o 	 w h i c h 	 a x i s .
4 . 	 I f 	 t h e 	 g r a p h 	 o f 	 e q u a t i o n 	 2 x 	 + 	 k y 	 = 	 1 0 k , 	 i n t e r s e c t 	 x - a x i s 	 a t 	 p o i n t 	 ( 5 , 0 ) . 	 F i n d 	 v a l u e 	 o f 	 k .
5 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 x 	 f r o m 	 t h e 	 a d j a c e n t 	 f i g u r e .
6 . 	 F i n d 	 t h e 	 r a t i o 	 o f 	 t o t a l 	 s u r f a c e 	 a r e a 	 o f 	 a 	 s p h e r e 	 a n d 	 a 	 s o l i d 	 h e m i s p h e r e 	 o f 	 s a m e 	 r a d i u s .
S e c t i o n - B
7 . 	 F a c t o r i s e : 	
8 . 	 F i n d 	 t h e 	 c o o r d i n a t e s 	 o f 	 t h e 	 p o i n t 	 w h e r e 	 t h e 	 g r a p h 	 o f 	 t h e 	 e q u a t i o n 	 5 x 	 + 	 2 y 	 = 1 0 	 i n t e r s e c t
b o t h 	 a x e s .
9 . 	 T h e 	 s i d e s 	 o f 	 a 	 t r i a n g l e 	 a r e 	 2 2 c m , 	 2 0 c m 	 a n d 	 1 8 	 c m . 	 F i n d 	 i t s 	 a r e a .
2 	 / 	 1 2
1 0 . 	 T h e 	 t w o 	 c o n s e c u t i v e 	 c l a s s 	 m a r k s 	 o f 	 a 	 d i s t r i b u t i o n 	 a r e 	 5 2 	 & 	 5 7 . 	 F i n d 	 t h e 	 c l a s s 	 l i m i t s .
1 1 . 	 A 	 d i e 	 i s 	 r o l l e d 	 2 0 0 	 t i m e s 	 & 	 i t s 	 o u t c o m e s 	 a r e 	 r e l e a s e d 	 a s 	 b e l o w :
O u t c o m e s 1 2 3 4 5 6
F r e q u e n c y 2 5 3 5 4 0 2 8 4 2 3 0
F i n d 	 t h e 	 p r o b a b i l i t y 	 o f 	 g e t t i n g :
i . 	 A 	 m u l t i p l e 	 o f 	 3 .
i i . 	 n o t a 	 p r i m e 	 n u m b e r .
1 2 . 	 C o n s i d e r 	 t h e 	 f o l l o w i n g 	 f r e q u e n c y 	 d i s t r i b u t i o n 	 w h i c h 	 g i v e s 	 t h e 	 w e i g h t s 	 o f 	 3 8 	 s t u d e n t s 	 o f 	 a
c l a s s :
W e i g h t s 	 ( k g ) 3 1 - 3 5 3 6 - 4 0 4 1 - 4 5 4 6 - 5 0 5 1 - 5 5 5 6 - 6 0 6 1 - 6 5 6 6 - 7 0 T o t a l
N o . 	 o f 	 S t d . 9 5 1 4 3 1 2 2 2 3 8
i . 	 F i n d 	 t h e 	 p r o b a b i l i t y 	 t h a t 	 t h e 	 w e i g h t 	 o f 	 a 	 s t u d e n t 	 i n 	 t h e 	 c l a s s 	 l i e s 	 b e t w e e n 	 3 6 - 4 5 	 k g .
i i . 	 G i v e 	 o n e 	 e v e n t 	 i n 	 t h i s 	 c o n t e x t 	 h a v i n g 	 p r o b a b i l i t y 	 z e r o .
S e c t i o n - C
1 3 . 	 I f 	 , 	 f i n d 	
1 4 . 	 S i m p l i f y :
1 5 . 	 P l o t 	 t h e 	 p o i n t s 	 A ( 1 , 1 ) , 	 B 	 ( - 1 , 5 ) , 	 C ( 7 , 9 ) 	 a n d 	 D 	 ( 9 , 5 ) . 	 N a m e 	 t h e 	 t y p e 	 o f 	 f i g u r e 	 A B C D . 	 I n 	 w h i c h
q u a d r a n t 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 d i a g o n a l s 	 l i e ?
1 6 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 S h o w 	 t h a t 	 X Y | | E F .
1 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A B = A C , 	 	 t h e n 	 p r o v e 	 t h a t 	 	 i s 	 a n 	 i s o s c e l l e s
t r i a n g l e .
Page 3


1 	 / 	 1 2
C B S E 	 C l a s s 	 9 	 M a t h e m a t i c s
S a m p l e 	 P a p e r
G e n e r a l 	 I n s u t r u c t i o n s :
1 . 	 A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y .
2 . 	 T h e 	 q u e s t i o n 	 p a p e r 	 c o n s i s t s 	 o f 	 3 0 	 q u e s t i o n s 	 d i v i d e d 	 i n t o 	 f o u r 	 s e c t i o n 	 A , 	 B , 	 C , 	 a n d 	 D .
S e c t i o n - A 	 c o m p r o s e s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h ; 	 S e c t i o n - B 	 c o m p r i s e s 	 o f 	 6
q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h ; 	 S e c t i o n - C 	 c o m p r i s e s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h 	 a n d
s e c t i o n - D 	 c o m p r i s e s 	 o f 	 8 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
3 . 	 T h e r e 	 i s 	 n o 	 o v e r a l l 	 c h o i c e 	 i n 	 t h i s 	 q u e s t i o n 	 p a p e r .
4 . 	 U s e 	 o f 	 c a l c u l a t o r 	 i s 	 n o t 	 p e r m i t t e d .
S e c t i o n 	 - 	 A
1 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 ( 6 4 )
1 / 2
	 x 	 ( 1 2 5 )
1 / 3
.
2 . 	 I f 	 p ( x ) = x
3
- 3 x
2
	 + 	 2 x , 	 t h e n 	 f i n d 	 t h e 	 v a l u e 	 o f 	 p ( 1 ) .
3 . 	 P o i n t s 	 A 	 ( 8 , 	 4 ) 	 & 	 B 	 ( - 2 , 4 ) 	 l i e 	 o n 	 a 	 l i n e . 	 A B 	 i s 	 p a r a l l e l 	 t o 	 w h i c h 	 a x i s .
4 . 	 I f 	 t h e 	 g r a p h 	 o f 	 e q u a t i o n 	 2 x 	 + 	 k y 	 = 	 1 0 k , 	 i n t e r s e c t 	 x - a x i s 	 a t 	 p o i n t 	 ( 5 , 0 ) . 	 F i n d 	 v a l u e 	 o f 	 k .
5 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 x 	 f r o m 	 t h e 	 a d j a c e n t 	 f i g u r e .
6 . 	 F i n d 	 t h e 	 r a t i o 	 o f 	 t o t a l 	 s u r f a c e 	 a r e a 	 o f 	 a 	 s p h e r e 	 a n d 	 a 	 s o l i d 	 h e m i s p h e r e 	 o f 	 s a m e 	 r a d i u s .
S e c t i o n - B
7 . 	 F a c t o r i s e : 	
8 . 	 F i n d 	 t h e 	 c o o r d i n a t e s 	 o f 	 t h e 	 p o i n t 	 w h e r e 	 t h e 	 g r a p h 	 o f 	 t h e 	 e q u a t i o n 	 5 x 	 + 	 2 y 	 = 1 0 	 i n t e r s e c t
b o t h 	 a x e s .
9 . 	 T h e 	 s i d e s 	 o f 	 a 	 t r i a n g l e 	 a r e 	 2 2 c m , 	 2 0 c m 	 a n d 	 1 8 	 c m . 	 F i n d 	 i t s 	 a r e a .
2 	 / 	 1 2
1 0 . 	 T h e 	 t w o 	 c o n s e c u t i v e 	 c l a s s 	 m a r k s 	 o f 	 a 	 d i s t r i b u t i o n 	 a r e 	 5 2 	 & 	 5 7 . 	 F i n d 	 t h e 	 c l a s s 	 l i m i t s .
1 1 . 	 A 	 d i e 	 i s 	 r o l l e d 	 2 0 0 	 t i m e s 	 & 	 i t s 	 o u t c o m e s 	 a r e 	 r e l e a s e d 	 a s 	 b e l o w :
O u t c o m e s 1 2 3 4 5 6
F r e q u e n c y 2 5 3 5 4 0 2 8 4 2 3 0
F i n d 	 t h e 	 p r o b a b i l i t y 	 o f 	 g e t t i n g :
i . 	 A 	 m u l t i p l e 	 o f 	 3 .
i i . 	 n o t a 	 p r i m e 	 n u m b e r .
1 2 . 	 C o n s i d e r 	 t h e 	 f o l l o w i n g 	 f r e q u e n c y 	 d i s t r i b u t i o n 	 w h i c h 	 g i v e s 	 t h e 	 w e i g h t s 	 o f 	 3 8 	 s t u d e n t s 	 o f 	 a
c l a s s :
W e i g h t s 	 ( k g ) 3 1 - 3 5 3 6 - 4 0 4 1 - 4 5 4 6 - 5 0 5 1 - 5 5 5 6 - 6 0 6 1 - 6 5 6 6 - 7 0 T o t a l
N o . 	 o f 	 S t d . 9 5 1 4 3 1 2 2 2 3 8
i . 	 F i n d 	 t h e 	 p r o b a b i l i t y 	 t h a t 	 t h e 	 w e i g h t 	 o f 	 a 	 s t u d e n t 	 i n 	 t h e 	 c l a s s 	 l i e s 	 b e t w e e n 	 3 6 - 4 5 	 k g .
i i . 	 G i v e 	 o n e 	 e v e n t 	 i n 	 t h i s 	 c o n t e x t 	 h a v i n g 	 p r o b a b i l i t y 	 z e r o .
S e c t i o n - C
1 3 . 	 I f 	 , 	 f i n d 	
1 4 . 	 S i m p l i f y :
1 5 . 	 P l o t 	 t h e 	 p o i n t s 	 A ( 1 , 1 ) , 	 B 	 ( - 1 , 5 ) , 	 C ( 7 , 9 ) 	 a n d 	 D 	 ( 9 , 5 ) . 	 N a m e 	 t h e 	 t y p e 	 o f 	 f i g u r e 	 A B C D . 	 I n 	 w h i c h
q u a d r a n t 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 d i a g o n a l s 	 l i e ?
1 6 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 S h o w 	 t h a t 	 X Y | | E F .
1 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A B = A C , 	 	 t h e n 	 p r o v e 	 t h a t 	 	 i s 	 a n 	 i s o s c e l l e s
t r i a n g l e .
3 	 / 	 1 2
1 8 . 	 P , 	 Q 	 & 	 R 	 a r e 	 r e s p e c t i v e l y , 	 t h e 	 m i d 	 p o i n t s 	 o f 	 s i d e s 	 B C , 	 C A 	 & 	 A B 	 o f 	 a 	 t r i a n g l e 	 A B C . 	 P R 	 & 	 B Q
m e e t 	 a t 	 X . 	 C R 	 & 	 P Q 	 m e e t 	 a t 	 Y . 	 P r o v e 	 t h a t 	 . 	
1 9 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 O 	 i s 	 t h e 	 c e n t r e 	 o f 	 a 	 c i r c l e . 	 P r o v e 	 t h a t 	 .
2 0 . 	 C o n s t r u c t 	 	 s u c h 	 t h a t 	 B C = 	 8 c m , 	 , 	 A B - A C = 3 . 5 c m
2 1 . 	 I f 	 h , 	 c 	 a n d 	 v 	 r e s p e c t i v e l y , 	 a r e 	 t h e 	 h e i g h t , 	 t h e 	 c u r v e d 	 s u r f a c e 	 a r e a 	 a n d 	 v o l u m e 	 o f 	 a 	 c o n e ,
p r o v e 	 t h a t
2 2 . 	 T h e 	 r a d i u s 	 o f 	 a 	 s p h e r e 	 i s 	 1 0 	 c m . 	 I f 	 t h e 	 r a d i u s 	 i s 	 i n c r e a s e d 	 b y 	 1 	 c m . 	 T h e n 	 p r o v e 	 t h a t
v o l u m e 	 o f 	 t h e 	 s p h e r e 	 i s 	 i n c r e a s e d 	 b y 	 3 3 . 1 % .
S e c t i o n - D
E x p r e s s 	 	 i n 	 t h e 	 f o r m 	 , 	 w h e r e 	 p 	 a n d 	 q 	 a r e 	 i n t e g e r s 	 a n d 	 .
2 4 . 	 V e r i f y :
Page 4


1 	 / 	 1 2
C B S E 	 C l a s s 	 9 	 M a t h e m a t i c s
S a m p l e 	 P a p e r
G e n e r a l 	 I n s u t r u c t i o n s :
1 . 	 A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y .
2 . 	 T h e 	 q u e s t i o n 	 p a p e r 	 c o n s i s t s 	 o f 	 3 0 	 q u e s t i o n s 	 d i v i d e d 	 i n t o 	 f o u r 	 s e c t i o n 	 A , 	 B , 	 C , 	 a n d 	 D .
S e c t i o n - A 	 c o m p r o s e s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h ; 	 S e c t i o n - B 	 c o m p r i s e s 	 o f 	 6
q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h ; 	 S e c t i o n - C 	 c o m p r i s e s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h 	 a n d
s e c t i o n - D 	 c o m p r i s e s 	 o f 	 8 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
3 . 	 T h e r e 	 i s 	 n o 	 o v e r a l l 	 c h o i c e 	 i n 	 t h i s 	 q u e s t i o n 	 p a p e r .
4 . 	 U s e 	 o f 	 c a l c u l a t o r 	 i s 	 n o t 	 p e r m i t t e d .
S e c t i o n 	 - 	 A
1 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 ( 6 4 )
1 / 2
	 x 	 ( 1 2 5 )
1 / 3
.
2 . 	 I f 	 p ( x ) = x
3
- 3 x
2
	 + 	 2 x , 	 t h e n 	 f i n d 	 t h e 	 v a l u e 	 o f 	 p ( 1 ) .
3 . 	 P o i n t s 	 A 	 ( 8 , 	 4 ) 	 & 	 B 	 ( - 2 , 4 ) 	 l i e 	 o n 	 a 	 l i n e . 	 A B 	 i s 	 p a r a l l e l 	 t o 	 w h i c h 	 a x i s .
4 . 	 I f 	 t h e 	 g r a p h 	 o f 	 e q u a t i o n 	 2 x 	 + 	 k y 	 = 	 1 0 k , 	 i n t e r s e c t 	 x - a x i s 	 a t 	 p o i n t 	 ( 5 , 0 ) . 	 F i n d 	 v a l u e 	 o f 	 k .
5 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 x 	 f r o m 	 t h e 	 a d j a c e n t 	 f i g u r e .
6 . 	 F i n d 	 t h e 	 r a t i o 	 o f 	 t o t a l 	 s u r f a c e 	 a r e a 	 o f 	 a 	 s p h e r e 	 a n d 	 a 	 s o l i d 	 h e m i s p h e r e 	 o f 	 s a m e 	 r a d i u s .
S e c t i o n - B
7 . 	 F a c t o r i s e : 	
8 . 	 F i n d 	 t h e 	 c o o r d i n a t e s 	 o f 	 t h e 	 p o i n t 	 w h e r e 	 t h e 	 g r a p h 	 o f 	 t h e 	 e q u a t i o n 	 5 x 	 + 	 2 y 	 = 1 0 	 i n t e r s e c t
b o t h 	 a x e s .
9 . 	 T h e 	 s i d e s 	 o f 	 a 	 t r i a n g l e 	 a r e 	 2 2 c m , 	 2 0 c m 	 a n d 	 1 8 	 c m . 	 F i n d 	 i t s 	 a r e a .
2 	 / 	 1 2
1 0 . 	 T h e 	 t w o 	 c o n s e c u t i v e 	 c l a s s 	 m a r k s 	 o f 	 a 	 d i s t r i b u t i o n 	 a r e 	 5 2 	 & 	 5 7 . 	 F i n d 	 t h e 	 c l a s s 	 l i m i t s .
1 1 . 	 A 	 d i e 	 i s 	 r o l l e d 	 2 0 0 	 t i m e s 	 & 	 i t s 	 o u t c o m e s 	 a r e 	 r e l e a s e d 	 a s 	 b e l o w :
O u t c o m e s 1 2 3 4 5 6
F r e q u e n c y 2 5 3 5 4 0 2 8 4 2 3 0
F i n d 	 t h e 	 p r o b a b i l i t y 	 o f 	 g e t t i n g :
i . 	 A 	 m u l t i p l e 	 o f 	 3 .
i i . 	 n o t a 	 p r i m e 	 n u m b e r .
1 2 . 	 C o n s i d e r 	 t h e 	 f o l l o w i n g 	 f r e q u e n c y 	 d i s t r i b u t i o n 	 w h i c h 	 g i v e s 	 t h e 	 w e i g h t s 	 o f 	 3 8 	 s t u d e n t s 	 o f 	 a
c l a s s :
W e i g h t s 	 ( k g ) 3 1 - 3 5 3 6 - 4 0 4 1 - 4 5 4 6 - 5 0 5 1 - 5 5 5 6 - 6 0 6 1 - 6 5 6 6 - 7 0 T o t a l
N o . 	 o f 	 S t d . 9 5 1 4 3 1 2 2 2 3 8
i . 	 F i n d 	 t h e 	 p r o b a b i l i t y 	 t h a t 	 t h e 	 w e i g h t 	 o f 	 a 	 s t u d e n t 	 i n 	 t h e 	 c l a s s 	 l i e s 	 b e t w e e n 	 3 6 - 4 5 	 k g .
i i . 	 G i v e 	 o n e 	 e v e n t 	 i n 	 t h i s 	 c o n t e x t 	 h a v i n g 	 p r o b a b i l i t y 	 z e r o .
S e c t i o n - C
1 3 . 	 I f 	 , 	 f i n d 	
1 4 . 	 S i m p l i f y :
1 5 . 	 P l o t 	 t h e 	 p o i n t s 	 A ( 1 , 1 ) , 	 B 	 ( - 1 , 5 ) , 	 C ( 7 , 9 ) 	 a n d 	 D 	 ( 9 , 5 ) . 	 N a m e 	 t h e 	 t y p e 	 o f 	 f i g u r e 	 A B C D . 	 I n 	 w h i c h
q u a d r a n t 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 d i a g o n a l s 	 l i e ?
1 6 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 S h o w 	 t h a t 	 X Y | | E F .
1 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A B = A C , 	 	 t h e n 	 p r o v e 	 t h a t 	 	 i s 	 a n 	 i s o s c e l l e s
t r i a n g l e .
3 	 / 	 1 2
1 8 . 	 P , 	 Q 	 & 	 R 	 a r e 	 r e s p e c t i v e l y , 	 t h e 	 m i d 	 p o i n t s 	 o f 	 s i d e s 	 B C , 	 C A 	 & 	 A B 	 o f 	 a 	 t r i a n g l e 	 A B C . 	 P R 	 & 	 B Q
m e e t 	 a t 	 X . 	 C R 	 & 	 P Q 	 m e e t 	 a t 	 Y . 	 P r o v e 	 t h a t 	 . 	
1 9 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 O 	 i s 	 t h e 	 c e n t r e 	 o f 	 a 	 c i r c l e . 	 P r o v e 	 t h a t 	 .
2 0 . 	 C o n s t r u c t 	 	 s u c h 	 t h a t 	 B C = 	 8 c m , 	 , 	 A B - A C = 3 . 5 c m
2 1 . 	 I f 	 h , 	 c 	 a n d 	 v 	 r e s p e c t i v e l y , 	 a r e 	 t h e 	 h e i g h t , 	 t h e 	 c u r v e d 	 s u r f a c e 	 a r e a 	 a n d 	 v o l u m e 	 o f 	 a 	 c o n e ,
p r o v e 	 t h a t
2 2 . 	 T h e 	 r a d i u s 	 o f 	 a 	 s p h e r e 	 i s 	 1 0 	 c m . 	 I f 	 t h e 	 r a d i u s 	 i s 	 i n c r e a s e d 	 b y 	 1 	 c m . 	 T h e n 	 p r o v e 	 t h a t
v o l u m e 	 o f 	 t h e 	 s p h e r e 	 i s 	 i n c r e a s e d 	 b y 	 3 3 . 1 % .
S e c t i o n - D
E x p r e s s 	 	 i n 	 t h e 	 f o r m 	 , 	 w h e r e 	 p 	 a n d 	 q 	 a r e 	 i n t e g e r s 	 a n d 	 .
2 4 . 	 V e r i f y :
4 	 / 	 1 2
a
3
	 + 	 b
3
	 + 	 c
3
	 - 	 3 a b c 	
2 5 . 	 A 	 p h a r m a c i s t 	 n e e d s 	 t o 	 s t r e n g t h e n 	 a 	 1 5 % 	 a l c o h o l 	 s o l u t i o n 	 t o 	 o n e 	 o f 	 3 2 % 	 a l c o h o l . 	 H o w
m u c h 	 p u r e 	 a l c o h o l 	 s h o u l d 	 b e 	 a d d e d 	 t o 	 8 0 0 	 m 	 O f 	 1 5 % 	 S o l u t i o n ?
2 6 . 	 I n 	 t h e 	 f i g u r e 	 t w o 	 s t r a i g h t 	 l i n e s 	 P Q 	 & 	 R S 	 i n t e r s e c t 	 e a c h 	 o t h e r 	 a t 	 O . 	 I f 	 , 	 f i n d
t h e 	 v a l u e s 	 o f 	 a , 	 b 	 & c .
2 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A D = B D = C D . 	 P r o v e 	 t h a t 	 	 i s 	 r i g h t 	 a n g l e .
2 8 . 	 I n 	 a 	 p a r a l l e l o g r a m 	 A B C D , 	 E & F 	 a r e 	 t h e 	 m i d 	 P o i n t s 	 s i d e s 	 A B 	 & 	 C D 	 r e s p e c t i v e l y . 	 S h o w 	 t h a t
t h e 	 l i n e 	 s e g m e n t 	 A F 	 & 	 E C 	 t r i s e c t 	 t h e 	 d i a g o n a l 	 B D .
2 9 . 	 T h e 	 r e s i d e n t i a l 	 c o l o n y 	 h a s 	 p o p u l a t i o n 	 o f 	 5 4 0 0 	 a n d 	 6 0 	 l i t r e s 	 o f 	 w a t e r 	 i s 	 r e q u i r e d 	 p e r
p e r s o n 	 p e r 	 d a y . 	 F o r 	 t h e 	 e f f e c t i v e 	 u t i l i z a t i o n 	 o f 	 r a i n 	 w a t e r , 	 a 	 g r o u p 	 o f 	 p e o p l e 	 d e c i d e d 	 f o r
W A T E R 	 H A R V E S T I N G . 	 T h e y 	 c o n s t r u c t e d 	 a 	 w a t e r 	 r e s e r v o i r 	 m e a s u r i n g 	 4 9 m 	 x 	 2 7 m 	 x 	 2 5 m
t o 	 c o l l e c t 	 t h e 	 r a i n 	 w a t e r . 	 I f 	 t h i s 	 w a t e r 	 r e s e r v o i r s 	 i s 	 f u l l 	 o f 	 w a t e r 	 t h e n 	 f o r 	 h o w 	 m a n y 	 d a y s 	 i t
w i l l 	 l a s t 	 f o r 	 t h e 	 c o l o n y
Page 5


1 	 / 	 1 2
C B S E 	 C l a s s 	 9 	 M a t h e m a t i c s
S a m p l e 	 P a p e r
G e n e r a l 	 I n s u t r u c t i o n s :
1 . 	 A l l 	 q u e s t i o n s 	 a r e 	 c o m p u l s o r y .
2 . 	 T h e 	 q u e s t i o n 	 p a p e r 	 c o n s i s t s 	 o f 	 3 0 	 q u e s t i o n s 	 d i v i d e d 	 i n t o 	 f o u r 	 s e c t i o n 	 A , 	 B , 	 C , 	 a n d 	 D .
S e c t i o n - A 	 c o m p r o s e s 	 o f 	 6 	 q u e s t i o n s 	 o f 	 1 	 m a r k 	 e a c h ; 	 S e c t i o n - B 	 c o m p r i s e s 	 o f 	 6
q u e s t i o n s 	 o f 	 2 	 m a r k s 	 e a c h ; 	 S e c t i o n - C 	 c o m p r i s e s 	 o f 	 1 0 	 q u e s t i o n s 	 o f 	 3 	 m a r k s 	 e a c h 	 a n d
s e c t i o n - D 	 c o m p r i s e s 	 o f 	 8 	 q u e s t i o n s 	 o f 	 4 	 m a r k s 	 e a c h .
3 . 	 T h e r e 	 i s 	 n o 	 o v e r a l l 	 c h o i c e 	 i n 	 t h i s 	 q u e s t i o n 	 p a p e r .
4 . 	 U s e 	 o f 	 c a l c u l a t o r 	 i s 	 n o t 	 p e r m i t t e d .
S e c t i o n 	 - 	 A
1 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 ( 6 4 )
1 / 2
	 x 	 ( 1 2 5 )
1 / 3
.
2 . 	 I f 	 p ( x ) = x
3
- 3 x
2
	 + 	 2 x , 	 t h e n 	 f i n d 	 t h e 	 v a l u e 	 o f 	 p ( 1 ) .
3 . 	 P o i n t s 	 A 	 ( 8 , 	 4 ) 	 & 	 B 	 ( - 2 , 4 ) 	 l i e 	 o n 	 a 	 l i n e . 	 A B 	 i s 	 p a r a l l e l 	 t o 	 w h i c h 	 a x i s .
4 . 	 I f 	 t h e 	 g r a p h 	 o f 	 e q u a t i o n 	 2 x 	 + 	 k y 	 = 	 1 0 k , 	 i n t e r s e c t 	 x - a x i s 	 a t 	 p o i n t 	 ( 5 , 0 ) . 	 F i n d 	 v a l u e 	 o f 	 k .
5 . 	 F i n d 	 t h e 	 v a l u e 	 o f 	 x 	 f r o m 	 t h e 	 a d j a c e n t 	 f i g u r e .
6 . 	 F i n d 	 t h e 	 r a t i o 	 o f 	 t o t a l 	 s u r f a c e 	 a r e a 	 o f 	 a 	 s p h e r e 	 a n d 	 a 	 s o l i d 	 h e m i s p h e r e 	 o f 	 s a m e 	 r a d i u s .
S e c t i o n - B
7 . 	 F a c t o r i s e : 	
8 . 	 F i n d 	 t h e 	 c o o r d i n a t e s 	 o f 	 t h e 	 p o i n t 	 w h e r e 	 t h e 	 g r a p h 	 o f 	 t h e 	 e q u a t i o n 	 5 x 	 + 	 2 y 	 = 1 0 	 i n t e r s e c t
b o t h 	 a x e s .
9 . 	 T h e 	 s i d e s 	 o f 	 a 	 t r i a n g l e 	 a r e 	 2 2 c m , 	 2 0 c m 	 a n d 	 1 8 	 c m . 	 F i n d 	 i t s 	 a r e a .
2 	 / 	 1 2
1 0 . 	 T h e 	 t w o 	 c o n s e c u t i v e 	 c l a s s 	 m a r k s 	 o f 	 a 	 d i s t r i b u t i o n 	 a r e 	 5 2 	 & 	 5 7 . 	 F i n d 	 t h e 	 c l a s s 	 l i m i t s .
1 1 . 	 A 	 d i e 	 i s 	 r o l l e d 	 2 0 0 	 t i m e s 	 & 	 i t s 	 o u t c o m e s 	 a r e 	 r e l e a s e d 	 a s 	 b e l o w :
O u t c o m e s 1 2 3 4 5 6
F r e q u e n c y 2 5 3 5 4 0 2 8 4 2 3 0
F i n d 	 t h e 	 p r o b a b i l i t y 	 o f 	 g e t t i n g :
i . 	 A 	 m u l t i p l e 	 o f 	 3 .
i i . 	 n o t a 	 p r i m e 	 n u m b e r .
1 2 . 	 C o n s i d e r 	 t h e 	 f o l l o w i n g 	 f r e q u e n c y 	 d i s t r i b u t i o n 	 w h i c h 	 g i v e s 	 t h e 	 w e i g h t s 	 o f 	 3 8 	 s t u d e n t s 	 o f 	 a
c l a s s :
W e i g h t s 	 ( k g ) 3 1 - 3 5 3 6 - 4 0 4 1 - 4 5 4 6 - 5 0 5 1 - 5 5 5 6 - 6 0 6 1 - 6 5 6 6 - 7 0 T o t a l
N o . 	 o f 	 S t d . 9 5 1 4 3 1 2 2 2 3 8
i . 	 F i n d 	 t h e 	 p r o b a b i l i t y 	 t h a t 	 t h e 	 w e i g h t 	 o f 	 a 	 s t u d e n t 	 i n 	 t h e 	 c l a s s 	 l i e s 	 b e t w e e n 	 3 6 - 4 5 	 k g .
i i . 	 G i v e 	 o n e 	 e v e n t 	 i n 	 t h i s 	 c o n t e x t 	 h a v i n g 	 p r o b a b i l i t y 	 z e r o .
S e c t i o n - C
1 3 . 	 I f 	 , 	 f i n d 	
1 4 . 	 S i m p l i f y :
1 5 . 	 P l o t 	 t h e 	 p o i n t s 	 A ( 1 , 1 ) , 	 B 	 ( - 1 , 5 ) , 	 C ( 7 , 9 ) 	 a n d 	 D 	 ( 9 , 5 ) . 	 N a m e 	 t h e 	 t y p e 	 o f 	 f i g u r e 	 A B C D . 	 I n 	 w h i c h
q u a d r a n t 	 t h e 	 p o i n t 	 o f 	 i n t e r s e c t i o n 	 o f 	 d i a g o n a l s 	 l i e ?
1 6 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 S h o w 	 t h a t 	 X Y | | E F .
1 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A B = A C , 	 	 t h e n 	 p r o v e 	 t h a t 	 	 i s 	 a n 	 i s o s c e l l e s
t r i a n g l e .
3 	 / 	 1 2
1 8 . 	 P , 	 Q 	 & 	 R 	 a r e 	 r e s p e c t i v e l y , 	 t h e 	 m i d 	 p o i n t s 	 o f 	 s i d e s 	 B C , 	 C A 	 & 	 A B 	 o f 	 a 	 t r i a n g l e 	 A B C . 	 P R 	 & 	 B Q
m e e t 	 a t 	 X . 	 C R 	 & 	 P Q 	 m e e t 	 a t 	 Y . 	 P r o v e 	 t h a t 	 . 	
1 9 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 O 	 i s 	 t h e 	 c e n t r e 	 o f 	 a 	 c i r c l e . 	 P r o v e 	 t h a t 	 .
2 0 . 	 C o n s t r u c t 	 	 s u c h 	 t h a t 	 B C = 	 8 c m , 	 , 	 A B - A C = 3 . 5 c m
2 1 . 	 I f 	 h , 	 c 	 a n d 	 v 	 r e s p e c t i v e l y , 	 a r e 	 t h e 	 h e i g h t , 	 t h e 	 c u r v e d 	 s u r f a c e 	 a r e a 	 a n d 	 v o l u m e 	 o f 	 a 	 c o n e ,
p r o v e 	 t h a t
2 2 . 	 T h e 	 r a d i u s 	 o f 	 a 	 s p h e r e 	 i s 	 1 0 	 c m . 	 I f 	 t h e 	 r a d i u s 	 i s 	 i n c r e a s e d 	 b y 	 1 	 c m . 	 T h e n 	 p r o v e 	 t h a t
v o l u m e 	 o f 	 t h e 	 s p h e r e 	 i s 	 i n c r e a s e d 	 b y 	 3 3 . 1 % .
S e c t i o n - D
E x p r e s s 	 	 i n 	 t h e 	 f o r m 	 , 	 w h e r e 	 p 	 a n d 	 q 	 a r e 	 i n t e g e r s 	 a n d 	 .
2 4 . 	 V e r i f y :
4 	 / 	 1 2
a
3
	 + 	 b
3
	 + 	 c
3
	 - 	 3 a b c 	
2 5 . 	 A 	 p h a r m a c i s t 	 n e e d s 	 t o 	 s t r e n g t h e n 	 a 	 1 5 % 	 a l c o h o l 	 s o l u t i o n 	 t o 	 o n e 	 o f 	 3 2 % 	 a l c o h o l . 	 H o w
m u c h 	 p u r e 	 a l c o h o l 	 s h o u l d 	 b e 	 a d d e d 	 t o 	 8 0 0 	 m 	 O f 	 1 5 % 	 S o l u t i o n ?
2 6 . 	 I n 	 t h e 	 f i g u r e 	 t w o 	 s t r a i g h t 	 l i n e s 	 P Q 	 & 	 R S 	 i n t e r s e c t 	 e a c h 	 o t h e r 	 a t 	 O . 	 I f 	 , 	 f i n d
t h e 	 v a l u e s 	 o f 	 a , 	 b 	 & c .
2 7 . 	 I n 	 t h e 	 g i v e n 	 f i g u r e , 	 i f 	 A D = B D = C D . 	 P r o v e 	 t h a t 	 	 i s 	 r i g h t 	 a n g l e .
2 8 . 	 I n 	 a 	 p a r a l l e l o g r a m 	 A B C D , 	 E & F 	 a r e 	 t h e 	 m i d 	 P o i n t s 	 s i d e s 	 A B 	 & 	 C D 	 r e s p e c t i v e l y . 	 S h o w 	 t h a t
t h e 	 l i n e 	 s e g m e n t 	 A F 	 & 	 E C 	 t r i s e c t 	 t h e 	 d i a g o n a l 	 B D .
2 9 . 	 T h e 	 r e s i d e n t i a l 	 c o l o n y 	 h a s 	 p o p u l a t i o n 	 o f 	 5 4 0 0 	 a n d 	 6 0 	 l i t r e s 	 o f 	 w a t e r 	 i s 	 r e q u i r e d 	 p e r
p e r s o n 	 p e r 	 d a y . 	 F o r 	 t h e 	 e f f e c t i v e 	 u t i l i z a t i o n 	 o f 	 r a i n 	 w a t e r , 	 a 	 g r o u p 	 o f 	 p e o p l e 	 d e c i d e d 	 f o r
W A T E R 	 H A R V E S T I N G . 	 T h e y 	 c o n s t r u c t e d 	 a 	 w a t e r 	 r e s e r v o i r 	 m e a s u r i n g 	 4 9 m 	 x 	 2 7 m 	 x 	 2 5 m
t o 	 c o l l e c t 	 t h e 	 r a i n 	 w a t e r . 	 I f 	 t h i s 	 w a t e r 	 r e s e r v o i r s 	 i s 	 f u l l 	 o f 	 w a t e r 	 t h e n 	 f o r 	 h o w 	 m a n y 	 d a y s 	 i t
w i l l 	 l a s t 	 f o r 	 t h e 	 c o l o n y
5 	 / 	 1 2
3 0 . 	 T h e 	 F o l l o w i n g 	 t a b l e 	 s h o w s 	 t h e 	 l i f e 	 o f 	 L E D 	 b u l b s .
L i f e 	 T i m e 	 ( i n 	 h o u r s ) 3 0 0 - 4 0 0 4 0 0 - 5 0 0 5 0 0 - 6 0 0 6 0 0 - 7 0 0 7 0 0 - 8 0 0 8 0 0 - 9 0 0 9 0 0 - 1 0 0 0
N o . 	 o f 	 B u l b s 1 4 5 6 6 0 8 6 7 4 6 2 4 8
i . 	 R e p r e s e n t 	 t h e 	 a b o v e 	 i n f o r m a t i o n 	 w i t h 	 t h e 	 h e l p e r 	 a 	 h i s t o g r a m 	 & 	 f r e q u e n c y 	 p l o y g o n .
i i . 	 H o w 	 m a n y 	 b u l b s 	 h a v e 	 a 	 l i f e t i m e 	 o f 	 7 0 0 	 h o u r s 	 & 	 m o r e ?

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FAQs on Class 9 Math: Sample Practice Question Paper- 1 (With Solutions)

1. What is the importance of practicing sample question papers for Class 9 Math?

Ans. Practicing sample question papers for Class 9 Math is important as it helps students understand the exam pattern, familiarize themselves with different types of questions, and improve their time management skills. It also allows them to identify their weak areas and work on them before the actual exam.

2. How can sample practice question papers help in preparing for Class 9 Math exams?

Ans. Sample practice question papers provide students with an opportunity to assess their knowledge and understanding of the subject. By solving these papers, they can gauge their level of preparedness and identify areas where they need to focus more. It also helps them in developing a strategy to attempt the actual exam and boosts their confidence.

3. Are the solutions provided with the sample practice question papers helpful?

Ans. Yes, the solutions provided with the sample practice question papers are extremely helpful. They not only help students understand the correct method of solving a particular problem but also provide them with a step-by-step explanation. It enables students to learn from their mistakes and improve their problem-solving skills.

4. How should one use the sample practice question papers effectively for Class 9 Math preparation?

Ans. To use the sample practice question papers effectively, students should start by attempting the questions without referring to the solutions. Once they have completed the paper, they can compare their answers with the provided solutions and identify any mistakes or areas where they struggled. They should then revise those topics and attempt the paper again to assess their progress.

5. Can solving sample practice question papers guarantee success in Class 9 Math exams?

Ans. Solving sample practice question papers alone cannot guarantee success in Class 9 Math exams. However, it is an essential part of the preparation process. Regular practice with these papers can improve a student's problem-solving skills, accuracy, and speed. It enhances their overall understanding of the subject and increases their chances of performing well in the exams.

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