# Sample Paper | Class IX | Mathematics | CBSE | 2008

Sample Paper – 2008

Class – Mathematics

Class – IX

# General Instructions:

( i  ) All questions are compulsory.

( ii )  The question  paper consists of 30 questions divided  into four sections –A, B, C

and  D. Section  A  contains  10  questions of  1  mark  each, Section  B  is of  5

questions of  2 marks  each, Section  C  is of 10 questions of 3 marks each  and

section  D is  of  5 questions of 6 marks each.

( iii )   There  is  no  overall choice. However, an internal choice   has been provided in

sections B,C and D

( iv )  In  question   on  construction,  the  drawing  should be  neat and  exactly as per

the given measurements.

( v )  Use of calculator is not permitted.

SECTION A

( Qns 1 – 10 carry 1 mark each )

1. Find four rational numbers between 3/5 and 4/5.
2. Find P(1) and P(2) if P(x)=  3x+1
3. In which quadrant or on which axis do each of the following points lie? . (- 2,4), (-1, 0) , (1,2) and (-3, -5)
4. Find the value of  k  if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
5. Write any two postulates ofEuclid
6. If x + y = w + z , then show that AOB is a line  AD and BC equal perpendiculars to a line segment AB ,Show that CD bisects AB

1. Find x and y if AB // CD , Ð APQ = 500 and Ð PRD = 1270.

1. Evaluate 103 ×107 by using a suitable identity.
2. Simplify 22/3 . 21/3 .
3. Write two solutions of 2x + y = 7.

SECTION – B

( Qns 11 – 16 carry 2 marks each )

1. Find remainder when x3  + 3x2  + 3x +1 is divided by (x-1) by using factor theorem.
2. Prove that angle opposite to equal sides of an isosceles triangle are equal.
3. Draw the graph of x + y = 3 .
4. Expand (x – 2y )3
5. Expand (2x + 1) 3  .
6. Rationalise  1/ ?7.

SECTION – C

( Qns 17 – 28 carry 3 marks each )

1. Find the value of k  if x – 1 is a  factor of x2  – 3x  + k

1. Simplify 1/ (?7 – ?2).
2. Factorise  9x2  + 6xy + y2
3. Solve 2x + 1= x – 3 and represent  the solutions on the Cartesian plane.
4. In figure , line PQ and RS intersect each other at O. IfÐ  POR : Ð  ROQ = 5:7.Find all the angles.

1. Prove that the sum of the angles of a triangle is 180.

1. In figure  OA =OBand OC =OD Show that ?AOD  @ ?BOC.

1. In ?ABC ,the bisector AD of A is perpendicular to BC. Show that AB =AC.

1. In figure QT^ PR, Ð TQR =40 and Ð SPR =30 ,find x and y.

1. Express the following equations in the form of ax + by + c =0 (i) x – y/5 =10

(ii) y-2 =0

1. Express 0.3333….. in the form of p/q.
2. Evaluate (999)3.

SECTION – C

( Qns 29 – 34 carry 6marks each )

1. Factorise 49a2 + 70ab + 25b2      (i) 25/4 x2 – y2 / 9
2. If the point (3,4) lies on the graph 3y= ax +7,find the value of a.
3. In figure the sides AB and AC of a triangle are produced to points E and D respectively  .If bisectors BF and CG of  ÐCBE and Ð BCD respectively meet at the point O ,then prove that ÐBOC = 90 -1/2 ÐBAC.

1. Line segment AB is parallel to another line segment CD,O is themid-point  ofAD. Show that (i) ?AOB @ ?DOC    (ii) O is also themid-point  ofBC.

1. In an isosceles triangle ABC with AB =AC , D and E are points on BC such that BE=CD. Show that AD=AE.

34.Factorise (i) 8x3  –  64y 3  (ii) 125a3  + 27b3     .

—————————————