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

**Sample Paper – 2008**

**Class – Mathematics**

**Class – IX **

** **

# Marks: 80

# 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 )

- Find four rational numbers between 3/5 and 4/5.
- Find P(1) and P(2) if P(x)= 3x+1
- In which quadrant or on which axis do each of the following points lie? . (- 2,4), (-1, 0) , (1,2) and (-3, -5)
- Find the value of k if x = 2, y = 1 is a solution of the equation 2x + 3y = k.
- Write any two postulates ofEuclid
- 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

- Find x and y if AB // CD , Ð APQ = 50
^{0}and Ð PRD = 127^{0}.

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

**SECTION – B**

( Qns 11 – 16 carry 2 marks each )

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

**SECTION – C**

( Qns 17 – 28 carry 3 marks each )

- Find the value of k if x – 1 is a factor of x
^{2}– 3x + k

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

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

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

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

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

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

(ii) y-2 =0

- Express 0.3333….. in the form of p/q.
- Evaluate (999)
^{3}.

**SECTION – C**

( Qns 29 – 34 carry 6marks each )

- Factorise 49a
^{2}+ 70ab + 25b^{2}(i) 25/4 x^{2}– y^{2}/ 9 - If the point (3,4) lies on the graph 3y= ax +7,find the value of a.
- 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.

- 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.

- 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) 8x^{3} – 64y ^{3} (ii) 125a^{3} + 27b^{3 }.

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