Sample Paper | Class IX | Mathematics | CBSE | 2008
Sample Paper – 2008
Class – Mathematics
Class – IX
( 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.
( 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 = 500 and Ð PRD = 1270.
- Evaluate 103 ×107 by using a suitable identity.
- Simplify 22/3 . 21/3 .
- Write two solutions of 2x + y = 7.
SECTION – B
( Qns 11 – 16 carry 2 marks each )
- Find remainder when x3 + 3x2 + 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 x2 – 3x + k
- Simplify 1/ (?7 – ?2).
- Factorise 9x2 + 6xy + y2
- 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 49a2 + 70ab + 25b2 (i) 25/4 x2 – y2 / 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) 8x3 – 64y 3 (ii) 125a3 + 27b3 .