Class 9 | math | sample paper

 

Annual Examination 

Class :IX                   Subject :MATHEMATICS     Time: 03:00 Hour

M.M.  80      Set:A  

General Instructions:

·         All questions are compulsory.

·         Numerals in right side margined indicates the marks of respective question.

Section-A                                                        1×6=6

1.      Choose correct option from the following:

                    i.       

  Section-B                                                       2×6=12

2.      Express 0.5̅7̅ in the form of p/q, where p and q are integers.

3.      The polynomial 2x³-kx²+ 7x -1 when divided by x-1 leaves the remainder 3.Then find the value of k.

4.      Find distances of points C (-3,-2) and D (5, 2) from x-axis and y-axis.

5.      If x=2, y=1 is a solution of the equation 2x+3y=k, find the value of k.

6.      State any two Euclid’s axioms.

7.      Three angles of a quadrilateral measure 110°, 82° and 68° .Find the measure of the fourth angle.

Section-C                                                     3×10=30

8.      Represent √̅1̅0̅.̅5 on the number line.

9.      Find the values of a and b, if  = a + b .

10.  Find the value of (x-y)³ + (y-z)³ + (z-x)³.

11.  If a+b+c=5 and ab + bc + ca =12, find a²+b²+c².

OR

         Factorise: (i) x²+5x-24       (ii) x²-4x-21.

12.  In which quadrant or on which axis do each of the points (-2,4), (3,-1), (-1,1), (1,2),   (-3,-5), (5,0 ) lie?

13.  There are two scales of measuring the temperature, namely degree Fahrenheit (°F) and degree  Celsius (°C). The relation between the two scales is given by F=  C + 32.

                                  i.            If the temperature is 50°C .What is the temperature in Fahrenheit?

                                ii.            If the temperature is 86°F .What is the temperature in celsius?

                              iii.            Find the numeral value of the temperature which is the same in both the scales.

14.  Prove that every line segment has one and only one mid point.

15.  If in the figure , AB∥CD and CD∥EF, then find ∠BCE.

16.  Let ∆ABC and ∆DEF be two triangles given in such a way that AB∥DE ,AB=DE, BC∥EF and BC=EF.

Prove that (i) AC∥DF and AC =DF

                    (ii) ∆ABC≅∆DEF

17.  Construct an angle of 75° using ruler and compass only.

Section-D                                                           4×8=32

18.  Prove that

OR

            If   ,show that qx²-px+q=0

19.  Verify that : x³+y³+z³-3xyz= (x+y+z)[(x-y)²+(y-z)²+(z-x)²]

20.  Plot the points (2,3), (3,-4) ,(-4,5), (-5,-6), (-2,0), (0,5), (0,-5), and (-5,0) on the graph sheet.

21.  Draw the graph of equation x+ 2y-3=0

22.  P,Q,R and S are respectively the mid points of the sides AB,BC,CD and DA of a quadrilateral ABCD.Show that

                                i.            PQ∥AC and PQ= AC.

                              ii.            PQ∥SR                                                                            

                            iii.            PQRS is a parallelogram.

23.  If the bisectors of angles ABC and ACB of a triangle ABC meet at a point O, then prove that ∠BOC=90°+ A.

24.  Prove that the sum of all the four angles of a quadrilateral is 360°.

25.  Construct a ∆ABC in which BC=6cm, ° and AB+AC=9cm.Measure AB and AC.

 

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