CLASS 9 | GUESS PAPER | MATH | CBSE

 

Half-Yearly Examination 2019

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

M.M.  80      Set:B

General Instructions:

·         All questions are compulsory.

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

Section-A                                                        1×6=6

1.      Find a rational numbers between 2 and 3.

2.      Determine the degree of the polynomial x³-5x+2.

3.      In which quadrant does the point (-7,-4) lie?

4.      In the given figure ,if AC=BD, then prove that AB=CD

5.      Find the measures of an angle which is 32° less than its supplement.

6.      Two supplementary angles are in the ratio 3:2. Find the angles.

  Section-B                                                       2×6=12

7.      Express 1.4̅ as a fraction in simplest form.

8.      Find the remainder when x⁴+x³-2x²+x+1 is divided by x-1.

9.      In which quadrants do the given points lie?

a)      (4,-2)     (b) (-3,7)   (c) (-1,-2)   (d) (3,6)

10.  If x=3k+2 and y=2k-1 is a solution of the equation 4x-3y+1=0, find the value of k.

11.  In the given figure, a ∆ABC is given in which AB=BC and BX=BY .Show that AX=CY.  

12.  Three angles of a quadrilateral are in the ratio 3:5:9:13.Find all angles of the quadrilaterals.

Section-C                                                     3×10=30

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

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

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

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

OR

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

17.  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?

18.  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.

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

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

21.  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

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

Section-D                                                           4×8=32

23.  Prove that

OR

            If   ,show that qx²-px+q=0

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

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

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

27.  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.

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

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

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

 

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