SAMPLE PAPER SA 1

              KENDRIYA VIDYALAYA BIJAPUR

                       SA-1 PRACTICE PAPER   2015-2016

Subject: math’s                                                    class : X                                      marks : 90                                                                                                                                         ------------------------------------------------------------------------

                               SECTION – A

Q1) what is the relationship between median, mode and mean.

(a)          Median= mode + mean

(b)         3median= mode+2 mean

(c)           Median = 2mode+3mean

(d)         2 median=2mode+mean

Q2) the graph of y=p(x) is given below. find the number of zeroes of p(x) in each case.

 a) 1          b) 2              c) 3                 d) 4  

       

 Q3) write the missing numbers x and y in the following factor tree ?

Q4)in given fig DE ll BC where AD=1.5 cm , AE=1 Cm BD=3cm , find EC.
  

SECTION B 

                                                          

QUESTION NUMBER 5 TO 10 CARRIES TWO MARK EACH  

Q5) find the zero of the following polynomial : 

              6x²- 3 - 7x 
Q6) divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder 
              i)       x3-3x²+5x-3         , g(x)= X2-2

Q7 ) if sinA=3/4 calculate cosA and tanA
Q8) let triangle ABC is congruent to triangle DEF and their areas be respectively 64 Cm2  AND  121 Cm2 . if EF=15.4 cm , find BC ? 

Q9)    Length (in mm)            Number of leaves
             118 - 126                           3
             127 - 135                           5
             136 - 144                           9
             145 - 153                          12
             154 - 162                           5
             163 - 171                           4
             172 - 180                           2

the length of 40 leaves of a plant are measured correct to the nearest  millimeter and the data obtained is represented in the above table ; find the median length of the leaves .

Q10) evaluate the following:
                                            
                             sin 30° + tan 45° – cosec 60° 
                             _______________________
                              sec 30° + cos 60° + cot 45°   
                            
                                       SECTION -C 

SECTION -C CARRIES 3 MARKS EACH

Q11) explain why 7x11x13+13 and 7x6x5x4x3x2x1+5   are composite numbers.

Q12) prove that  3+ 2root5 is irrational .

Q13) solve the following pair of linear equation ; 
                3x - y = 3.,9x-3y= 9                                                                                        
Q14) a fraction becomes 9/11 , if 2 is added to both the numerator and denominator ; if 3 is added to both the numerator and the denominator it become 5/6 find the fraction.

Q15 ) evalute : 
                     sin2 63+ sin2 27
                             -----------------------------
                    cos2 17+cos2 73 
Q16) in DE ll OQ and DF ll OR show that EF ll QR  

                     

             


       
                            
                             





Q17 ) in an equilateral triangle ABC , D is a point on side BC such  that BD=1/3 BC ,prove that 9 AD2 = 7 AB2  

Q18) 1+secA         =    sin2A   
        ---------             -------      prove that                                         secA             1- cosA    

Q19) the following table shows the age of the patients admitted in a hospital during a year : 
     
           Age (in years)                   number of patients 
                   5-15                                   6                 
                  15-25                                  11                
                  25-35                                  21                  
                  35-45                                  23
                  45-55                                  14               
                  55-65                                    5              
  find the mode of the data given?

Q20)  the following table gives the literacy rate ( in %) of 35 cities. find the mean literacy rate .
              
   

Literacy rate	45-55	55-65	65-75	75-85	85-95
Number of cities	03	10	11	08	03

                                          
                                     SECTION- D  

SECTION D CONTAINS 4 MARKS EACH 

Q21) prove that root 5 is irrational.

Q22) two poles of height 6m and 11 m stands on a plane ground . if the distance between the feet of the poles is 12 m . find the distance between their top .

Q23) if AD and PM are median of triangle ABC and PQR respectively where triangle ABC is congruent to triangle PQR prove that : AB/PQ = AD/PM.

Q24) if cotθ=7/8 . evaluate i) (1+sinθ) (1-sinθ) 
                                                --------------------
                                                (1+ cosθ) (1-cosθ)
                      ii) cot2θ 

Q25) 1+tan2A               

         -----------     =   
         1+cot2A 

Q26) (sin A + cosec A)2 + (cos A + sec A)2 = 7 + tan2A + cot2A.

Q27) find the equation for given pair of linear equation grapically
                    x+y=5 ,  2x + 2y = 10

Q28) the following distribution gives the daily income of 50 workers of a factory
     daily                                          no of 
      income (in rs)                         workers                                   
       100-120                       -                     12
        120-140                     -                     14
        140-160                     -                     08
        160-180                     -                     06
        180-200                     -                     10
       convert the distribution above to a less than type cumulative frequency distribution ,and draw its ogive.

Q29) obtain all other zeroes of 3x4 + 6x3 - 2x2-10x-5 if two of its zeroes are root 5/3 and - root 5/3. 

Q30) draw the graph of the equation x-y+1=0 and 3x+2y-12=0.determine the coordinates of the vertices of the triangle formed by the lines and the x-axis and shade the triangular region.

Q31) 100 surnames were randomly picked up from a local telephone and the frequency distribution of the number of letters in the english alphabets in the surnames was obtained as follows :

       no of                                    no of surnames
       letters                                       
          1-4                                        6
          4-7                                       30
          7-10                                      40
        10-13                                  16                                                   13-16                                   4
         16-19                                   4
determine the median number of letters in the surnames....


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WORKSHEET ON TRIANGLE

    

worksheet on real number

                     KENDRIYA  VIDYALAYA  VIJAYAPUR

Topic: Real Number

Name:                                                                                         Class:10

1.    If the HCF of 65 and 117 is expressible in the form 65 m -117,then the value of m is:

a)    4

b)    2

c)     3

d)    1

2.    If d =HCF (48,72), the value of d is:

a)    24

b)    48

c)     12

d)    72

3.    Given that HCF (26,91)=13,then LCM of (26,910 is:

a)    2366

b)    182

c)     91

d)    364

4.    If p,q are two consecutive natural numbers, then HCF (P,q) is:

a)    q

b)    p

c)     1

d)    Pq

5.    If p,q are two co-prime number.HCF (p,q) is:

a)    P

b)    q

c)     pq

d)    1

6.    If d=LCM (36,198),then the value of d is:

a)    396

b)    198

c)     36

d)    1

7.    If the HCF Of 85 and 153 is expressible in the form 85n-153, then value of n is:

a)    3

b)    2

c)     4

d)    1

8.    Given that LCM (91,26)=182,yhyen HCF (91,26) is:

a)    13

b)    26

c)     7

d)    9

9.    A rational number can be expressed as a terminating decimal if the denominator has factors

a)    2,3 or 5

b)    2 or 3

c)     3 or 5

d)    2 or 5

10. If least prime factor of a is 3 and least prime factors of b is 7:

a)    2

b)    3

c)     5

d)    11

11.If the HCF of 65 and 117 is expressible in form 65m – 117 ,then the  value                                   of m is:

a)    4

b)    2

c)     1

d)    3

12. According to Euclid’s division algorithm using Euclid’s division lemma for                   any positive integer a and b with a>b enables to find:

a)    HCF

b)    LCM

c)     Decimal expression

d)    Probability

13.If two positive integers a and b are written as a=x²y² and b=xy²; x,y are prime numbers then (a,b) is:

a)    Xy

b)    Xy

c)     x²y³

d)    x²y²

14.According to Euclid’s division algorithm HCf of any two positive integers a and  b with a>b  with a>b is obtained by appling Euclid’s division lemma to a and b to find p and q such that a=bq+r where r must satisify.

a)    1<r<b

b)    0<r<b

c)     0≤r<b

d)    0<r≤b

15.(√2-√3)(√3+√2)

a)    A real number

b)    A whole number

c)     A n irrational number

d)    A natural number

16.If n is any natural number , then which of the following expression ends with 0:

a)    (3*2)ⁿ

b)    (4*3)ⁿ

c)     (2*5)ⁿ

d)    (6*2)ⁿ

17.If two positive integersp and q can be expressed as

P=ab² and q=a³b; and a, b being prime numbers, then LCM (p,q) is

a)    ab

b)    a²b²

c)     a³b²

d)    a³b³

18.n-1 is divisible by 5, if n is of the form

a)    5K

b)    5K+1

c)     5K-1

d)    2K

19.For some integer ‘ x’ , every odd integer is of the form

a)    2x

b)    x+1

c)     x-1

d)    2x+1

20.The necessary condition on ‘n’ is irrational will be that

a)    n is a perfect sqare

b)    n is negative integer

c)     n is not a perfect square

d)    nothing can be said

21.  Which of the following is not irrational number?

a)    5-√3

b)    √5+√3

c)     4+√2

d)    5+√9

22.119²-111² is:

a)    Prime number

b)    Composite number

c)     An odd prime number

d)    An odd composite number

23.If a ,b are composite , then a²,b² are:

a)    Co-prime

b)    Not co-prime

c)     Odd number

d)    Even number

24. The decimal expansion of7/125 will terminate after how many places of decimal

a)    1

b)    2

c)     3

d)    43

25.Given that HCF(253,440)=11 and LCM(253,440)=253*R. The value of R is

a)    440

b)    40

c)     440

d)    253

26. n²-1 is divisible by 8, if n is

a)    An integer

b)    A natural number

c)     An odd integer

d)    An even integer

27.Euclid’s division lemma states that for two positive integers a and b, there exit unique integers q and r such that a=bq+r, where r must satisfy

a)    1<r<b

b)    0<r≤b

c)     0≤r<b

d)    0<r<b

28.( 2+√5)(2+√5) expansion is:

a)    A rational number

b)    A whole number

c)      An irrational number

d)    A natural number

29.Which is not an irrational number

a)    5-√3

b)    √2+√5

c)     4+√2

d)    6+√9

30.If p and q are odd positive  integers then sum of squares of these two numbers is

a)    Always odd

b)    Always even

c)     Integer

d)    Nothing can be said