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.
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 ?
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 .
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
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....
------------------------------------END-------------------------------
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 ?
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....
------------------------------------END-------------------------------
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