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# Maths Past Year Paper SA-1(Set -14) - 2014, Class 10, CBSE Class 10 Notes | EduRev

## Class 10 : Maths Past Year Paper SA-1(Set -14) - 2014, Class 10, CBSE Class 10 Notes | EduRev

``` Page 1

Summative Assessment-1 2014-2015
Mathematics
Class – X

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) Question paper contains 31 questions divide into 4 sections A, B, C and D.
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry
3 marks each. Question No. 21 to 31 carry 4 marks each.
d) There are no overall choices in the question paper.
e) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry 1 mark each.
1. In the figure l m  , 90 AOD ? = ° and 30 ODB ? = ° . Are OAC ? and ODB ? similar? If yes, by
which criterion?

2. In ABC ? , 90 C ? = ° , 45 A ? = ° and AB=10cm. find BC, using trigonometric ratios.
3. Find the value of
2 2
sin 12 sin 78 ° + ° .
4. If ‘less than type ogive’ and ‘more than type ogive’ for a given data are given, then how can
you find its median?

Section B
Question numbers 5 to 10 carry two marks each.
5. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division.
6. Find the prime factorization of the denominator of rational number expressed as 6. 12 in
simplest form.
7. Solve the following pair of linear equations using elimination method:
2x+3y=2 4x-3y-1
8. Two pillars of height 70m and 20m are standing 120m apart. If distance between their feet is
120m, find the distance between their tops.
Page 2

Summative Assessment-1 2014-2015
Mathematics
Class – X

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) Question paper contains 31 questions divide into 4 sections A, B, C and D.
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry
3 marks each. Question No. 21 to 31 carry 4 marks each.
d) There are no overall choices in the question paper.
e) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry 1 mark each.
1. In the figure l m  , 90 AOD ? = ° and 30 ODB ? = ° . Are OAC ? and ODB ? similar? If yes, by
which criterion?

2. In ABC ? , 90 C ? = ° , 45 A ? = ° and AB=10cm. find BC, using trigonometric ratios.
3. Find the value of
2 2
sin 12 sin 78 ° + ° .
4. If ‘less than type ogive’ and ‘more than type ogive’ for a given data are given, then how can
you find its median?

Section B
Question numbers 5 to 10 carry two marks each.
5. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division.
6. Find the prime factorization of the denominator of rational number expressed as 6. 12 in
simplest form.
7. Solve the following pair of linear equations using elimination method:
2x+3y=2 4x-3y-1
8. Two pillars of height 70m and 20m are standing 120m apart. If distance between their feet is
120m, find the distance between their tops.

9. If cos sin x a b ? ? = - and sin cos y a b ? ? = + , then prove that
2 2 2 2
a b x y + = + .
10. Form a frequency table for that the following cumulative frequency distribution.
Class limits More than
0
More than
10
More than
20
More than
30
More than
40
More than
50
Cumulative
Frequency
50 48 45 32 15 5

Section C
Question numbers 11 to 20 carry three marks each.
11. Show that 8
n
can never end with digit 0 for any natural number n.
12. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k.
13. On dividing
4 3 2
2 4 4 7 2 x x x x - - + + by a polynomial g(x), the quadrant and the remainder
were
2
2 4 x x - and 2x-2 respectively. Find g(x).
14. Ifa and ß are zeroes of a polynomial
2
8 6 9 x x + + , then form a polynomial whose zeroes are
2a and 2ß .
15. In ABC ? from any interior point O in the ? , OD BC ? and OE AC ? and OF AB ? are
drawn. Prove that
2 2 2 2 2 2 2 2 2
OA OB OC OD OE OF AF BD CE + + = + + + + +

16. A vertical pole of length 8 m costs a shadow 6 m long on the ground and at the same time a
tower casts a shadow 30 m long. Find the height of tower.
17. If tan A + cot A=2, then find the value of
2 2
tan cot A A +
18. Find the value of:
2 2
2 2
cos 67 tan 23 sin 59
sin 17 sin 73 cos31
ec ° - ° °
+
° + ° °

19. Traffic police of a city gave following distribution showing number of victims and their ages
in accidents in a year in their city. Find the median.
Age of victims
(in years)
0-15 15-30 30-45 45-60 60-75 75-90
Number of
victims
15 35 40 20 8 2
20. Weights of class IX students of a school are given in the following frequency distribution:
Weights (in kg) 35-40 40-45 45-50 50-55 55-60 60-65 65-70
Number of
students
2 9 15 25 12 6 1
Find the mode.

Page 3

Summative Assessment-1 2014-2015
Mathematics
Class – X

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) Question paper contains 31 questions divide into 4 sections A, B, C and D.
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry
3 marks each. Question No. 21 to 31 carry 4 marks each.
d) There are no overall choices in the question paper.
e) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry 1 mark each.
1. In the figure l m  , 90 AOD ? = ° and 30 ODB ? = ° . Are OAC ? and ODB ? similar? If yes, by
which criterion?

2. In ABC ? , 90 C ? = ° , 45 A ? = ° and AB=10cm. find BC, using trigonometric ratios.
3. Find the value of
2 2
sin 12 sin 78 ° + ° .
4. If ‘less than type ogive’ and ‘more than type ogive’ for a given data are given, then how can
you find its median?

Section B
Question numbers 5 to 10 carry two marks each.
5. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division.
6. Find the prime factorization of the denominator of rational number expressed as 6. 12 in
simplest form.
7. Solve the following pair of linear equations using elimination method:
2x+3y=2 4x-3y-1
8. Two pillars of height 70m and 20m are standing 120m apart. If distance between their feet is
120m, find the distance between their tops.

9. If cos sin x a b ? ? = - and sin cos y a b ? ? = + , then prove that
2 2 2 2
a b x y + = + .
10. Form a frequency table for that the following cumulative frequency distribution.
Class limits More than
0
More than
10
More than
20
More than
30
More than
40
More than
50
Cumulative
Frequency
50 48 45 32 15 5

Section C
Question numbers 11 to 20 carry three marks each.
11. Show that 8
n
can never end with digit 0 for any natural number n.
12. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k.
13. On dividing
4 3 2
2 4 4 7 2 x x x x - - + + by a polynomial g(x), the quadrant and the remainder
were
2
2 4 x x - and 2x-2 respectively. Find g(x).
14. Ifa and ß are zeroes of a polynomial
2
8 6 9 x x + + , then form a polynomial whose zeroes are
2a and 2ß .
15. In ABC ? from any interior point O in the ? , OD BC ? and OE AC ? and OF AB ? are
drawn. Prove that
2 2 2 2 2 2 2 2 2
OA OB OC OD OE OF AF BD CE + + = + + + + +

16. A vertical pole of length 8 m costs a shadow 6 m long on the ground and at the same time a
tower casts a shadow 30 m long. Find the height of tower.
17. If tan A + cot A=2, then find the value of
2 2
tan cot A A +
18. Find the value of:
2 2
2 2
cos 67 tan 23 sin 59
sin 17 sin 73 cos31
ec ° - ° °
+
° + ° °

19. Traffic police of a city gave following distribution showing number of victims and their ages
in accidents in a year in their city. Find the median.
Age of victims
(in years)
0-15 15-30 30-45 45-60 60-75 75-90
Number of
victims
15 35 40 20 8 2
20. Weights of class IX students of a school are given in the following frequency distribution:
Weights (in kg) 35-40 40-45 45-50 50-55 55-60 60-65 65-70
Number of
students
2 9 15 25 12 6 1
Find the mode.

Section D
Question numbers 21 to 31 carry four marks each.
21. Find the HCF of 256 and 36 using Euclid’s Division Algorithm. Also find their LCM and verify
that HCF LCM × =product of the two numbers.
22. The owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol/diesel.
The taxi charges in city comprises of fixed charges together with the charge for the distance
covered. For a journey of 12 km, the charge paid is Rs. 89 and for 20 km, the charge paid is
Rs. 145.
a) What will a person have a pay for travelling a distance of 30 km?
b) Why did he decide to use CNG for his taxi as a fuel?
23. Obtain all other zeroes of the polynomial
4 3 2
5 6 2 4 x x x x - + + - , if two of its zeroes are 1 3 +
and 1 3 -
24. A fraction becomes
1
2
when 1 is added to the numerator and it becomes
1
3
when 1 is
subtracted from the numerator and 2 is added to the denominator. Find the fraction. Also
find the number obtained when 5 is added to numerator and 4 is subtracted from the
denominator.
25. If ABC PQR ? ? ~ and ( ) ( ) ar ABC ar PQR ? = ? then prove that ABC PQR ? ? ? .
26. Prove: If a line is drawn parallel to one side of a triangle intersecting other two sides at
distinct points then it divides other two sides in equal ratio
27. If 30 ? = ° , verify the following:
a)
3
cos3 4cos 3cos ? ? ? = -
b) sin 2 2sin cos ? ? ? =
28. If
15
cot
8
? = , evaluate:
4cot 5sec 8cos
4
5tan cot 17sin
3
ec ? ? ?
? ? ?
- - + -
29. If cosec A + cot A=m, show that
2
2
1
cos
1
m
A
m
- =
+

30. Literacy rates of 40 cities is given in the following table. If it is given that mean literacy rate is
63.5, then find the missing frequencies x and y.
Literacy
rate
(in%)
35-
50
40-
45
45-
50
50-
55
55-
60
60-
65
65-
70
70-
75
75-
80
80-
85
85-
90
Number
of cities
1 2 3 x y 6 8 4 2 3 2

31. On the annual day of a school, age – wise participation of student is given in the following
frequency distribution table:
Age (in
years)
Less than
6
Less than
8
Less than
10
Less than
12
Less than
14
Less than
16
Less than
18
Number of 2 6 12 22 42 67 76
Page 4

Summative Assessment-1 2014-2015
Mathematics
Class – X

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) Question paper contains 31 questions divide into 4 sections A, B, C and D.
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to
10 are of short answer type questions, carrying 2 marks each. Question No. 11 to 20 carry
3 marks each. Question No. 21 to 31 carry 4 marks each.
d) There are no overall choices in the question paper.
e) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry 1 mark each.
1. In the figure l m  , 90 AOD ? = ° and 30 ODB ? = ° . Are OAC ? and ODB ? similar? If yes, by
which criterion?

2. In ABC ? , 90 C ? = ° , 45 A ? = ° and AB=10cm. find BC, using trigonometric ratios.
3. Find the value of
2 2
sin 12 sin 78 ° + ° .
4. If ‘less than type ogive’ and ‘more than type ogive’ for a given data are given, then how can
you find its median?

Section B
Question numbers 5 to 10 carry two marks each.
5. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division.
6. Find the prime factorization of the denominator of rational number expressed as 6. 12 in
simplest form.
7. Solve the following pair of linear equations using elimination method:
2x+3y=2 4x-3y-1
8. Two pillars of height 70m and 20m are standing 120m apart. If distance between their feet is
120m, find the distance between their tops.

9. If cos sin x a b ? ? = - and sin cos y a b ? ? = + , then prove that
2 2 2 2
a b x y + = + .
10. Form a frequency table for that the following cumulative frequency distribution.
Class limits More than
0
More than
10
More than
20
More than
30
More than
40
More than
50
Cumulative
Frequency
50 48 45 32 15 5

Section C
Question numbers 11 to 20 carry three marks each.
11. Show that 8
n
can never end with digit 0 for any natural number n.
12. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k.
13. On dividing
4 3 2
2 4 4 7 2 x x x x - - + + by a polynomial g(x), the quadrant and the remainder
were
2
2 4 x x - and 2x-2 respectively. Find g(x).
14. Ifa and ß are zeroes of a polynomial
2
8 6 9 x x + + , then form a polynomial whose zeroes are
2a and 2ß .
15. In ABC ? from any interior point O in the ? , OD BC ? and OE AC ? and OF AB ? are
drawn. Prove that
2 2 2 2 2 2 2 2 2
OA OB OC OD OE OF AF BD CE + + = + + + + +

16. A vertical pole of length 8 m costs a shadow 6 m long on the ground and at the same time a
tower casts a shadow 30 m long. Find the height of tower.
17. If tan A + cot A=2, then find the value of
2 2
tan cot A A +
18. Find the value of:
2 2
2 2
cos 67 tan 23 sin 59
sin 17 sin 73 cos31
ec ° - ° °
+
° + ° °

19. Traffic police of a city gave following distribution showing number of victims and their ages
in accidents in a year in their city. Find the median.
Age of victims
(in years)
0-15 15-30 30-45 45-60 60-75 75-90
Number of
victims
15 35 40 20 8 2
20. Weights of class IX students of a school are given in the following frequency distribution:
Weights (in kg) 35-40 40-45 45-50 50-55 55-60 60-65 65-70
Number of
students
2 9 15 25 12 6 1
Find the mode.

Section D
Question numbers 21 to 31 carry four marks each.
21. Find the HCF of 256 and 36 using Euclid’s Division Algorithm. Also find their LCM and verify
that HCF LCM × =product of the two numbers.
22. The owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol/diesel.
The taxi charges in city comprises of fixed charges together with the charge for the distance
covered. For a journey of 12 km, the charge paid is Rs. 89 and for 20 km, the charge paid is
Rs. 145.
a) What will a person have a pay for travelling a distance of 30 km?
b) Why did he decide to use CNG for his taxi as a fuel?
23. Obtain all other zeroes of the polynomial
4 3 2
5 6 2 4 x x x x - + + - , if two of its zeroes are 1 3 +
and 1 3 -
24. A fraction becomes
1
2
when 1 is added to the numerator and it becomes
1
3
when 1 is
subtracted from the numerator and 2 is added to the denominator. Find the fraction. Also
find the number obtained when 5 is added to numerator and 4 is subtracted from the
denominator.
25. If ABC PQR ? ? ~ and ( ) ( ) ar ABC ar PQR ? = ? then prove that ABC PQR ? ? ? .
26. Prove: If a line is drawn parallel to one side of a triangle intersecting other two sides at
distinct points then it divides other two sides in equal ratio
27. If 30 ? = ° , verify the following:
a)
3
cos3 4cos 3cos ? ? ? = -
b) sin 2 2sin cos ? ? ? =
28. If
15
cot
8
? = , evaluate:
4cot 5sec 8cos
4
5tan cot 17sin
3
ec ? ? ?
? ? ?
- - + -
29. If cosec A + cot A=m, show that
2
2
1
cos
1
m
A
m
- =
+

30. Literacy rates of 40 cities is given in the following table. If it is given that mean literacy rate is
63.5, then find the missing frequencies x and y.
Literacy
rate
(in%)
35-
50
40-
45
45-
50
50-
55
55-
60
60-
65
65-
70
70-
75
75-
80
80-
85
85-
90
Number
of cities
1 2 3 x y 6 8 4 2 3 2

31. On the annual day of a school, age – wise participation of student is given in the following
frequency distribution table:
Age (in
years)
Less than
6
Less than
8
Less than
10
Less than
12
Less than
14
Less than
16
Less than
18
Number of 2 6 12 22 42 67 76

students
Draw a ‘less than type’ ogive for the above data. Also, find median from the curve.
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