Maths Past Year Paper SA-1(Set -13) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Past Year Papers For Class 10

Class 10 : Maths Past Year Paper SA-1(Set -13) - 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 ABC ? , D and E are points on the sides AB and AC respectively such that DE BC  . If 
AB=6.75cm, AC=8.50cm and EC=6.8cm, then find BD. 
2. If 24 cot A=7, find the value of sin A. 
3. If 45 ? = ° , then find the value of
2 2
2cos 3sec ec ? ? + . 
4. What is the mean of x, x+1, x+2, x+3, x+4 and x+5? 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Find the HCF of the number 31, 310 and 3100. 
6. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division. 
7. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 5 
respectively. 
8. In the figure if AC=2m, OC=3m and OD=7m, then find BD. 
 
9. Solve the equation for? :
2
2 2
cos
3
cot cos
?
? ?
=
- 
10. Calculate the mode of the following data: 
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 ABC ? , D and E are points on the sides AB and AC respectively such that DE BC  . If 
AB=6.75cm, AC=8.50cm and EC=6.8cm, then find BD. 
2. If 24 cot A=7, find the value of sin A. 
3. If 45 ? = ° , then find the value of
2 2
2cos 3sec ec ? ? + . 
4. What is the mean of x, x+1, x+2, x+3, x+4 and x+5? 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Find the HCF of the number 31, 310 and 3100. 
6. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division. 
7. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 5 
respectively. 
8. In the figure if AC=2m, OC=3m and OD=7m, then find BD. 
 
9. Solve the equation for? :
2
2 2
cos
3
cot cos
?
? ?
=
- 
10. Calculate the mode of the following data: 
 
 
 
 
Class 
interval 
100-200 200-300 300-400 400-500 500-600 600-700 
Frequency 18 15 23 55 87 29 
 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Find LCM of 36, 54 and 63 by prime factorization method. Why LCM of numbers is always 
greater than or equal to each of the numbers? 
12. Solve by substitution: 
4
3 2 3
x y
x y
+ =
- = - 
13. Divide the polynomial
2 2
3 6 20 14 x x x - - + by the polynomial
2
5 6 x x - + and verify the division 
algorithm. 
14. Solve the following pair of equations by reducing them to a pair of linear equations: 
1 4
2
1 3
9
x y
x y
- =
+ =
 
15. From airport two aeroplane start at the same time. If speed of first aeroplane due North is 
500 km/hr and that of other due East is 650 km/hr, then find the distance of two aeroplanes 
after 2 hours. 
16. In the figure find CD, if it is given that AB=12cm, BC=13cm and AD=3cm. 
 
17. Prove that:
tan tan
2cos
sec 1 sec 1
ec
? ?
?
? ?
+ =
- +
 
18. If
21
sin
29
? = , evaluate
sec
tan sin
?
? ? - 
19. The given distribution shows the number of wickets taken by bowlers in inter-school 
competitions: 
Number of 
wickets 
0-3 3-6 6-9 9-12 12-15 
Number of 
bowlers 
9 3 5 3 1 
 
20. The median of the following frequency distribution is 28.5. Find the value of x and y, if sum of 
frequencies is 58. 
Class 0-10 10-20 20-30 30-40 40-50 50-60 
Frequency 2 x 20 15 7 y 
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 ABC ? , D and E are points on the sides AB and AC respectively such that DE BC  . If 
AB=6.75cm, AC=8.50cm and EC=6.8cm, then find BD. 
2. If 24 cot A=7, find the value of sin A. 
3. If 45 ? = ° , then find the value of
2 2
2cos 3sec ec ? ? + . 
4. What is the mean of x, x+1, x+2, x+3, x+4 and x+5? 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Find the HCF of the number 31, 310 and 3100. 
6. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division. 
7. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 5 
respectively. 
8. In the figure if AC=2m, OC=3m and OD=7m, then find BD. 
 
9. Solve the equation for? :
2
2 2
cos
3
cot cos
?
? ?
=
- 
10. Calculate the mode of the following data: 
 
 
 
 
Class 
interval 
100-200 200-300 300-400 400-500 500-600 600-700 
Frequency 18 15 23 55 87 29 
 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Find LCM of 36, 54 and 63 by prime factorization method. Why LCM of numbers is always 
greater than or equal to each of the numbers? 
12. Solve by substitution: 
4
3 2 3
x y
x y
+ =
- = - 
13. Divide the polynomial
2 2
3 6 20 14 x x x - - + by the polynomial
2
5 6 x x - + and verify the division 
algorithm. 
14. Solve the following pair of equations by reducing them to a pair of linear equations: 
1 4
2
1 3
9
x y
x y
- =
+ =
 
15. From airport two aeroplane start at the same time. If speed of first aeroplane due North is 
500 km/hr and that of other due East is 650 km/hr, then find the distance of two aeroplanes 
after 2 hours. 
16. In the figure find CD, if it is given that AB=12cm, BC=13cm and AD=3cm. 
 
17. Prove that:
tan tan
2cos
sec 1 sec 1
ec
? ?
?
? ?
+ =
- +
 
18. If
21
sin
29
? = , evaluate
sec
tan sin
?
? ? - 
19. The given distribution shows the number of wickets taken by bowlers in inter-school 
competitions: 
Number of 
wickets 
0-3 3-6 6-9 9-12 12-15 
Number of 
bowlers 
9 3 5 3 1 
 
20. The median of the following frequency distribution is 28.5. Find the value of x and y, if sum of 
frequencies is 58. 
Class 0-10 10-20 20-30 30-40 40-50 50-60 
Frequency 2 x 20 15 7 y 
 
 
 
 
 
Section D 
Question no. 21 to 30 carry four marks. 
21. Find the greatest 5 digit number which is exactly divisible by 12, 18 and 24. 
22. A group of girls and boys are made to stand in rows. If 4 students are extra in a row, there 
would be two rows less. If 4 students are less in a row, there would be 4 more rows. Find the 
number of students in the class. What is the motive behind making students stand rows? 
23. Find all other zeroes of the polynomial
4 3 2
2 19 9 9 x x x x - - + + , if two of its zeroes are 1 and -3. 
24. Smita scored 100 marks in a test getting 2 marks for each correct answer and losing 1 mark 
for each wrong answer. Had 4 marks been awarded for the each correct answer and 3 marks 
been deducted for the correct answer, then she would have again scored 100 marks. How 
many questions were there in the test, assuming she had attempted all the questions. 
25. In the figure 90 ABD XYD CDB ? = ? = ? = ° , AB=a, XY=c and CD=b, then prove that c(a+b)=ab. 
 
26. In the figure BED BDE ? = ? and E is the middle point of BC. Prove that
AF AD
CF BE
= 
 
27. If sin cos m n ? ? = , then show that: 
2 2
2 2
tan cot sin cos
tan cot sin cos
n m n m
n m n m
? ? ? ?
? ? ? ?
+ + +
= =
- - - 
28. If tan(A+B) is not defined and 
1
sin( )
2
A B - = ; A, B are acute angles, then evaluate: 
a) cos .cos sin .sin A B A B + 
b) 
tan tan
1 tan .tan
A B
A B
- +
 
29. Prove that following identity: 
2
2 2
sec cos
(1 cos tan ).(sin cos )
cos sec
A ec A
A A A A
ec A A
+ + - = - 
30. The mean of the following frequency distribution is 145. Find the missing frequencies x and 
y. 
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 ABC ? , D and E are points on the sides AB and AC respectively such that DE BC  . If 
AB=6.75cm, AC=8.50cm and EC=6.8cm, then find BD. 
2. If 24 cot A=7, find the value of sin A. 
3. If 45 ? = ° , then find the value of
2 2
2cos 3sec ec ? ? + . 
4. What is the mean of x, x+1, x+2, x+3, x+4 and x+5? 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Find the HCF of the number 31, 310 and 3100. 
6. Write the decimal expansion of
2 3
1717
2 5 ×
without actual division. 
7. Find the quadratic polynomial, the sum and product of whose zeroes are -3 and 5 
respectively. 
8. In the figure if AC=2m, OC=3m and OD=7m, then find BD. 
 
9. Solve the equation for? :
2
2 2
cos
3
cot cos
?
? ?
=
- 
10. Calculate the mode of the following data: 
 
 
 
 
Class 
interval 
100-200 200-300 300-400 400-500 500-600 600-700 
Frequency 18 15 23 55 87 29 
 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Find LCM of 36, 54 and 63 by prime factorization method. Why LCM of numbers is always 
greater than or equal to each of the numbers? 
12. Solve by substitution: 
4
3 2 3
x y
x y
+ =
- = - 
13. Divide the polynomial
2 2
3 6 20 14 x x x - - + by the polynomial
2
5 6 x x - + and verify the division 
algorithm. 
14. Solve the following pair of equations by reducing them to a pair of linear equations: 
1 4
2
1 3
9
x y
x y
- =
+ =
 
15. From airport two aeroplane start at the same time. If speed of first aeroplane due North is 
500 km/hr and that of other due East is 650 km/hr, then find the distance of two aeroplanes 
after 2 hours. 
16. In the figure find CD, if it is given that AB=12cm, BC=13cm and AD=3cm. 
 
17. Prove that:
tan tan
2cos
sec 1 sec 1
ec
? ?
?
? ?
+ =
- +
 
18. If
21
sin
29
? = , evaluate
sec
tan sin
?
? ? - 
19. The given distribution shows the number of wickets taken by bowlers in inter-school 
competitions: 
Number of 
wickets 
0-3 3-6 6-9 9-12 12-15 
Number of 
bowlers 
9 3 5 3 1 
 
20. The median of the following frequency distribution is 28.5. Find the value of x and y, if sum of 
frequencies is 58. 
Class 0-10 10-20 20-30 30-40 40-50 50-60 
Frequency 2 x 20 15 7 y 
 
 
 
 
 
Section D 
Question no. 21 to 30 carry four marks. 
21. Find the greatest 5 digit number which is exactly divisible by 12, 18 and 24. 
22. A group of girls and boys are made to stand in rows. If 4 students are extra in a row, there 
would be two rows less. If 4 students are less in a row, there would be 4 more rows. Find the 
number of students in the class. What is the motive behind making students stand rows? 
23. Find all other zeroes of the polynomial
4 3 2
2 19 9 9 x x x x - - + + , if two of its zeroes are 1 and -3. 
24. Smita scored 100 marks in a test getting 2 marks for each correct answer and losing 1 mark 
for each wrong answer. Had 4 marks been awarded for the each correct answer and 3 marks 
been deducted for the correct answer, then she would have again scored 100 marks. How 
many questions were there in the test, assuming she had attempted all the questions. 
25. In the figure 90 ABD XYD CDB ? = ? = ? = ° , AB=a, XY=c and CD=b, then prove that c(a+b)=ab. 
 
26. In the figure BED BDE ? = ? and E is the middle point of BC. Prove that
AF AD
CF BE
= 
 
27. If sin cos m n ? ? = , then show that: 
2 2
2 2
tan cot sin cos
tan cot sin cos
n m n m
n m n m
? ? ? ?
? ? ? ?
+ + +
= =
- - - 
28. If tan(A+B) is not defined and 
1
sin( )
2
A B - = ; A, B are acute angles, then evaluate: 
a) cos .cos sin .sin A B A B + 
b) 
tan tan
1 tan .tan
A B
A B
- +
 
29. Prove that following identity: 
2
2 2
sec cos
(1 cos tan ).(sin cos )
cos sec
A ec A
A A A A
ec A A
+ + - = - 
30. The mean of the following frequency distribution is 145. Find the missing frequencies x and 
y. 
 
 
 
 
Class 0-50 50-100 100-150 150-200 200-250 250-300 Total 
Frequency 6 x 64 52 y 14 200 
 
31. For one term, absentee record of students is given. If mean is 15.5, find the missing 
frequencies x and y. 
Number of 
days 
0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 Total 
Number of 
students 
15 16 x 8 y 8 6 4 70 
 
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