Maths Past Year Paper SA-1(Set -9) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Past Year Papers For Class 10

Class 10 : Maths Past Year Paper SA-1(Set -9) - 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  . 
2. If AB=6.75 cm, AC=8.50 cm and EC=6.8cm, find BD. 
3. If
1
tan
3
? = , find the value ofsin(90 ) ? ° - . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Explain whether 3 12 101 4 × × + is a prime number or a composite number. 
6. Prove that 2 2 is an irrational number. 
7. If the sum of two composite numbers is 108 and the difference of these numbers is 8 then 
find the numbers. 
8. In the figure, l m  and OAC OBD ? ? ~ . If 30 OAC ? = ° , OA=3cm, OC=2cm and OB=6cm, find 
OD. 
 
9. Prove that:
2 2 2 2
sec sec tan tan ? ? ? ? - = + 
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  . 
2. If AB=6.75 cm, AC=8.50 cm and EC=6.8cm, find BD. 
3. If
1
tan
3
? = , find the value ofsin(90 ) ? ° - . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Explain whether 3 12 101 4 × × + is a prime number or a composite number. 
6. Prove that 2 2 is an irrational number. 
7. If the sum of two composite numbers is 108 and the difference of these numbers is 8 then 
find the numbers. 
8. In the figure, l m  and OAC OBD ? ? ~ . If 30 OAC ? = ° , OA=3cm, OC=2cm and OB=6cm, find 
OD. 
 
9. Prove that:
2 2 2 2
sec sec tan tan ? ? ? ? - = + 
 
 
 
 
10. The following data shows the number of toys in a group of 30 children. Find the median 
number of toys with a child. 
Number of toys 0-2 2-4 4-6 6-8 
Number of 
children 
1 10 12 7 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Can the number 6
n
, where n is a natural number end with digit 5? Give reasons. 
12. On dividing 
3 2
5 8 2 x x x + + + by a polynomial g(x), the quotient and the remainder were 
2
4 3 x x + + and x – 1 respectively. Find g(x). 
13. What should be added in the polynomial 
4 3 2
5 7 3 4 x x x x + + + + so that it is completely 
divisible by 
2
2 1 x x + + ? 
14. If
3 2
8 8 x x x k - + + is completely divisible by x – 2, then find the value of k. 
15. In figure ABCD is a rectangle. If in ADE ? and ABF ? , E F ? = ? , then prove that 
AD AE
AB AF
= 
 
16. In the figure ABCD is a parallelogram and E divides BC in the ratio 1:3. DB and AE intersect at 
F. show that DF=4FB and AF=4FE. 
 
17. Prove that:
2 2 2 2
sec cot (90 ) cos (90 ) cos ? ? ? ? - ° - = ° - + 
18. cos a ecA p = and cot b A q = , then prove that 
2 2
2 2
1
p q
a b
- = 
19. Following is the age distribution of dengue patients admitted in a hospital during a week of 
October 2013: 
Age (in 
years) 
Less 
than 
10 
Less 
than 
20 
Less 
than 
30 
Less 
than 
40 
Less 
than  
50 
Less 
than 
60 
Less 
than 
70 
Less 
than 
80 
Number of 
patients 
30 35 55 69 90 115 135 150 
Draw a ‘less than type’ ogive for the above distribution. Also, obtain median from the curve. 
20. During a medical check-up of students of a class X, their weights were recorded as follows: 
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  . 
2. If AB=6.75 cm, AC=8.50 cm and EC=6.8cm, find BD. 
3. If
1
tan
3
? = , find the value ofsin(90 ) ? ° - . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Explain whether 3 12 101 4 × × + is a prime number or a composite number. 
6. Prove that 2 2 is an irrational number. 
7. If the sum of two composite numbers is 108 and the difference of these numbers is 8 then 
find the numbers. 
8. In the figure, l m  and OAC OBD ? ? ~ . If 30 OAC ? = ° , OA=3cm, OC=2cm and OB=6cm, find 
OD. 
 
9. Prove that:
2 2 2 2
sec sec tan tan ? ? ? ? - = + 
 
 
 
 
10. The following data shows the number of toys in a group of 30 children. Find the median 
number of toys with a child. 
Number of toys 0-2 2-4 4-6 6-8 
Number of 
children 
1 10 12 7 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Can the number 6
n
, where n is a natural number end with digit 5? Give reasons. 
12. On dividing 
3 2
5 8 2 x x x + + + by a polynomial g(x), the quotient and the remainder were 
2
4 3 x x + + and x – 1 respectively. Find g(x). 
13. What should be added in the polynomial 
4 3 2
5 7 3 4 x x x x + + + + so that it is completely 
divisible by 
2
2 1 x x + + ? 
14. If
3 2
8 8 x x x k - + + is completely divisible by x – 2, then find the value of k. 
15. In figure ABCD is a rectangle. If in ADE ? and ABF ? , E F ? = ? , then prove that 
AD AE
AB AF
= 
 
16. In the figure ABCD is a parallelogram and E divides BC in the ratio 1:3. DB and AE intersect at 
F. show that DF=4FB and AF=4FE. 
 
17. Prove that:
2 2 2 2
sec cot (90 ) cos (90 ) cos ? ? ? ? - ° - = ° - + 
18. cos a ecA p = and cot b A q = , then prove that 
2 2
2 2
1
p q
a b
- = 
19. Following is the age distribution of dengue patients admitted in a hospital during a week of 
October 2013: 
Age (in 
years) 
Less 
than 
10 
Less 
than 
20 
Less 
than 
30 
Less 
than 
40 
Less 
than  
50 
Less 
than 
60 
Less 
than 
70 
Less 
than 
80 
Number of 
patients 
30 35 55 69 90 115 135 150 
Draw a ‘less than type’ ogive for the above distribution. Also, obtain median from the curve. 
20. During a medical check-up of students of a class X, their weights were recorded as follows: 
 
 
 
 
Weight (in 
kg) 
Less 
than 
35 
Less 
than 
38 
Less 
than 
41 
Less 
than 
44 
Less 
than 
47 
Less 
than 
50 
Less 
than 
53 
Number of 
students 
0 4 6 8 18 33 40 
Draw a ‘less than type’ ogive for the above data, and hence obtain the median from its curve. 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Solve that square of any positive odd integer is of the form 8m+1 for some integer m. 
22. Solve the following pair of equations: 
2 3
1
4 9 5
2
x y x y
x y x y
+ =
- +
+ =
- +
 
23. Obtain all other zeroes of 
3 2
3 14 8 x x - + , if two of its zeroes are 
2
3
and 
2
3
- 
24. Draw the graph of the following pair of linear equations: 
3x+2y=15 and 3x-4y=-3 
Also shade the region bounded by these lines and y=0. Write the coordinates of vertices of 
the triangle. 
25. In , ABC AD BC ? ? and D lies on BC such that 4DB=CD, then prove that 
2 2 2
5 5 3 AB AC BC = - . 
26. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of 
their corresponding altitudes. 
27. Take 90 A = ° and 45 B = ° to verify that: 
a) sin( ) sin cos cos sin A B A B A B - = - 
b) cos( ) cos cos sin sin A B A B A B - = - 
28. If tan cot 4 ? ? + = , then find the values of: 
a) 
2 2
tan cot ? ? + 
b) 
2 2
cos sec ec ? ? + 
29. Prove the identify:
2 2
2
1 tan 1 tan
tan
1 cot 1 cot
A A
A
A A
+ - ? ? ? ?
= =
? ? ? ?
+ - ? ? ? ?
 
30. The literacy rate of females in 50 cities is given in the frequency distribution: 
Literacy 
rate (in 
%) 
20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 
Number 
of cities 
3 2 6 15 8 7 5 4 
Find the mode and median of this data. 
31. Heights of new born babies in a city hospital are as follows: 
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  . 
2. If AB=6.75 cm, AC=8.50 cm and EC=6.8cm, find BD. 
3. If
1
tan
3
? = , find the value ofsin(90 ) ? ° - . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Explain whether 3 12 101 4 × × + is a prime number or a composite number. 
6. Prove that 2 2 is an irrational number. 
7. If the sum of two composite numbers is 108 and the difference of these numbers is 8 then 
find the numbers. 
8. In the figure, l m  and OAC OBD ? ? ~ . If 30 OAC ? = ° , OA=3cm, OC=2cm and OB=6cm, find 
OD. 
 
9. Prove that:
2 2 2 2
sec sec tan tan ? ? ? ? - = + 
 
 
 
 
10. The following data shows the number of toys in a group of 30 children. Find the median 
number of toys with a child. 
Number of toys 0-2 2-4 4-6 6-8 
Number of 
children 
1 10 12 7 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Can the number 6
n
, where n is a natural number end with digit 5? Give reasons. 
12. On dividing 
3 2
5 8 2 x x x + + + by a polynomial g(x), the quotient and the remainder were 
2
4 3 x x + + and x – 1 respectively. Find g(x). 
13. What should be added in the polynomial 
4 3 2
5 7 3 4 x x x x + + + + so that it is completely 
divisible by 
2
2 1 x x + + ? 
14. If
3 2
8 8 x x x k - + + is completely divisible by x – 2, then find the value of k. 
15. In figure ABCD is a rectangle. If in ADE ? and ABF ? , E F ? = ? , then prove that 
AD AE
AB AF
= 
 
16. In the figure ABCD is a parallelogram and E divides BC in the ratio 1:3. DB and AE intersect at 
F. show that DF=4FB and AF=4FE. 
 
17. Prove that:
2 2 2 2
sec cot (90 ) cos (90 ) cos ? ? ? ? - ° - = ° - + 
18. cos a ecA p = and cot b A q = , then prove that 
2 2
2 2
1
p q
a b
- = 
19. Following is the age distribution of dengue patients admitted in a hospital during a week of 
October 2013: 
Age (in 
years) 
Less 
than 
10 
Less 
than 
20 
Less 
than 
30 
Less 
than 
40 
Less 
than  
50 
Less 
than 
60 
Less 
than 
70 
Less 
than 
80 
Number of 
patients 
30 35 55 69 90 115 135 150 
Draw a ‘less than type’ ogive for the above distribution. Also, obtain median from the curve. 
20. During a medical check-up of students of a class X, their weights were recorded as follows: 
 
 
 
 
Weight (in 
kg) 
Less 
than 
35 
Less 
than 
38 
Less 
than 
41 
Less 
than 
44 
Less 
than 
47 
Less 
than 
50 
Less 
than 
53 
Number of 
students 
0 4 6 8 18 33 40 
Draw a ‘less than type’ ogive for the above data, and hence obtain the median from its curve. 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Solve that square of any positive odd integer is of the form 8m+1 for some integer m. 
22. Solve the following pair of equations: 
2 3
1
4 9 5
2
x y x y
x y x y
+ =
- +
+ =
- +
 
23. Obtain all other zeroes of 
3 2
3 14 8 x x - + , if two of its zeroes are 
2
3
and 
2
3
- 
24. Draw the graph of the following pair of linear equations: 
3x+2y=15 and 3x-4y=-3 
Also shade the region bounded by these lines and y=0. Write the coordinates of vertices of 
the triangle. 
25. In , ABC AD BC ? ? and D lies on BC such that 4DB=CD, then prove that 
2 2 2
5 5 3 AB AC BC = - . 
26. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of 
their corresponding altitudes. 
27. Take 90 A = ° and 45 B = ° to verify that: 
a) sin( ) sin cos cos sin A B A B A B - = - 
b) cos( ) cos cos sin sin A B A B A B - = - 
28. If tan cot 4 ? ? + = , then find the values of: 
a) 
2 2
tan cot ? ? + 
b) 
2 2
cos sec ec ? ? + 
29. Prove the identify:
2 2
2
1 tan 1 tan
tan
1 cot 1 cot
A A
A
A A
+ - ? ? ? ?
= =
? ? ? ?
+ - ? ? ? ?
 
30. The literacy rate of females in 50 cities is given in the frequency distribution: 
Literacy 
rate (in 
%) 
20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 
Number 
of cities 
3 2 6 15 8 7 5 4 
Find the mode and median of this data. 
31. Heights of new born babies in a city hospital are as follows: 
 
 
 
 
Height 
(in cm) 
40-42 42-44 44-46 46-48 48-50 50-52 52-54 54-56 56-58 
Number 
of babies 
1 4 17 18 x 25 20 6 2 
If mode of the data is 51 cm, find the unknown frequency x. 
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