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

## 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
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
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
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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