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# Maths Past Year Paper SA-1(Set -4) - 2014, Class 10, CBSE Class 10 Notes | EduRev

## Class 10 : Maths Past Year Paper SA-1(Set -4) - 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of
the ladder from the base of the wall.
2. In a ABC ? , write tan
2
A B +
in terms of angle C.
3. In ABC ? , 90 , 45 C A ? = ° ? = ° and AB=10 cm. find BC, using trigonometric ratios.
4. Find the median of the following distribution:
i
x 1 2 3 4 5 6 7 8
i
f 2 4 6 5 8 0 3 2

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Write the number n in usual form, whose prime factorization is given below:
7 6
2 5 13 n = × × . Also find the number of zeroes it contains?
6. Find the smallest natural by which 1200 should be multiplied so that the square root of the
product is a rational number.
7. Find the zeroes of the quadratic polynomial
2
8 16 t t + + and verify the relationship between
the zeroes and the coefficients.
8. In the figure, l m  amd OAC OBD ? ? ~ . If AC=5 cm, OA=3 cm and BD=2 cm, find OB.

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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of
the ladder from the base of the wall.
2. In a ABC ? , write tan
2
A B +
in terms of angle C.
3. In ABC ? , 90 , 45 C A ? = ° ? = ° and AB=10 cm. find BC, using trigonometric ratios.
4. Find the median of the following distribution:
i
x 1 2 3 4 5 6 7 8
i
f 2 4 6 5 8 0 3 2

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Write the number n in usual form, whose prime factorization is given below:
7 6
2 5 13 n = × × . Also find the number of zeroes it contains?
6. Find the smallest natural by which 1200 should be multiplied so that the square root of the
product is a rational number.
7. Find the zeroes of the quadratic polynomial
2
8 16 t t + + and verify the relationship between
the zeroes and the coefficients.
8. In the figure, l m  amd OAC OBD ? ? ~ . If AC=5 cm, OA=3 cm and BD=2 cm, find OB.

9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +

10. Given below is the distribution of weekly pocket money received by students of a class.
Calculate the pocket money that is received by most of the students.
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-120 120-140
Number
of
students
2 2 3 12 18 5 2

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 5 is an irrational number.
12. Solve by elimination:
9x+10y=29
10x+9y=28
13. Divide the polynomial
4 3 2
3 5 4 10 2 x x x x - + + - by the polynomial
3
2 x x - and verify the
division algorithm.
14. Find the HCF of numbers 72 and 96 by Euclid’s division algorithm and express it in the form
96m+72n, where m and n are integers.
15. If the area of two similar triangles ABC and DEF are
2
25cm and
2
81cm respectively and one
side of ABC ? is equal to 20 cm, then find the corresponding side of DEF ? .
16. A boy of height 95 cm is walking away from base of a lamp post at a speed of 1.5 m/s. if the
lamp post is 3.8 m above the ground, find the length of his shadow after 5 seconds.
17. If
12
sin
13
u = , 0 90 u ° < < ° , find the value of
2 2
2
sin cos 1
2sin cos tan
u u
u u u
- ×
18. When is an equation called ‘an identity’. Prove the trigonometric identify
2 2
1 tan sec A A + =
19. Following data shows pocket money of students of class VI in a school:
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-
120
120-
140
140-
160
No. of
students
2 9 12 15 13 10 7 5
Draw a ‘less than type’ ogive for the above data.
20. If the mean of the following distribution is 54, find the value of the missing frequency x:
Class 0-20 20-40 40-60 60-80 80-100
Frequency 16 14 24 26 x

Section D
Questions 21 to 31 carry 4 marks each.
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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of
the ladder from the base of the wall.
2. In a ABC ? , write tan
2
A B +
in terms of angle C.
3. In ABC ? , 90 , 45 C A ? = ° ? = ° and AB=10 cm. find BC, using trigonometric ratios.
4. Find the median of the following distribution:
i
x 1 2 3 4 5 6 7 8
i
f 2 4 6 5 8 0 3 2

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Write the number n in usual form, whose prime factorization is given below:
7 6
2 5 13 n = × × . Also find the number of zeroes it contains?
6. Find the smallest natural by which 1200 should be multiplied so that the square root of the
product is a rational number.
7. Find the zeroes of the quadratic polynomial
2
8 16 t t + + and verify the relationship between
the zeroes and the coefficients.
8. In the figure, l m  amd OAC OBD ? ? ~ . If AC=5 cm, OA=3 cm and BD=2 cm, find OB.

9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +

10. Given below is the distribution of weekly pocket money received by students of a class.
Calculate the pocket money that is received by most of the students.
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-120 120-140
Number
of
students
2 2 3 12 18 5 2

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 5 is an irrational number.
12. Solve by elimination:
9x+10y=29
10x+9y=28
13. Divide the polynomial
4 3 2
3 5 4 10 2 x x x x - + + - by the polynomial
3
2 x x - and verify the
division algorithm.
14. Find the HCF of numbers 72 and 96 by Euclid’s division algorithm and express it in the form
96m+72n, where m and n are integers.
15. If the area of two similar triangles ABC and DEF are
2
25cm and
2
81cm respectively and one
side of ABC ? is equal to 20 cm, then find the corresponding side of DEF ? .
16. A boy of height 95 cm is walking away from base of a lamp post at a speed of 1.5 m/s. if the
lamp post is 3.8 m above the ground, find the length of his shadow after 5 seconds.
17. If
12
sin
13
u = , 0 90 u ° < < ° , find the value of
2 2
2
sin cos 1
2sin cos tan
u u
u u u
- ×
18. When is an equation called ‘an identity’. Prove the trigonometric identify
2 2
1 tan sec A A + =
19. Following data shows pocket money of students of class VI in a school:
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-
120
120-
140
140-
160
No. of
students
2 9 12 15 13 10 7 5
Draw a ‘less than type’ ogive for the above data.
20. If the mean of the following distribution is 54, find the value of the missing frequency x:
Class 0-20 20-40 40-60 60-80 80-100
Frequency 16 14 24 26 x

Section D
Questions 21 to 31 carry 4 marks each.

21. Rita, Krish and Zara start solving a puzzle together. They take 12, 18 and 21 minutes
respectively to solve the puzzle. After how much time will they start solving a new puzzle
together?
22. Rajesh donated some money and looks to a school for poor children. Money and books can be
represented by the zeroes (i.e. , a ß ) of the polynomial
2
( ) 2 5 7 p x x x = - + . Akshita who is
friend of Rajesh, also got inspired by him and donated the money and books in the form of a
polynomial whose zeroes are 2 3 a ß + and 3 2 a ß + . Find the polynomial whose zeroes are
2 3 a ß + and 3 2 a ß + .
Why did Akshita got inspired by Rajesh?
23. A lending library has a fixed charge for the first two days and an additional charge for each
day thereafter. Reema paid Rs 30 for a book kept for 6 days, while Smita paid Rs 40 for the
book she kept for 8 days. Find the fixed charge and the charge for each extra day. If Sonu kept
book for 4 days, how much he will have to pay?
24. Obtain all other zeroes of the polynomial
4 3 2
3 3 15 10 x x x x + - - - , if two of its zeroes are 5
and 5 -
25. In a parallelogram ABCD, middle point of CD is M. A line segment BM is drawn which cuts AC
at L and meets AD extended at E. prove that EL=2BL

26. In ABC ? , AD BC ? and D lies on BC such that 4BD=CD, then prove that
2 2 2
5 5 3 AB AC BC = -
27. Evaluate:
2 2 2
2 2 2 2
cos 25 cos 65 2cos 39 2cot 39 tan 51
3tan 23 tan 33 tan 60 sin 60 tan 67 tan 57
sec 40 cot 50 sin 20 sin 70
ec ° + ° ° - °· °
+ - °· °· °· °· °· °
° - ° ° + °

28. If tan sin m ? ? + = and tan sin n ? ? - = , prove that
2 2
4 m n mn - = .
29. If A, B, C are interior angles of a triangle ABC then prove that:
a) sin cos
2 2
B C A + ? ?
=
? ?
? ?

b) tan cot
2 2
C A B + ? ?
=
? ?
? ?

30. Median marks of students are 22 (out of 40) and total number of students in the class is 50.
Find the missing frequencies x and y in the following distribution:
Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of
students
1 5 8 x y 10 7 5
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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of
the ladder from the base of the wall.
2. In a ABC ? , write tan
2
A B +
in terms of angle C.
3. In ABC ? , 90 , 45 C A ? = ° ? = ° and AB=10 cm. find BC, using trigonometric ratios.
4. Find the median of the following distribution:
i
x 1 2 3 4 5 6 7 8
i
f 2 4 6 5 8 0 3 2

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Write the number n in usual form, whose prime factorization is given below:
7 6
2 5 13 n = × × . Also find the number of zeroes it contains?
6. Find the smallest natural by which 1200 should be multiplied so that the square root of the
product is a rational number.
7. Find the zeroes of the quadratic polynomial
2
8 16 t t + + and verify the relationship between
the zeroes and the coefficients.
8. In the figure, l m  amd OAC OBD ? ? ~ . If AC=5 cm, OA=3 cm and BD=2 cm, find OB.

9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +

10. Given below is the distribution of weekly pocket money received by students of a class.
Calculate the pocket money that is received by most of the students.
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-120 120-140
Number
of
students
2 2 3 12 18 5 2

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 5 is an irrational number.
12. Solve by elimination:
9x+10y=29
10x+9y=28
13. Divide the polynomial
4 3 2
3 5 4 10 2 x x x x - + + - by the polynomial
3
2 x x - and verify the
division algorithm.
14. Find the HCF of numbers 72 and 96 by Euclid’s division algorithm and express it in the form
96m+72n, where m and n are integers.
15. If the area of two similar triangles ABC and DEF are
2
25cm and
2
81cm respectively and one
side of ABC ? is equal to 20 cm, then find the corresponding side of DEF ? .
16. A boy of height 95 cm is walking away from base of a lamp post at a speed of 1.5 m/s. if the
lamp post is 3.8 m above the ground, find the length of his shadow after 5 seconds.
17. If
12
sin
13
u = , 0 90 u ° < < ° , find the value of
2 2
2
sin cos 1
2sin cos tan
u u
u u u
- ×
18. When is an equation called ‘an identity’. Prove the trigonometric identify
2 2
1 tan sec A A + =
19. Following data shows pocket money of students of class VI in a school:
Pocket
Money
(in Rs.)
0-20 20-40 40-60 60-80 80-100 100-
120
120-
140
140-
160
No. of
students
2 9 12 15 13 10 7 5
Draw a ‘less than type’ ogive for the above data.
20. If the mean of the following distribution is 54, find the value of the missing frequency x:
Class 0-20 20-40 40-60 60-80 80-100
Frequency 16 14 24 26 x

Section D
Questions 21 to 31 carry 4 marks each.

21. Rita, Krish and Zara start solving a puzzle together. They take 12, 18 and 21 minutes
respectively to solve the puzzle. After how much time will they start solving a new puzzle
together?
22. Rajesh donated some money and looks to a school for poor children. Money and books can be
represented by the zeroes (i.e. , a ß ) of the polynomial
2
( ) 2 5 7 p x x x = - + . Akshita who is
friend of Rajesh, also got inspired by him and donated the money and books in the form of a
polynomial whose zeroes are 2 3 a ß + and 3 2 a ß + . Find the polynomial whose zeroes are
2 3 a ß + and 3 2 a ß + .
Why did Akshita got inspired by Rajesh?
23. A lending library has a fixed charge for the first two days and an additional charge for each
day thereafter. Reema paid Rs 30 for a book kept for 6 days, while Smita paid Rs 40 for the
book she kept for 8 days. Find the fixed charge and the charge for each extra day. If Sonu kept
book for 4 days, how much he will have to pay?
24. Obtain all other zeroes of the polynomial
4 3 2
3 3 15 10 x x x x + - - - , if two of its zeroes are 5
and 5 -
25. In a parallelogram ABCD, middle point of CD is M. A line segment BM is drawn which cuts AC
at L and meets AD extended at E. prove that EL=2BL

26. In ABC ? , AD BC ? and D lies on BC such that 4BD=CD, then prove that
2 2 2
5 5 3 AB AC BC = -
27. Evaluate:
2 2 2
2 2 2 2
cos 25 cos 65 2cos 39 2cot 39 tan 51
3tan 23 tan 33 tan 60 sin 60 tan 67 tan 57
sec 40 cot 50 sin 20 sin 70
ec ° + ° ° - °· °
+ - °· °· °· °· °· °
° - ° ° + °

28. If tan sin m ? ? + = and tan sin n ? ? - = , prove that
2 2
4 m n mn - = .
29. If A, B, C are interior angles of a triangle ABC then prove that:
a) sin cos
2 2
B C A + ? ?
=
? ?
? ?

b) tan cot
2 2
C A B + ? ?
=
? ?
? ?

30. Median marks of students are 22 (out of 40) and total number of students in the class is 50.
Find the missing frequencies x and y in the following distribution:
Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40
No. of
students
1 5 8 x y 10 7 5

31. On Sports day of a school, age-wise participation of students is shown in the following
distribution:
Age (in
years)
5-7 7-9 9-11 11-13 13-15 15-17 17-19
Number
of
students
x 15 18 30 50 48 y
Find the missing frequencies when sum of frequencies is 181. Also, the mode of the data.
```
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