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

## Class 10 : Maths Past Year Paper SA-1(Set -1) - 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 of Section – A are very short type questions, carrying 1 mark each.
Question No. 5 to 10 of Section – B are of short answer type questions, carrying 2 marks
each. Question No. 11 to 20 of Section – C carry 3 marks each. Question No. 21 to 31 of
Section – D 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 PQR ? , E and F points on the sides PQ and PR respectively such that EF QR  . If PE=6 cm,
QE=2 cm and FR=3cm, then find PF.
2. Find the value of
1 cos36 3 sec16
. .
3 sin 54 2 cos 74 ec
° °
- ° °

3. If
1
tan
3
? = , find the value of sin(90 ) ? ° -
4. Write the empirical relationship between the three measures of central tendency.

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Find the value of:
2 2 1 4 2
( 1) ( 1) ( 1) ( 1)
n n n n + +
- + - + - + - , where n is any positive odd integer.
6. Determine the values of m and n so that the prime factorization of 10500 is expressible as
2 3 5 7
m n
× × ×
7. Find the zeroes of the quadratic polynomial
2
7 12 x x - + and verify the relationship between
the zeroes and the coefficients.
8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm.
9. Simplify:
tan 28 1
[tan 20 .tan 60 .tan 70 ]
cot 62 3
°
÷ ° ° °
°

10. Given below is a cumulative frequency distribution table showing daily income of 50 workers
of a factory:
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 of Section – A are very short type questions, carrying 1 mark each.
Question No. 5 to 10 of Section – B are of short answer type questions, carrying 2 marks
each. Question No. 11 to 20 of Section – C carry 3 marks each. Question No. 21 to 31 of
Section – D 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 PQR ? , E and F points on the sides PQ and PR respectively such that EF QR  . If PE=6 cm,
QE=2 cm and FR=3cm, then find PF.
2. Find the value of
1 cos36 3 sec16
. .
3 sin 54 2 cos 74 ec
° °
- ° °

3. If
1
tan
3
? = , find the value of sin(90 ) ? ° -
4. Write the empirical relationship between the three measures of central tendency.

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Find the value of:
2 2 1 4 2
( 1) ( 1) ( 1) ( 1)
n n n n + +
- + - + - + - , where n is any positive odd integer.
6. Determine the values of m and n so that the prime factorization of 10500 is expressible as
2 3 5 7
m n
× × ×
7. Find the zeroes of the quadratic polynomial
2
7 12 x x - + and verify the relationship between
the zeroes and the coefficients.
8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm.
9. Simplify:
tan 28 1
[tan 20 .tan 60 .tan 70 ]
cot 62 3
°
÷ ° ° °
°

10. Given below is a cumulative frequency distribution table showing daily income of 50 workers
of a factory:

Daily income
(in Rs.)
More than or
equal to 200
More than or
equal to 300
More than or
equal to 400
More than or
equal to 500
More than or
equal to 600
Number of
workers
50 42 30 18 05
Draw cumulative frequency curve (ogive) ‘of more than’ type for this data.

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 8 is an irrational number.
12. Solve the following pair of equations for x and y:
4
5 7 y
x
+ =
3
4 5 y
x
+ =
13. Solve the following pair of linear equations by the elimination method:
2x+3y=7
3x-2y=3
14. What should be added in the polynomial
4 3 2
3 4 6 4 x x x - - + so that it is completely divisible
by
2
2 x -
15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that
2 2 2
2 2 AB AC BC = -
16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA  and
PR BD  , then prove that QR AD 

17. Prove that:
(1 + tan A + cot A).(sin A – cos A)=sin A. tan A – cot A. cos A
18. Evaluate:
2 2
sec .cos (90 ) tan .cot(90 ) sin 55 sin 35
tan10 .tan 20 .tan 60 .tan 70 .tan80
ec ? ? ? ? ° - - ° - + ° + °
° ° ° ° °

19. Heights of students of class X are given in the following frequency distribution:
Height (in cm) 150-155 155-160 160-165 165-170 170-175
Number of
students
15 8 20 12 5
Find the modal height.
20. A school conducted a test (of 100 marks) in English for students of class X. The marks
obtained by students are shown in the following table:
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 of Section – A are very short type questions, carrying 1 mark each.
Question No. 5 to 10 of Section – B are of short answer type questions, carrying 2 marks
each. Question No. 11 to 20 of Section – C carry 3 marks each. Question No. 21 to 31 of
Section – D 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 PQR ? , E and F points on the sides PQ and PR respectively such that EF QR  . If PE=6 cm,
QE=2 cm and FR=3cm, then find PF.
2. Find the value of
1 cos36 3 sec16
. .
3 sin 54 2 cos 74 ec
° °
- ° °

3. If
1
tan
3
? = , find the value of sin(90 ) ? ° -
4. Write the empirical relationship between the three measures of central tendency.

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Find the value of:
2 2 1 4 2
( 1) ( 1) ( 1) ( 1)
n n n n + +
- + - + - + - , where n is any positive odd integer.
6. Determine the values of m and n so that the prime factorization of 10500 is expressible as
2 3 5 7
m n
× × ×
7. Find the zeroes of the quadratic polynomial
2
7 12 x x - + and verify the relationship between
the zeroes and the coefficients.
8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm.
9. Simplify:
tan 28 1
[tan 20 .tan 60 .tan 70 ]
cot 62 3
°
÷ ° ° °
°

10. Given below is a cumulative frequency distribution table showing daily income of 50 workers
of a factory:

Daily income
(in Rs.)
More than or
equal to 200
More than or
equal to 300
More than or
equal to 400
More than or
equal to 500
More than or
equal to 600
Number of
workers
50 42 30 18 05
Draw cumulative frequency curve (ogive) ‘of more than’ type for this data.

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 8 is an irrational number.
12. Solve the following pair of equations for x and y:
4
5 7 y
x
+ =
3
4 5 y
x
+ =
13. Solve the following pair of linear equations by the elimination method:
2x+3y=7
3x-2y=3
14. What should be added in the polynomial
4 3 2
3 4 6 4 x x x - - + so that it is completely divisible
by
2
2 x -
15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that
2 2 2
2 2 AB AC BC = -
16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA  and
PR BD  , then prove that QR AD 

17. Prove that:
(1 + tan A + cot A).(sin A – cos A)=sin A. tan A – cot A. cos A
18. Evaluate:
2 2
sec .cos (90 ) tan .cot(90 ) sin 55 sin 35
tan10 .tan 20 .tan 60 .tan 70 .tan80
ec ? ? ? ? ° - - ° - + ° + °
° ° ° ° °

19. Heights of students of class X are given in the following frequency distribution:
Height (in cm) 150-155 155-160 160-165 165-170 170-175
Number of
students
15 8 20 12 5
Find the modal height.
20. A school conducted a test (of 100 marks) in English for students of class X. The marks
obtained by students are shown in the following table:

Marks
obtained
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-
100
Number
of
students
1 2 4 15 15 25 15 10 2 1
Find the modal marks.
Section D
Questions 21 to 31 carry 4 marks each.
21. State Euclid division Lemma. Using it show that square of any positive integer is either of the
form 5cm or 5 1 m ± , where m is an integer.
22. On the independence day celebration in the school, number of students participated in the
celebration. School management has decided to distribute some sweets amongst the
participants and athe audience. If total number of sweets were represented by
4 3 2
8 14 2 7 8 x x x x + - + - , each one received
2
2 2 1 x x + - sweets and 14x – 10 remained
undistributed, find the number of students to whom sweets were distributed.
23. If a polynomial
4 3 2
2 3 6 3 2 x x x x - - + + - is divided by another polynomial
2
2 3 4 x x - - + , then
remainder is px+q. Find the value of p and q.
24. Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks
for each wrong answer. Had 4 marks been awarded for each correct answer and 1 mark been
deducted for each incorrect answer, then she would have scored 250 marks. How many
questions were there in the test, if she attempted all the questions.
25. In the given figure, AB and CD are two pillars P is a point on BD such that BP=16 m and
PD=12 m. If CD=16 m and AC=52 m, then find AB and AP when it is given that 90 APC ? = °

26. If ABC DEF ? ? ~ and AX, DY are respectively the medians of ABC ? and DEF ? . Then prove
that
a) ABX DEY ? ? ~
b) ACX DFY ? ? ~
c)
AX BC
DY EF
=
27. Given that ( )
tan tan
tan A – B
1 tan .tan
A B
A B
- =
+
; evaluate tan15° in two ways.
a) Taking 60 , 45 A B = ° = °
b) Taking 45 , 30 A B = ° = °
28. If
4
tan 5
tan
?
?
+ = , find sin? and cos? .
29. If x=cot A + cos A = cot A – cos A; prove that:
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 of Section – A are very short type questions, carrying 1 mark each.
Question No. 5 to 10 of Section – B are of short answer type questions, carrying 2 marks
each. Question No. 11 to 20 of Section – C carry 3 marks each. Question No. 21 to 31 of
Section – D 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 PQR ? , E and F points on the sides PQ and PR respectively such that EF QR  . If PE=6 cm,
QE=2 cm and FR=3cm, then find PF.
2. Find the value of
1 cos36 3 sec16
. .
3 sin 54 2 cos 74 ec
° °
- ° °

3. If
1
tan
3
? = , find the value of sin(90 ) ? ° -
4. Write the empirical relationship between the three measures of central tendency.

Section B
Question numbers 5 to 10 carry 2 marks each.
5. Find the value of:
2 2 1 4 2
( 1) ( 1) ( 1) ( 1)
n n n n + +
- + - + - + - , where n is any positive odd integer.
6. Determine the values of m and n so that the prime factorization of 10500 is expressible as
2 3 5 7
m n
× × ×
7. Find the zeroes of the quadratic polynomial
2
7 12 x x - + and verify the relationship between
the zeroes and the coefficients.
8. Find the side of a rhombus whose diagonal are of length 60 cm and 80 cm.
9. Simplify:
tan 28 1
[tan 20 .tan 60 .tan 70 ]
cot 62 3
°
÷ ° ° °
°

10. Given below is a cumulative frequency distribution table showing daily income of 50 workers
of a factory:

Daily income
(in Rs.)
More than or
equal to 200
More than or
equal to 300
More than or
equal to 400
More than or
equal to 500
More than or
equal to 600
Number of
workers
50 42 30 18 05
Draw cumulative frequency curve (ogive) ‘of more than’ type for this data.

Section C
Question number from 11 to 20 carry 3 marks each.
11. Prove that 8 is an irrational number.
12. Solve the following pair of equations for x and y:
4
5 7 y
x
+ =
3
4 5 y
x
+ =
13. Solve the following pair of linear equations by the elimination method:
2x+3y=7
3x-2y=3
14. What should be added in the polynomial
4 3 2
3 4 6 4 x x x - - + so that it is completely divisible
by
2
2 x -
15. In ABC ? , perpendicular drawn from A intersects BC at D such that 3 DB=CD. Prove that
2 2 2
2 2 AB AC BC = -
16. In the figure ABC ? and DBC ? have same base BC and lie on the same side. If PQ BA  and
PR BD  , then prove that QR AD 

17. Prove that:
(1 + tan A + cot A).(sin A – cos A)=sin A. tan A – cot A. cos A
18. Evaluate:
2 2
sec .cos (90 ) tan .cot(90 ) sin 55 sin 35
tan10 .tan 20 .tan 60 .tan 70 .tan80
ec ? ? ? ? ° - - ° - + ° + °
° ° ° ° °

19. Heights of students of class X are given in the following frequency distribution:
Height (in cm) 150-155 155-160 160-165 165-170 170-175
Number of
students
15 8 20 12 5
Find the modal height.
20. A school conducted a test (of 100 marks) in English for students of class X. The marks
obtained by students are shown in the following table:

Marks
obtained
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-
100
Number
of
students
1 2 4 15 15 25 15 10 2 1
Find the modal marks.
Section D
Questions 21 to 31 carry 4 marks each.
21. State Euclid division Lemma. Using it show that square of any positive integer is either of the
form 5cm or 5 1 m ± , where m is an integer.
22. On the independence day celebration in the school, number of students participated in the
celebration. School management has decided to distribute some sweets amongst the
participants and athe audience. If total number of sweets were represented by
4 3 2
8 14 2 7 8 x x x x + - + - , each one received
2
2 2 1 x x + - sweets and 14x – 10 remained
undistributed, find the number of students to whom sweets were distributed.
23. If a polynomial
4 3 2
2 3 6 3 2 x x x x - - + + - is divided by another polynomial
2
2 3 4 x x - - + , then
remainder is px+q. Find the value of p and q.
24. Mini scored 150 marks in a test getting 3 marks for each correct answer and losing 2 marks
for each wrong answer. Had 4 marks been awarded for each correct answer and 1 mark been
deducted for each incorrect answer, then she would have scored 250 marks. How many
questions were there in the test, if she attempted all the questions.
25. In the given figure, AB and CD are two pillars P is a point on BD such that BP=16 m and
PD=12 m. If CD=16 m and AC=52 m, then find AB and AP when it is given that 90 APC ? = °

26. If ABC DEF ? ? ~ and AX, DY are respectively the medians of ABC ? and DEF ? . Then prove
that
a) ABX DEY ? ? ~
b) ACX DFY ? ? ~
c)
AX BC
DY EF
=
27. Given that ( )
tan tan
tan A – B
1 tan .tan
A B
A B
- =
+
; evaluate tan15° in two ways.
a) Taking 60 , 45 A B = ° = °
b) Taking 45 , 30 A B = ° = °
28. If
4
tan 5
tan
?
?
+ = , find sin? and cos? .
29. If x=cot A + cos A = cot A – cos A; prove that:

2
2
1
2
x y x y
x y
? ? - - ? ?
+ =
? ? ? ?
+
? ?
? ?

30. The annual profits earned by shops of a particular shopping mall are given in the following
distribution:
Profit
(in
lakh)
5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50
Number
of
shops
4 8 15 20 25 18 12 7 3
Draw a ‘less than type’ ogive and a ‘more than type’ ogive for this data.
31. In a check-up of heart beat rate of 50 females, it was found that median heart beat is 78. Find
the missing frequencies
1
f and
2
f in the following frequency distribution:
Number
of heart
beats per
minute
64-68 68-72 72-76 76-80 80-84 84-88 88-92
Number
of females
4 5
1
f
2
f 9 7 1

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