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

Past Year Papers For Class 10

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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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