CBSE Math Past Year Paper SA-1: Set 7 (2014) - Class 10 PDF Download

 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 PQR ? , if B and C are points on the sides PR and QR respectively such that RB=10cm, 
PR=18cm, BC=15 cm and CQ=15 cm, then find whether BC is parallel to QR or not. 
2. In a right angled ABC ? , if 90 B ? = ° , AC=25 cm and BC=7cm, then find tan A. 
3. Find the value of
tan 30 .tan 60
tan 45
° °
°
 
4. Life time of electric bulbs are given in the following frequency distribution: 
Life Time 
(in hours) 
250-300 300-350 350-400 400-450 450-500 
Number 
of bulbs 
5 14 21 12 10 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Explain why1 2 3 4 5 6 7 5 × × × × × × + is a composite number? 
6. Show that any positive even integer can be written in the form 6q, 6q+2, 6q+4, where q is an 
integer. 
7. Solve the following pair of linear equations: 
x+3y=9 
2x-y+3=0 
8. In a rectangle ABCD, E is middle point of AD. If AD=40 m, AB=48m then find EB. 
9. Show that: 
1 sin
sec tan
1 sin
A
A A
A
- + - +
 
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 PQR ? , if B and C are points on the sides PR and QR respectively such that RB=10cm, 
PR=18cm, BC=15 cm and CQ=15 cm, then find whether BC is parallel to QR or not. 
2. In a right angled ABC ? , if 90 B ? = ° , AC=25 cm and BC=7cm, then find tan A. 
3. Find the value of
tan 30 .tan 60
tan 45
° °
°
 
4. Life time of electric bulbs are given in the following frequency distribution: 
Life Time 
(in hours) 
250-300 300-350 350-400 400-450 450-500 
Number 
of bulbs 
5 14 21 12 10 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Explain why1 2 3 4 5 6 7 5 × × × × × × + is a composite number? 
6. Show that any positive even integer can be written in the form 6q, 6q+2, 6q+4, where q is an 
integer. 
7. Solve the following pair of linear equations: 
x+3y=9 
2x-y+3=0 
8. In a rectangle ABCD, E is middle point of AD. If AD=40 m, AB=48m then find EB. 
9. Show that: 
1 sin
sec tan
1 sin
A
A A
A
- + - +
 
 
 
 
 
10. Ramesh is a cricket player. He played 50 matches in a year. His data regarding runs scored is 
given below. Calculate his average score. 
Score 
(runs) 
0-20 20-40 40-60 60-80 80-100 100-120 
Number of 
matches 
5 11 13 7 8 4 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that3 5 2 - is an irrational number. 
12. Check whether polynomial x-1 is a factor of the polynomial
3 2
8 19 12. x x x - + - . Verify by 
division algorithm. 
13. If
4 3 2
2 6 6 x x x x k - + - + is completely divisible by
2
2 3 x x - + , then find the value of k. 
14. If zeroes of the polynomial
2
4 2 x x a + + area and
2
a
, then find the value of a. 
15. Two right triangles ABC and DBC are drawn on the same hypotenuse. BC and on same side of 
BC. If AC and BD intersect at P, then prove that AP PC BP PD × = × . 
16. In a trapezium diagonals AC and BD intersect at O. if AB=3CD, then find ration of areas of 
triangles COD and AOB. 
17. If 2sinA : 3cosA=3:4, then find the values of tan A, cosec A and cos A. 
18. cos a ecA p = and cot b A q = , then prove that
2 2
2 2
1
p q
a b
- = 
19. Calculate the mean for the following frequency distribution: 
Class 10-30 30-50 50-70 70-90 90-110 
Frequency 15 18 25 10 2 
 
20. The following observations are about the heights of 800 persons. Draw a ‘less than type’ 
ogive for the data: 
Height  
(in cm) 
135-
140 
140-
145 
145-
150 
150-
155 
155-
160 
160-
165 
165-
170 
170-
175 
Number of 
persons 
50 70 80 150 170 100 95 85 
 
Section D 
Question no. 21 to 30 carry four marks. 
21. The sum of LCM and HCF of two numbers is 7380. If the LCM of these numbers is 7340 more 
than their HCF, find the product of the two numbers. 
22. An old person decided to donate some property and assets before his death to different 
orphanage for the well-being of the children living there. His total property is represented by
4 3 2
4 8 5 x x x x + - + - and the number of orphanages contacted is given by
2
1 x x - + . The left 
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 PQR ? , if B and C are points on the sides PR and QR respectively such that RB=10cm, 
PR=18cm, BC=15 cm and CQ=15 cm, then find whether BC is parallel to QR or not. 
2. In a right angled ABC ? , if 90 B ? = ° , AC=25 cm and BC=7cm, then find tan A. 
3. Find the value of
tan 30 .tan 60
tan 45
° °
°
 
4. Life time of electric bulbs are given in the following frequency distribution: 
Life Time 
(in hours) 
250-300 300-350 350-400 400-450 450-500 
Number 
of bulbs 
5 14 21 12 10 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Explain why1 2 3 4 5 6 7 5 × × × × × × + is a composite number? 
6. Show that any positive even integer can be written in the form 6q, 6q+2, 6q+4, where q is an 
integer. 
7. Solve the following pair of linear equations: 
x+3y=9 
2x-y+3=0 
8. In a rectangle ABCD, E is middle point of AD. If AD=40 m, AB=48m then find EB. 
9. Show that: 
1 sin
sec tan
1 sin
A
A A
A
- + - +
 
 
 
 
 
10. Ramesh is a cricket player. He played 50 matches in a year. His data regarding runs scored is 
given below. Calculate his average score. 
Score 
(runs) 
0-20 20-40 40-60 60-80 80-100 100-120 
Number of 
matches 
5 11 13 7 8 4 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that3 5 2 - is an irrational number. 
12. Check whether polynomial x-1 is a factor of the polynomial
3 2
8 19 12. x x x - + - . Verify by 
division algorithm. 
13. If
4 3 2
2 6 6 x x x x k - + - + is completely divisible by
2
2 3 x x - + , then find the value of k. 
14. If zeroes of the polynomial
2
4 2 x x a + + area and
2
a
, then find the value of a. 
15. Two right triangles ABC and DBC are drawn on the same hypotenuse. BC and on same side of 
BC. If AC and BD intersect at P, then prove that AP PC BP PD × = × . 
16. In a trapezium diagonals AC and BD intersect at O. if AB=3CD, then find ration of areas of 
triangles COD and AOB. 
17. If 2sinA : 3cosA=3:4, then find the values of tan A, cosec A and cos A. 
18. cos a ecA p = and cot b A q = , then prove that
2 2
2 2
1
p q
a b
- = 
19. Calculate the mean for the following frequency distribution: 
Class 10-30 30-50 50-70 70-90 90-110 
Frequency 15 18 25 10 2 
 
20. The following observations are about the heights of 800 persons. Draw a ‘less than type’ 
ogive for the data: 
Height  
(in cm) 
135-
140 
140-
145 
145-
150 
150-
155 
155-
160 
160-
165 
165-
170 
170-
175 
Number of 
persons 
50 70 80 150 170 100 95 85 
 
Section D 
Question no. 21 to 30 carry four marks. 
21. The sum of LCM and HCF of two numbers is 7380. If the LCM of these numbers is 7340 more 
than their HCF, find the product of the two numbers. 
22. An old person decided to donate some property and assets before his death to different 
orphanage for the well-being of the children living there. His total property is represented by
4 3 2
4 8 5 x x x x + - + - and the number of orphanages contacted is given by
2
1 x x - + . The left 
 
 
 
 
over amount he kept for his remaining life. Find the amount of money received by each 
orphanage and the amount of money he kept for himself. 
23. Find all other zeroes of the polynomial
4 3 2
2 19 9 9 x x x x - - + + , if two of its zeroes are 1 and -3. 
24. The area of a rectangle reduce by 
2
160m if its length is increased by 5m and breadth is 
reduce by 4m. However if length is decreased by 10m and breadt is increased by 2m, then its 
area is decreased by
2
100m . Find the dimensions of the rectangle. 
25. In the figure DEPG is a square and 90 BAC ? = °. Prove that 
 
a) AGF DBG ? ? ~ 
b) AGF EFC ? ? ~ 
c) DBG EFC ? ? ~ 
d) 
2
DE BD EC = × 
26. In a figure of ABC ? , P is the middle point of BC and Q is middle point of AP. If extended BQ 
meets AC at R, then prove that
1
2
RA CA = 
 
27. If sec tan p ? ? + = ; show that
2
2
1
cos 1
1
p
ec
p
?
- =
+
 
28. Prove that:
tan sec 1 1 sin cos
tan sec 1 cos 1 sin
A A A A
A A A A
+ - +
= =
- + - 
29. Literacy rates of 40 cities is given in the following table. If it is given that mean literacy rate is 
63.5, then find the missing frequencies x and y. 
Literacy 
rate 
(in%) 
35-
50 
40-
45 
45-
50 
50-
55 
55-
60 
60-
65 
65-
70 
70-
75 
75-
80 
80-
85 
85-
90 
Number 
of cities 
1 2 3 x y 6 8 4 2 3 2 
 
30. In a hospital, during the month of October 2013, number of patients admitted for dengue and 
their ages are as follows: 
Age 
(in years) 
0-8 8-16 16-24 24-32 32-40 40-48 48-56 56-64 64-72 
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 PQR ? , if B and C are points on the sides PR and QR respectively such that RB=10cm, 
PR=18cm, BC=15 cm and CQ=15 cm, then find whether BC is parallel to QR or not. 
2. In a right angled ABC ? , if 90 B ? = ° , AC=25 cm and BC=7cm, then find tan A. 
3. Find the value of
tan 30 .tan 60
tan 45
° °
°
 
4. Life time of electric bulbs are given in the following frequency distribution: 
Life Time 
(in hours) 
250-300 300-350 350-400 400-450 450-500 
Number 
of bulbs 
5 14 21 12 10 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. Explain why1 2 3 4 5 6 7 5 × × × × × × + is a composite number? 
6. Show that any positive even integer can be written in the form 6q, 6q+2, 6q+4, where q is an 
integer. 
7. Solve the following pair of linear equations: 
x+3y=9 
2x-y+3=0 
8. In a rectangle ABCD, E is middle point of AD. If AD=40 m, AB=48m then find EB. 
9. Show that: 
1 sin
sec tan
1 sin
A
A A
A
- + - +
 
 
 
 
 
10. Ramesh is a cricket player. He played 50 matches in a year. His data regarding runs scored is 
given below. Calculate his average score. 
Score 
(runs) 
0-20 20-40 40-60 60-80 80-100 100-120 
Number of 
matches 
5 11 13 7 8 4 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that3 5 2 - is an irrational number. 
12. Check whether polynomial x-1 is a factor of the polynomial
3 2
8 19 12. x x x - + - . Verify by 
division algorithm. 
13. If
4 3 2
2 6 6 x x x x k - + - + is completely divisible by
2
2 3 x x - + , then find the value of k. 
14. If zeroes of the polynomial
2
4 2 x x a + + area and
2
a
, then find the value of a. 
15. Two right triangles ABC and DBC are drawn on the same hypotenuse. BC and on same side of 
BC. If AC and BD intersect at P, then prove that AP PC BP PD × = × . 
16. In a trapezium diagonals AC and BD intersect at O. if AB=3CD, then find ration of areas of 
triangles COD and AOB. 
17. If 2sinA : 3cosA=3:4, then find the values of tan A, cosec A and cos A. 
18. cos a ecA p = and cot b A q = , then prove that
2 2
2 2
1
p q
a b
- = 
19. Calculate the mean for the following frequency distribution: 
Class 10-30 30-50 50-70 70-90 90-110 
Frequency 15 18 25 10 2 
 
20. The following observations are about the heights of 800 persons. Draw a ‘less than type’ 
ogive for the data: 
Height  
(in cm) 
135-
140 
140-
145 
145-
150 
150-
155 
155-
160 
160-
165 
165-
170 
170-
175 
Number of 
persons 
50 70 80 150 170 100 95 85 
 
Section D 
Question no. 21 to 30 carry four marks. 
21. The sum of LCM and HCF of two numbers is 7380. If the LCM of these numbers is 7340 more 
than their HCF, find the product of the two numbers. 
22. An old person decided to donate some property and assets before his death to different 
orphanage for the well-being of the children living there. His total property is represented by
4 3 2
4 8 5 x x x x + - + - and the number of orphanages contacted is given by
2
1 x x - + . The left 
 
 
 
 
over amount he kept for his remaining life. Find the amount of money received by each 
orphanage and the amount of money he kept for himself. 
23. Find all other zeroes of the polynomial
4 3 2
2 19 9 9 x x x x - - + + , if two of its zeroes are 1 and -3. 
24. The area of a rectangle reduce by 
2
160m if its length is increased by 5m and breadth is 
reduce by 4m. However if length is decreased by 10m and breadt is increased by 2m, then its 
area is decreased by
2
100m . Find the dimensions of the rectangle. 
25. In the figure DEPG is a square and 90 BAC ? = °. Prove that 
 
a) AGF DBG ? ? ~ 
b) AGF EFC ? ? ~ 
c) DBG EFC ? ? ~ 
d) 
2
DE BD EC = × 
26. In a figure of ABC ? , P is the middle point of BC and Q is middle point of AP. If extended BQ 
meets AC at R, then prove that
1
2
RA CA = 
 
27. If sec tan p ? ? + = ; show that
2
2
1
cos 1
1
p
ec
p
?
- =
+
 
28. Prove that:
tan sec 1 1 sin cos
tan sec 1 cos 1 sin
A A A A
A A A A
+ - +
= =
- + - 
29. Literacy rates of 40 cities is given in the following table. If it is given that mean literacy rate is 
63.5, then find the missing frequencies x and y. 
Literacy 
rate 
(in%) 
35-
50 
40-
45 
45-
50 
50-
55 
55-
60 
60-
65 
65-
70 
70-
75 
75-
80 
80-
85 
85-
90 
Number 
of cities 
1 2 3 x y 6 8 4 2 3 2 
 
30. In a hospital, during the month of October 2013, number of patients admitted for dengue and 
their ages are as follows: 
Age 
(in years) 
0-8 8-16 16-24 24-32 32-40 40-48 48-56 56-64 64-72 
 
 
 
 
Number of 
patients 
10 12 8 25 15 11 21 30 22