Maths Past Year Paper SA-1(Set -15) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Mathematics (Maths) Class 10

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Class 10 : Maths Past Year Paper SA-1(Set -15) - 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 XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ  . If 
AY=2.2cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. If tan cot 2 ? ? + = , then find the value of
2 2
tan cot ? ? + . 
3. If 45 ? = ° , then find the value of
2 2
2sin 3cos ec ? ? + ? 
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 
Find the class mark of the modal class interval. 
 
Section B 
Question numbers 5 to 10 are two marks each. 
5. Find whether decimal expansion of 
13
64
is a terminating or non-terminating decimal. If it 
terminates, find the number of decimal places its decimal expansion has. 
6. Write the decimal expansion of 
27
1250
without actual division. 
7. Ifa and ß are the zeroes of a polynomial
2
9 12 4 y y + + , then find the value of a ß aß + + . 
8. Are the given figures similar? Give reason. 
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 XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ  . If 
AY=2.2cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. If tan cot 2 ? ? + = , then find the value of
2 2
tan cot ? ? + . 
3. If 45 ? = ° , then find the value of
2 2
2sin 3cos ec ? ? + ? 
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 
Find the class mark of the modal class interval. 
 
Section B 
Question numbers 5 to 10 are two marks each. 
5. Find whether decimal expansion of 
13
64
is a terminating or non-terminating decimal. If it 
terminates, find the number of decimal places its decimal expansion has. 
6. Write the decimal expansion of 
27
1250
without actual division. 
7. Ifa and ß are the zeroes of a polynomial
2
9 12 4 y y + + , then find the value of a ß aß + + . 
8. Are the given figures similar? Give reason. 
 
 
 
 
 
9. Simplify: (1-sin A)(tan A + sec A) 
10. The following distribution shows the daily pocket allowance of children of a locality: 
Daily pocket 
allowance (in Rs.) 
12 15 20 25 30 
Number of 
children 
8 7 15 6 4 
Find the median of the data. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 3 5 + is an irrational number. 
12. Solve for x and y: 
x+4y=27xy 
x+2y=21xy 
13. Determine graphically whether the following pair of linear equations  
2x-3y=8 
4x-6y=16 has 
a) A unique solution, 
b) Infinitely many solution or 
c) No solution 
14. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k. 
15. As shown in the figure, a 26m long ladder is placed at A. if it is placed along wall PQ, it 
reaches a height of 24m whereas it reaches a height of 10m if it is placed against wall RS. 
Find the distance between the walls. 
 
16. If in ABC ? , AD is median and AM BC ? , then prove that 
2 2 2 2
1
2
2
AB AC AD BC + = + 
17. Prove that: 
2 2
2 2
2 2
cos
sec cos 2
cos sin
sin A A
A ec A
A A
+ = · - 
18. In ABC ? , right angled at C, if
1
tan
3
A = , show that sin A. cos B + cos A. sin B=1 
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 XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ  . If 
AY=2.2cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. If tan cot 2 ? ? + = , then find the value of
2 2
tan cot ? ? + . 
3. If 45 ? = ° , then find the value of
2 2
2sin 3cos ec ? ? + ? 
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 
Find the class mark of the modal class interval. 
 
Section B 
Question numbers 5 to 10 are two marks each. 
5. Find whether decimal expansion of 
13
64
is a terminating or non-terminating decimal. If it 
terminates, find the number of decimal places its decimal expansion has. 
6. Write the decimal expansion of 
27
1250
without actual division. 
7. Ifa and ß are the zeroes of a polynomial
2
9 12 4 y y + + , then find the value of a ß aß + + . 
8. Are the given figures similar? Give reason. 
 
 
 
 
 
9. Simplify: (1-sin A)(tan A + sec A) 
10. The following distribution shows the daily pocket allowance of children of a locality: 
Daily pocket 
allowance (in Rs.) 
12 15 20 25 30 
Number of 
children 
8 7 15 6 4 
Find the median of the data. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 3 5 + is an irrational number. 
12. Solve for x and y: 
x+4y=27xy 
x+2y=21xy 
13. Determine graphically whether the following pair of linear equations  
2x-3y=8 
4x-6y=16 has 
a) A unique solution, 
b) Infinitely many solution or 
c) No solution 
14. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k. 
15. As shown in the figure, a 26m long ladder is placed at A. if it is placed along wall PQ, it 
reaches a height of 24m whereas it reaches a height of 10m if it is placed against wall RS. 
Find the distance between the walls. 
 
16. If in ABC ? , AD is median and AM BC ? , then prove that 
2 2 2 2
1
2
2
AB AC AD BC + = + 
17. Prove that: 
2 2
2 2
2 2
cos
sec cos 2
cos sin
sin A A
A ec A
A A
+ = · - 
18. In ABC ? , right angled at C, if
1
tan
3
A = , show that sin A. cos B + cos A. sin B=1 
 
 
 
 
19. In a study on asthmatic patients, the following frequency distribution was obtained. Find the 
average (mean) age at the detection. 
Age at detection 
(in years) 
0-9 10-19 20-29 30-39 40-49 
Number of 
patients 
12 25 13 10 5 
 
20. For the following distribution, draw a ‘less than type’ ogive and from the curve, find the 
median. 
Marks 
obtained 
Less 
than 
20 
Less 
than 
30 
Less 
than 
40 
Less 
than 
50 
Less 
than 
60 
Less 
than 
70 
Less 
than 
80 
Less 
than 
90 
Less 
than 
100 
Number 
of 
students 
2 7 17 40 60 82 85 90 100 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Dhudnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from 
these containers is poured into glasses of equal capacity to their brim. Find the minimum 
number of glasses that can be filled. 
22. The ratio of incomes of two persons A and B is 9:7and the ratio of their expenditure is 4:3. If 
their savings are Rs. 200 per month, find their monthly incomes. 
Why is it necessary to save money? 
23. Find all the zeroes of
4 3 2
5 15 12 x x x x - + + - , if it is given that two of its zeroes are 1 and 4. 
24. A boat goes 30 km upstream and 20 km downstream in 7 hours. In 6 hours, it can go 18 km 
upstream and 30 km downstream. Determine the speed of the stream and that of the boat in 
still water. 
25. In ABC ? , AD BC ? and D lies on BC such that 4DB=CD, then proves that 
2 2 2
5 5 3 AB AC BC = - 
26. ABC is an isosceles triangle in which 90 B ? = ° and 3 2 AC m = . Two equilateral triangles ACP 
and ABQ are drawn on the sides AC and AB. Find the ratio of area ( ) ABQ ? and area ( ) ACP ? . 
27. In the adjoining figure, ABCD is a rectangle with breadth BC=7cm and 30 CAB ? = ° . Find the 
length of side AB of the rectangle and length of diagonal AC. If the 60 CAB ? = ° , then what is 
the size of the side AB of the rectangle (use 3 1.73 = and 2 1.41 = , if required) 
 
28. If cos sin a b c ? ? - = , then prove that 
2 2 2
sin cos a b a b c ? ? + = ± + - 
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 XYZ ? , A and B are points on the sides XY and XZ respectively such that AB YZ  . If 
AY=2.2cm, XB=3.3cm and XZ=6.6cm, then find AX. 
2. If tan cot 2 ? ? + = , then find the value of
2 2
tan cot ? ? + . 
3. If 45 ? = ° , then find the value of
2 2
2sin 3cos ec ? ? + ? 
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 
Find the class mark of the modal class interval. 
 
Section B 
Question numbers 5 to 10 are two marks each. 
5. Find whether decimal expansion of 
13
64
is a terminating or non-terminating decimal. If it 
terminates, find the number of decimal places its decimal expansion has. 
6. Write the decimal expansion of 
27
1250
without actual division. 
7. Ifa and ß are the zeroes of a polynomial
2
9 12 4 y y + + , then find the value of a ß aß + + . 
8. Are the given figures similar? Give reason. 
 
 
 
 
 
9. Simplify: (1-sin A)(tan A + sec A) 
10. The following distribution shows the daily pocket allowance of children of a locality: 
Daily pocket 
allowance (in Rs.) 
12 15 20 25 30 
Number of 
children 
8 7 15 6 4 
Find the median of the data. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 3 5 + is an irrational number. 
12. Solve for x and y: 
x+4y=27xy 
x+2y=21xy 
13. Determine graphically whether the following pair of linear equations  
2x-3y=8 
4x-6y=16 has 
a) A unique solution, 
b) Infinitely many solution or 
c) No solution 
14. If
4 3 2
4 7 4 7 x x x x k + - - + is completely divisible by
3
x x - , then find the value of k. 
15. As shown in the figure, a 26m long ladder is placed at A. if it is placed along wall PQ, it 
reaches a height of 24m whereas it reaches a height of 10m if it is placed against wall RS. 
Find the distance between the walls. 
 
16. If in ABC ? , AD is median and AM BC ? , then prove that 
2 2 2 2
1
2
2
AB AC AD BC + = + 
17. Prove that: 
2 2
2 2
2 2
cos
sec cos 2
cos sin
sin A A
A ec A
A A
+ = · - 
18. In ABC ? , right angled at C, if
1
tan
3
A = , show that sin A. cos B + cos A. sin B=1 
 
 
 
 
19. In a study on asthmatic patients, the following frequency distribution was obtained. Find the 
average (mean) age at the detection. 
Age at detection 
(in years) 
0-9 10-19 20-29 30-39 40-49 
Number of 
patients 
12 25 13 10 5 
 
20. For the following distribution, draw a ‘less than type’ ogive and from the curve, find the 
median. 
Marks 
obtained 
Less 
than 
20 
Less 
than 
30 
Less 
than 
40 
Less 
than 
50 
Less 
than 
60 
Less 
than 
70 
Less 
than 
80 
Less 
than 
90 
Less 
than 
100 
Number 
of 
students 
2 7 17 40 60 82 85 90 100 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Dhudnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from 
these containers is poured into glasses of equal capacity to their brim. Find the minimum 
number of glasses that can be filled. 
22. The ratio of incomes of two persons A and B is 9:7and the ratio of their expenditure is 4:3. If 
their savings are Rs. 200 per month, find their monthly incomes. 
Why is it necessary to save money? 
23. Find all the zeroes of
4 3 2
5 15 12 x x x x - + + - , if it is given that two of its zeroes are 1 and 4. 
24. A boat goes 30 km upstream and 20 km downstream in 7 hours. In 6 hours, it can go 18 km 
upstream and 30 km downstream. Determine the speed of the stream and that of the boat in 
still water. 
25. In ABC ? , AD BC ? and D lies on BC such that 4DB=CD, then proves that 
2 2 2
5 5 3 AB AC BC = - 
26. ABC is an isosceles triangle in which 90 B ? = ° and 3 2 AC m = . Two equilateral triangles ACP 
and ABQ are drawn on the sides AC and AB. Find the ratio of area ( ) ABQ ? and area ( ) ACP ? . 
27. In the adjoining figure, ABCD is a rectangle with breadth BC=7cm and 30 CAB ? = ° . Find the 
length of side AB of the rectangle and length of diagonal AC. If the 60 CAB ? = ° , then what is 
the size of the side AB of the rectangle (use 3 1.73 = and 2 1.41 = , if required) 
 
28. If cos sin a b c ? ? - = , then prove that 
2 2 2
sin cos a b a b c ? ? + = ± + - 
 
 
 
 
29. Given thatsin( ) sin cos cos sin A B A B A B - = · - · . Find the value ofsin15° in two ways. 
a) Taking 60 , 45 A B = ° = ° , and  
b) Taking 45 , 30 A B = ° = ° 
30. A class test in mathematics was conducted for class VI of a school. Following distribution 
gives marks (out of 60) of students: 
Marks 0-10 10-20 20-30 30-40 40-50 50-60 
Number of 
students 
8 22 12 10 5 3 
Find the mean of the marks obtained. 
31. In an examination, 150 students appeared, and their marks (out of 200) are given in the 
following distribution. Find the missing frequencies x and y, when it is given that mean 
marks is 103. 
Marks 0-25 25-50 50-75 75-100 100-125 125-150 150-175 175-200 
Number 
of 
students 
2 10 x 30 y 15 12 4 
 
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