Maths Past Year Paper SA-1(Set -8) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Created by: Indu Gupta

Class 10 : Maths Past Year Paper SA-1(Set -8) - 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. If LCM(12,28)=84, find HCF(12,28). 
2. Write the polynomial whose zeroes are -5 and 4. 
3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 
4. If sec A + tan A = 7, then find sec A – tan A. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 
6. After how many decimal places, the decimal expansion of 
3 4
37
2 5
will terminate? 
7. For what value of k, the pair of equations 4x-3y=9, 2x+ky=11 has no solution? 
8. If 
3
sin
2
A = , find the value of 
2
2cot 1 A - . 
9. If A, B and C are interior angles of a ABC ? , prove that: tan cot
2 2
B C A + ? ?
=
? ?
? ?
 
10. Find x and y from the following cumulative frequency distribution: 
Classes 0-8 8-16 16-24 24-32 32-40 
Frequency 15 x 15 18 9 
Cumulativ
e 
frequency 
15 28 43 y 70 
 
 
Section C 
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. If LCM(12,28)=84, find HCF(12,28). 
2. Write the polynomial whose zeroes are -5 and 4. 
3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 
4. If sec A + tan A = 7, then find sec A – tan A. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 
6. After how many decimal places, the decimal expansion of 
3 4
37
2 5
will terminate? 
7. For what value of k, the pair of equations 4x-3y=9, 2x+ky=11 has no solution? 
8. If 
3
sin
2
A = , find the value of 
2
2cot 1 A - . 
9. If A, B and C are interior angles of a ABC ? , prove that: tan cot
2 2
B C A + ? ?
=
? ?
? ?
 
10. Find x and y from the following cumulative frequency distribution: 
Classes 0-8 8-16 16-24 24-32 32-40 
Frequency 15 x 15 18 9 
Cumulativ
e 
frequency 
15 28 43 y 70 
 
 
Section C 
 
 
 
 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is rational. 
12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 
13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the 
number obtained by reversing the order of the digits of the number. Find the number. 
14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide 
his entire land among his four children as shown in the figure. D, E, F are mid-points of sides 
AB, BC and AC respectively. 
 
Find ratio of area of EFD ? to area of ABC ? . 
Is length of 
1
2
DF BC = ? Why? 
Which values of Krishna can one imbibe in his life? 
15. ABCD is a trapezium in which AB DC  and its diagonal intersect each other at the point O. 
Show that 
AO CO
BO DO
= . 
16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively,  
 
Prove that 
a) ABC AMP ? ? ~ 
b) 
CA BC
PA MP
= 
17. Find the value of sin 60° geometrically 
18. State whether the following are true or false. Justify your answer. 
sin(A+B)=sin A + sin B 
The value of tan A is always less than 1. 
12
sec
5
A = for some value of A ? 
19. Prove that: 
cos(90 ) 1 sin(90 )
2cos
1 sin(90 ) cos(90 )
ec
? ?
?
? ?
° - + ° - + =
+ ° - ° - 
20. Find the mode of the following frequency distribution: 
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. If LCM(12,28)=84, find HCF(12,28). 
2. Write the polynomial whose zeroes are -5 and 4. 
3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 
4. If sec A + tan A = 7, then find sec A – tan A. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 
6. After how many decimal places, the decimal expansion of 
3 4
37
2 5
will terminate? 
7. For what value of k, the pair of equations 4x-3y=9, 2x+ky=11 has no solution? 
8. If 
3
sin
2
A = , find the value of 
2
2cot 1 A - . 
9. If A, B and C are interior angles of a ABC ? , prove that: tan cot
2 2
B C A + ? ?
=
? ?
? ?
 
10. Find x and y from the following cumulative frequency distribution: 
Classes 0-8 8-16 16-24 24-32 32-40 
Frequency 15 x 15 18 9 
Cumulativ
e 
frequency 
15 28 43 y 70 
 
 
Section C 
 
 
 
 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is rational. 
12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 
13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the 
number obtained by reversing the order of the digits of the number. Find the number. 
14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide 
his entire land among his four children as shown in the figure. D, E, F are mid-points of sides 
AB, BC and AC respectively. 
 
Find ratio of area of EFD ? to area of ABC ? . 
Is length of 
1
2
DF BC = ? Why? 
Which values of Krishna can one imbibe in his life? 
15. ABCD is a trapezium in which AB DC  and its diagonal intersect each other at the point O. 
Show that 
AO CO
BO DO
= . 
16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively,  
 
Prove that 
a) ABC AMP ? ? ~ 
b) 
CA BC
PA MP
= 
17. Find the value of sin 60° geometrically 
18. State whether the following are true or false. Justify your answer. 
sin(A+B)=sin A + sin B 
The value of tan A is always less than 1. 
12
sec
5
A = for some value of A ? 
19. Prove that: 
cos(90 ) 1 sin(90 )
2cos
1 sin(90 ) cos(90 )
ec
? ?
?
? ?
° - + ° - + =
+ ° - ° - 
20. Find the mode of the following frequency distribution: 
 
 
 
 
Classes 0-6 6-12 12-18 18-24 24-30 
Frequency 7 5 10 12 6 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides 
in distinct points the other two side are divided in the same ratio. 
22. BL and CM are median of a triangle ABC right angled at A. Prove that 
2 2 2
4[ ] 5 BL CM BC + = 
 
23. Divide 
4 3 2
3 5 7 2 5 x x x x + - + + by 
2
3 1 x x + + and verify the division algorithm. 
24. Find the other zeroes of the polynomial 
4 3 2
9 3 18 x x x x + - - + , if it is given that two of its 
zeroes are 3 or 3 - 
25. Radha wants to construct a rectangular garden for children and other to play. The area of this 
rectangle remains the same if the length is increased by 7m and breadth is decreased by 3m. 
the area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. 
Find dimensions of the rectangular garden. 
26. Represent the following pair of equations graphically and write the coordinates of point 
where the lines intersect the y-axis: 
x+3yy=6; 
2x-3y=12 
27. Calculate the average daily income (in Rs) of the following data about workers working in a 
company: 
Average daily income (in Rs.) Number of workers 
Less than 100 12 
Less than 200 28 
Less than 300 34 
Less than 400 41 
Less than 500 50 
28. Prove that:
1 cos sin 1 sin
cos sin 1 cos
? ? ?
? ? ?
- + +
=
+ - 
29. Prove that:
sec 1 sec 1
2cos
sec 1 sec 1
ec
? ?
?
? ?
- +
+ =
+ - 
30. The following distribution shows the daily pocket allowance given to the children of a 
multistoried building. The average daily pocket allowance is Rs 18. Meera is one of the 
children, residing in the same building, who instead of spending his daily pocket money 
prefers to save it. 
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. If LCM(12,28)=84, find HCF(12,28). 
2. Write the polynomial whose zeroes are -5 and 4. 
3. If 7x+9y=42 and 9x+7y=22, then find the value of x + y. 
4. If sec A + tan A = 7, then find sec A – tan A. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the HCF of 240 and 228 using Euclid’s division algorithm. 
6. After how many decimal places, the decimal expansion of 
3 4
37
2 5
will terminate? 
7. For what value of k, the pair of equations 4x-3y=9, 2x+ky=11 has no solution? 
8. If 
3
sin
2
A = , find the value of 
2
2cot 1 A - . 
9. If A, B and C are interior angles of a ABC ? , prove that: tan cot
2 2
B C A + ? ?
=
? ?
? ?
 
10. Find x and y from the following cumulative frequency distribution: 
Classes 0-8 8-16 16-24 24-32 32-40 
Frequency 15 x 15 18 9 
Cumulativ
e 
frequency 
15 28 43 y 70 
 
 
Section C 
 
 
 
 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is rational. 
12. Show that square of any positive integer is of the form 4m or 4m+1, where m is any integer. 
13. The sum of the digits of a two digit number is 9. Also, nine times this number is twice the 
number obtained by reversing the order of the digits of the number. Find the number. 
14. Krishna, a farmer, has a piece of land in the shape of equilateral triangle. He wants to divide 
his entire land among his four children as shown in the figure. D, E, F are mid-points of sides 
AB, BC and AC respectively. 
 
Find ratio of area of EFD ? to area of ABC ? . 
Is length of 
1
2
DF BC = ? Why? 
Which values of Krishna can one imbibe in his life? 
15. ABCD is a trapezium in which AB DC  and its diagonal intersect each other at the point O. 
Show that 
AO CO
BO DO
= . 
16. In the figure, ABC and AMP are two right triangles, right angled at B and M respectively,  
 
Prove that 
a) ABC AMP ? ? ~ 
b) 
CA BC
PA MP
= 
17. Find the value of sin 60° geometrically 
18. State whether the following are true or false. Justify your answer. 
sin(A+B)=sin A + sin B 
The value of tan A is always less than 1. 
12
sec
5
A = for some value of A ? 
19. Prove that: 
cos(90 ) 1 sin(90 )
2cos
1 sin(90 ) cos(90 )
ec
? ?
?
? ?
° - + ° - + =
+ ° - ° - 
20. Find the mode of the following frequency distribution: 
 
 
 
 
Classes 0-6 6-12 12-18 18-24 24-30 
Frequency 7 5 10 12 6 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides 
in distinct points the other two side are divided in the same ratio. 
22. BL and CM are median of a triangle ABC right angled at A. Prove that 
2 2 2
4[ ] 5 BL CM BC + = 
 
23. Divide 
4 3 2
3 5 7 2 5 x x x x + - + + by 
2
3 1 x x + + and verify the division algorithm. 
24. Find the other zeroes of the polynomial 
4 3 2
9 3 18 x x x x + - - + , if it is given that two of its 
zeroes are 3 or 3 - 
25. Radha wants to construct a rectangular garden for children and other to play. The area of this 
rectangle remains the same if the length is increased by 7m and breadth is decreased by 3m. 
the area remains unaffected if the length is decreased by 7m and breadth is increased by 5m. 
Find dimensions of the rectangular garden. 
26. Represent the following pair of equations graphically and write the coordinates of point 
where the lines intersect the y-axis: 
x+3yy=6; 
2x-3y=12 
27. Calculate the average daily income (in Rs) of the following data about workers working in a 
company: 
Average daily income (in Rs.) Number of workers 
Less than 100 12 
Less than 200 28 
Less than 300 34 
Less than 400 41 
Less than 500 50 
28. Prove that:
1 cos sin 1 sin
cos sin 1 cos
? ? ?
? ? ?
- + +
=
+ - 
29. Prove that:
sec 1 sec 1
2cos
sec 1 sec 1
ec
? ?
?
? ?
- +
+ =
+ - 
30. The following distribution shows the daily pocket allowance given to the children of a 
multistoried building. The average daily pocket allowance is Rs 18. Meera is one of the 
children, residing in the same building, who instead of spending his daily pocket money 
prefers to save it. 
 
 
 
 
Daily 
pocket 
allowance 
11-13 13-15 15-17 17-19 19-21 21-23 23-25 
Number of 
children 
7 6 9 13 x 5 4 
Find the missing frequency x. 
Which moral values of Meera can one imbibein his life? 
31. The following gives the daily wages (in Rs.) of 58 workers of a factory. 
Daily 
wages 
20-40 40-60 60-80 80-100 100-120 120-140 140-160 
Number of 
workers 
4 6 10 16 12 7 3 
Convert the above distribution into a less than cumulative frequency distribution. Draw its 
ogive and find the median. 
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