Maths Past Year Paper SA-1(Set -6) - 2014, Class 10, CBSE Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Maths Past Year Paper SA-1(Set -6) - 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of 
the ladder from the base of the wall. 
2. If tan cot 2 ? ? + = , then find the value of 
2 2
tan cot ? ? + 
3. If
5
cos
4
ec? = , find the value of cot? . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 
6. What is the decimal expansion of the rational number
201
250
? 
7. Find the quadratic polynomial whose zeroes are 4 and
3
5
- . 
8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 
 
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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of 
the ladder from the base of the wall. 
2. If tan cot 2 ? ? + = , then find the value of 
2 2
tan cot ? ? + 
3. If
5
cos
4
ec? = , find the value of cot? . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 
6. What is the decimal expansion of the rational number
201
250
? 
7. Find the quadratic polynomial whose zeroes are 4 and
3
5
- . 
8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 
 
 
 
 
 
9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +
 
10. In a section of class X, heights of 50 students are shown in the following table: 
Height 
(in cm) 
148 154 160 150 152 149 155 
Number 
of 
students 
3 7 2 12 8 14 4 
Find the median height of this section. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is an irrational number. 
12. Solve for x and y: 
11 1
10
9 4
5
x y
x y
- =
- =
 
13. If one zero of the polynomial 
2
( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value 
of a. 
14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines 
represented by the pair are: 
a) Intersecting 
b) Coincident 
c) Parallel 
15. In the figure of , ABC DE AC ?  . If DC AP  , where point P lies on BC produced, then shows 
that  
BE BC
BC CP
= 
  
16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and
ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 
17. When is an equation called ‘an identity’. Prove that trigonometric identity
2 2
1 tan sec A A + = . 
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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of 
the ladder from the base of the wall. 
2. If tan cot 2 ? ? + = , then find the value of 
2 2
tan cot ? ? + 
3. If
5
cos
4
ec? = , find the value of cot? . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 
6. What is the decimal expansion of the rational number
201
250
? 
7. Find the quadratic polynomial whose zeroes are 4 and
3
5
- . 
8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 
 
 
 
 
 
9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +
 
10. In a section of class X, heights of 50 students are shown in the following table: 
Height 
(in cm) 
148 154 160 150 152 149 155 
Number 
of 
students 
3 7 2 12 8 14 4 
Find the median height of this section. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is an irrational number. 
12. Solve for x and y: 
11 1
10
9 4
5
x y
x y
- =
- =
 
13. If one zero of the polynomial 
2
( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value 
of a. 
14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines 
represented by the pair are: 
a) Intersecting 
b) Coincident 
c) Parallel 
15. In the figure of , ABC DE AC ?  . If DC AP  , where point P lies on BC produced, then shows 
that  
BE BC
BC CP
= 
  
16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and
ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 
17. When is an equation called ‘an identity’. Prove that trigonometric identity
2 2
1 tan sec A A + = . 
 
 
 
 
18. If
12
cos
13
A = ,then verify that: 
35
sin (1 tan )
156
A A - = 
19. Following frequency distribution gives the heights of students of class IX in a school: 
Height (in cm) 141-145 146-150 151-155 156-160 161-165 
Number of 
students 
8 18 20 12 2 
Find the median height. 
20. The following frequency distribution gives the marks (out of 50) of students in a class test: 
Marks 0-10 10-20 20-30 30-40 40-50 
Number of 
students 
10 24 38 22 6 
Using step deviation method to find the mean marks. 
 
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 owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol /diesel. 
The taxi charges in city comprises of fixed charges together with the charge for the distance 
covered. For a journey of 12 km, the charge paid is Rs. 89 and for journey of 20 km, the 
charge paid is Rs. 145. 
a) What will a person have to pay for travelling a distance of 30km? 
b) Why did he decide to use CNG for his taxi as a fuel? 
23. If a polynomial
4 3 2
3 4 16 15 14 x x a x - - + + is divided by another polynomial
2
4 x - , the 
remainder comes out to be px + q. Find the value of p and q. 
24. Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditures are 
in the ratio 4:3. If each of them saves Rs 50 at the end of the month, find their pocket money. 
25. Find the length of the diagonal of the rectangle BCDE if BCA DCF ? = ? . AC=6m and CF=13m. 
 
26. If in the ABC ? , AD is median and AM BC ? , then prove that 
2 2 2 2
2( ) AB AC AD BD + = + 
27. Prove that:
2 2
sin tan cos cot 2sin cos tan cot ? ? ? ? ? ? ? ? · + · + · = + 
28. If A, B, C are interior angles of a triangle ABC then 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 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. A ladder 10 m long reaches a window 6 m above the ground. Find the distance of the foot of 
the ladder from the base of the wall. 
2. If tan cot 2 ? ? + = , then find the value of 
2 2
tan cot ? ? + 
3. If
5
cos
4
ec? = , find the value of cot? . 
4. In the following table, find x and y, where f and c.f. have their usual meanings: 
Class interval 0-8 8-16 16-24 24-32 
f 2 10 y 5 
c.f. x 12 30 35 
 
Section B 
Question number 5 to 10 carry two marks each. 
5. How many irrational numbers lie between 2 and 3 ? Write any two of them. 
6. What is the decimal expansion of the rational number
201
250
? 
7. Find the quadratic polynomial whose zeroes are 4 and
3
5
- . 
8. In the figure if B C ? = ? , prove that OAB ODC ? ? ~ . 
 
 
 
 
 
9. Show that:
1 sin
sec tan
1 sin
A
A A
A
- = - +
 
10. In a section of class X, heights of 50 students are shown in the following table: 
Height 
(in cm) 
148 154 160 150 152 149 155 
Number 
of 
students 
3 7 2 12 8 14 4 
Find the median height of this section. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Prove that 2 is an irrational number. 
12. Solve for x and y: 
11 1
10
9 4
5
x y
x y
- =
- =
 
13. If one zero of the polynomial 
2
( 2) 6 5 a x x a + + + is reciprocal of the other, then find the value 
of a. 
14. Given a linear equation 2x+3y=10. Write another linear equation, so that the lines 
represented by the pair are: 
a) Intersecting 
b) Coincident 
c) Parallel 
15. In the figure of , ABC DE AC ?  . If DC AP  , where point P lies on BC produced, then shows 
that  
BE BC
BC CP
= 
  
16. In two triangles ABC and PQR, if AD and PS are medians to ABC ? and PQR ? respectively and
ABD PQS ? ? ~ , then prove that ABC PQR ? ? ~ . 
17. When is an equation called ‘an identity’. Prove that trigonometric identity
2 2
1 tan sec A A + = . 
 
 
 
 
18. If
12
cos
13
A = ,then verify that: 
35
sin (1 tan )
156
A A - = 
19. Following frequency distribution gives the heights of students of class IX in a school: 
Height (in cm) 141-145 146-150 151-155 156-160 161-165 
Number of 
students 
8 18 20 12 2 
Find the median height. 
20. The following frequency distribution gives the marks (out of 50) of students in a class test: 
Marks 0-10 10-20 20-30 30-40 40-50 
Number of 
students 
10 24 38 22 6 
Using step deviation method to find the mean marks. 
 
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 owner of a taxi company decides to run all the taxi on CNG fuels instead of petrol /diesel. 
The taxi charges in city comprises of fixed charges together with the charge for the distance 
covered. For a journey of 12 km, the charge paid is Rs. 89 and for journey of 20 km, the 
charge paid is Rs. 145. 
a) What will a person have to pay for travelling a distance of 30km? 
b) Why did he decide to use CNG for his taxi as a fuel? 
23. If a polynomial
4 3 2
3 4 16 15 14 x x a x - - + + is divided by another polynomial
2
4 x - , the 
remainder comes out to be px + q. Find the value of p and q. 
24. Pocket money of Zahira and Zohra are in the ratio 6:5 and the ratio of their expenditures are 
in the ratio 4:3. If each of them saves Rs 50 at the end of the month, find their pocket money. 
25. Find the length of the diagonal of the rectangle BCDE if BCA DCF ? = ? . AC=6m and CF=13m. 
 
26. If in the ABC ? , AD is median and AM BC ? , then prove that 
2 2 2 2
2( ) AB AC AD BD + = + 
27. Prove that:
2 2
sin tan cos cot 2sin cos tan cot ? ? ? ? ? ? ? ? · + · + · = + 
28. If A, B, C are interior angles of a triangle ABC then prove that: 
 
 
 
 
a) sin cos
2 2
B C A +
= 
b) tan cot
2 2
C A B +
= 
29. If sec tan x ? ? - = , show that
1
sec tan
x
? ? + = and hence find the values of cos? andsin? . 
30. In a certain locality, monthly consumptions of electricity (in unit) of 122 families are given in 
the following table. 
Mode is given to be 139, find the missing frequencies x and y. 
Electricity 
consumed 
70-90 90-110 110-130 130-
150 
150-
170 
170-
190 
190-
210 
210-
230 
Number of 
families 
x 10 y 40 18 9 8 3 
 
31. In a locality, weekly expenditure of 40 families on fruits and vegetable (n rupees) is given in 
the following frequency distribution: 
Expenditure 
(in Rs.) 
500-700 700-900 900-1100 1100-1300 1300-1500 
Number of 
families 
6 8 10 9 7 
Find the mean weekly expenditure. 
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