Maths Past Year Paper SA-1(Set -3) - 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 -3) - 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. Write an irrational number between 2 and 3. 
2. Find the value of 
2 2
104 103 - . 
3. In figure AB CD  , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 
 
4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Express 2.3 in the form of 
p
q
, where p and q are integers and 0 q ? . 
6. If a+b=10 and ab=16, then find 
2 2
a b + . 
7. Prove that “Two distinct lines cannot have more than one point in common”. 
8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 
 
9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. 
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. Write an irrational number between 2 and 3. 
2. Find the value of 
2 2
104 103 - . 
3. In figure AB CD  , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 
 
4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Express 2.3 in the form of 
p
q
, where p and q are integers and 0 q ? . 
6. If a+b=10 and ab=16, then find 
2 2
a b + . 
7. Prove that “Two distinct lines cannot have more than one point in common”. 
8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 
 
9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. 
 
 
 
 
10. In which quadrant or on which axis do the points (-3, -1), (-3,4), (-1, 0) and (0,5) lie? 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Simplify: 
8 4 16
4
81x y z . 
12. Find the value of 
2
3
1
3
4
64 1 25
125 64
256
625
- ? ?
+ +
? ?
? ?
? ?
? ?
? ?
. 
13. Find the value of k for which 2k+1 is a factor of the polynomial 
3 2 2
2 ( 1) x x k x k + - + - 
14. Check whether 
2
4 4 x x + + is a factor of the polynomial 
3 2
2 4 8 x x x - + + . 
15. In given figure, GM and HL are bisector of AGH ? and GHD ? respectively, such that 
GM HL  . Show that AB CD  . 
 
16. In the figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that 
( )
1
2
DAE C B ? = ? - ? . 
 
17. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is 
equidistant from A and B. 
18. In given figure, find a + b. 
 
19. In the figure, ABCD is a square of side 6m. P, Q, R and S are mid-point of AB, BC, CD and DA 
respectively. Find the area of the shaded region. 
 
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. Write an irrational number between 2 and 3. 
2. Find the value of 
2 2
104 103 - . 
3. In figure AB CD  , 135 BCD ? = ° and 130 EAB ? = ° . Then find the measure of x. 
 
4. If the abscissa of a point is x and ordinate is y, when what are the coordinates of the point? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Express 2.3 in the form of 
p
q
, where p and q are integers and 0 q ? . 
6. If a+b=10 and ab=16, then find 
2 2
a b + . 
7. Prove that “Two distinct lines cannot have more than one point in common”. 
8. In the figure, if ABD ACE ? = ? , then prove that AB=AC. 
 
9. The sides of a triangle are 12cm, 16cm and 20 cm. find its area. 
 
 
 
 
10. In which quadrant or on which axis do the points (-3, -1), (-3,4), (-1, 0) and (0,5) lie? 
 
Section C 
Question number from 11 to 20 carry 3 marks each. 
11. Simplify: 
8 4 16
4
81x y z . 
12. Find the value of 
2
3
1
3
4
64 1 25
125 64
256
625
- ? ?
+ +
? ?
? ?
? ?
? ?
? ?
. 
13. Find the value of k for which 2k+1 is a factor of the polynomial 
3 2 2
2 ( 1) x x k x k + - + - 
14. Check whether 
2
4 4 x x + + is a factor of the polynomial 
3 2
2 4 8 x x x - + + . 
15. In given figure, GM and HL are bisector of AGH ? and GHD ? respectively, such that 
GM HL  . Show that AB CD  . 
 
16. In the figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that 
( )
1
2
DAE C B ? = ? - ? . 
 
17. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is 
equidistant from A and B. 
18. In given figure, find a + b. 
 
19. In the figure, ABCD is a square of side 6m. P, Q, R and S are mid-point of AB, BC, CD and DA 
respectively. Find the area of the shaded region. 
 
 
 
 
 
20. Find the percentage increase in the area of a triangle if its each side is doubled. 
 
Section D 
Questions 21 to 31 carry 4 marks each. 
21. Given 2 1.4142 = and 2 1.4142 = . Find the value of 
1
3 2 1 - - correct to three places of 
decimal. 
22. Simply: 
( )( )
( )( )
2 2 3 3
3 5 2 2
+ - + - 
23. Find the value of ‘a’ in the polynomial 
3 2
( ) 2 8 p x x ax x a = + - + , when it is given that it is 
completely divisible by x-3. Hence factorise the polynomial. 
24. State factor theorem. Using factor theorem, factorise 
3 2
3 3 x x x - - + . 
25. Find the value of the polynomial 
4 3 2
( ) 4 3 1 p x x x x = - - - at x=1, 
1 1
, 2
3 2
and - - . 
26. If the polynomial 
3 2
9 6 23 4 x x x p + - + is exactly divisible by x+1, then find value of p. Hence 
factorise the polynomial. 
27. In a school, students were asked by their teacher to plant trees around the school to reduce 
air pollution. What value is being inculcated in them? 
28. Diagonals PR and SQ of a quadrilateral PQRS meet at O. Prove that PQ + QR + RS + SP<2(PR +  
QS) 
29. In figure, AO and DO are the bisectors of A ? and D ? respectively of the quadrilateral ABCD. 
Prove that ( )
1
2
AOD B C ? = ? + ? 
 
30. In the given figure, AB=AC and BE, CF are bisectors of B ? and C ? respectively. Prove that 
EBC FCB ? ? ? . 
 
31. Show that in a right angled triangle the hypotenuse is the longest side. 
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