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# Maths Past Year Paper SA-1(Set -3) - 2014, Class 10, CBSE Class 10 Notes | EduRev

## 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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