Maths Past Year Paper SA-1(Set -4) - 2016, Class 9, CBSE Class 9 Notes | EduRev

 Page 1


SUMMATIVE ASSESSMENT – 1 –(2016 – 17) 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks each, Section B comprises of 6 questions of 2 marks
each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 11
questions of 4 marks each.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION A 
1. Simplify 
3
64 .
2. Find zero of the Polynomial 2 3 x +
3. Two supplementary angles are in the ratio 5:4.  Find the measures of angles.
4. In which quadrants do the points ( ) ( ) 3,3 2, 5 x andy - - -  lie?
SECTION B 
5. If  2 x k -  is a factor of ( )
5 2 2
4 2 2 3, . f x x k x x k find k = - + + +
6. Expand ( )
3
2 3 x y - .
7. Define:-
1. Parallel lines
2. Perpendicular lines.
8. In the figure of
0
, 20 ABC A ? ? =  and
0
40 C ? =  .  If the bisector pf the angle B meets AC
at X, prove that BC>XC.
9. In which  quadrant or on which axis do the points ( ) ( ) ( ) ( ) 0, 3 , 3,9 , 7,4 5, 3 and - - -  lie?
10. If lengths of the diagonals of a rhombus are 300m and 160m, find the side and area of the
rhombus.
Page 2


SUMMATIVE ASSESSMENT – 1 –(2016 – 17) 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks each, Section B comprises of 6 questions of 2 marks
each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 11
questions of 4 marks each.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION A 
1. Simplify 
3
64 .
2. Find zero of the Polynomial 2 3 x +
3. Two supplementary angles are in the ratio 5:4.  Find the measures of angles.
4. In which quadrants do the points ( ) ( ) 3,3 2, 5 x andy - - -  lie?
SECTION B 
5. If  2 x k -  is a factor of ( )
5 2 2
4 2 2 3, . f x x k x x k find k = - + + +
6. Expand ( )
3
2 3 x y - .
7. Define:-
1. Parallel lines
2. Perpendicular lines.
8. In the figure of
0
, 20 ABC A ? ? =  and
0
40 C ? =  .  If the bisector pf the angle B meets AC
at X, prove that BC>XC.
9. In which  quadrant or on which axis do the points ( ) ( ) ( ) ( ) 0, 3 , 3,9 , 7,4 5, 3 and - - -  lie?
10. If lengths of the diagonals of a rhombus are 300m and 160m, find the side and area of the
rhombus.
SECTION C 
11. Examine whether 3  is rational or irrational.
12. Express 2.123  in the form of
p
q
 . 
13. Solve: ( )
2
2 3 4 x y z - +
14. What are the possible expressions for the dimensions of a cuboid whose volume is
2
24 4 8 . Ky ky k - - 15. Write any three Euclid’s postulates.
16. In the figure, BM and DN are both perpendiculars to AC and BM=DN.  Prove that AC
bisects BD.
17. In the given figure, . PO AB ?   IF : : 1:3:5 x y z = , then find the measures of x, y and z.
18. In the figure, line l  is the bisector of . AOB ?  D is a point on l, DL OA ?  and DM OB ? .
Prove that
i. OMD OLD ? ? ?
(ii) DM=DL 
Page 3


SUMMATIVE ASSESSMENT – 1 –(2016 – 17) 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks each, Section B comprises of 6 questions of 2 marks
each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 11
questions of 4 marks each.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION A 
1. Simplify 
3
64 .
2. Find zero of the Polynomial 2 3 x +
3. Two supplementary angles are in the ratio 5:4.  Find the measures of angles.
4. In which quadrants do the points ( ) ( ) 3,3 2, 5 x andy - - -  lie?
SECTION B 
5. If  2 x k -  is a factor of ( )
5 2 2
4 2 2 3, . f x x k x x k find k = - + + +
6. Expand ( )
3
2 3 x y - .
7. Define:-
1. Parallel lines
2. Perpendicular lines.
8. In the figure of
0
, 20 ABC A ? ? =  and
0
40 C ? =  .  If the bisector pf the angle B meets AC
at X, prove that BC>XC.
9. In which  quadrant or on which axis do the points ( ) ( ) ( ) ( ) 0, 3 , 3,9 , 7,4 5, 3 and - - -  lie?
10. If lengths of the diagonals of a rhombus are 300m and 160m, find the side and area of the
rhombus.
SECTION C 
11. Examine whether 3  is rational or irrational.
12. Express 2.123  in the form of
p
q
 . 
13. Solve: ( )
2
2 3 4 x y z - +
14. What are the possible expressions for the dimensions of a cuboid whose volume is
2
24 4 8 . Ky ky k - - 15. Write any three Euclid’s postulates.
16. In the figure, BM and DN are both perpendiculars to AC and BM=DN.  Prove that AC
bisects BD.
17. In the given figure, . PO AB ?   IF : : 1:3:5 x y z = , then find the measures of x, y and z.
18. In the figure, line l  is the bisector of . AOB ?  D is a point on l, DL OA ?  and DM OB ? .
Prove that
i. OMD OLD ? ? ?
(ii) DM=DL 
19. On the graph paper, plot a point A(-2,-2).  Reflect point A in x-axis and y-axis.  Let these
points be B and C respectively.  Guess the measure of BAC ? .
20. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an
equilateral triangle of side 8cm.  Find the area of the figure so formed.
SECTION D 
21. If  a =
2 1
2 1
a
+
=
- then find the values of a and b. 
22. Give examples of two irrational numbers whose:-
1. Difference is a rational number.
2. sum is a rational number.
3. product is a rational number.
4. division is a rational number.
Justify also. 
23. If
2
1 x -  is a factor of
2 3 2
, px qx rx sx t + + + +  show that 0 p r t q s + + = + = .
24. Divide polynomial ( )
4 3 2
4 4 3 4 p x x x x x = - + - +  by qx=x-1 and find what should be added
in p(x) so that it is divisible by qx).
25. Simplify:-
( ) ( ) ( )
( ) ( ) ( )
3 3 3
2 2 2 2 2 2
3 3 3
x y y z z x
x y y z z x
- + - + - - + - + - 26. If 3 2 5 5 6 10 15 14 a b c and ab bc ac - + = + - = , find the value of :
3 3 3
27 125 90 8 . a c abc b + + -
Page 4


SUMMATIVE ASSESSMENT – 1 –(2016 – 17) 
SUBJECT – MATHEMATICS 
CLASS: IX 
Time: 3Hrs  M.M: 90 
General Instruction: 
1. All questions are compulsory.
2. The paper consists of 31 questions divided into four sections A, B, C and D. Section A
comprises of 4 questions of 1 marks each, Section B comprises of 6 questions of 2 marks
each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 11
questions of 4 marks each.
3. There is no overall choice.
4. Use of calculator is not permitted.
SECTION A 
1. Simplify 
3
64 .
2. Find zero of the Polynomial 2 3 x +
3. Two supplementary angles are in the ratio 5:4.  Find the measures of angles.
4. In which quadrants do the points ( ) ( ) 3,3 2, 5 x andy - - -  lie?
SECTION B 
5. If  2 x k -  is a factor of ( )
5 2 2
4 2 2 3, . f x x k x x k find k = - + + +
6. Expand ( )
3
2 3 x y - .
7. Define:-
1. Parallel lines
2. Perpendicular lines.
8. In the figure of
0
, 20 ABC A ? ? =  and
0
40 C ? =  .  If the bisector pf the angle B meets AC
at X, prove that BC>XC.
9. In which  quadrant or on which axis do the points ( ) ( ) ( ) ( ) 0, 3 , 3,9 , 7,4 5, 3 and - - -  lie?
10. If lengths of the diagonals of a rhombus are 300m and 160m, find the side and area of the
rhombus.
SECTION C 
11. Examine whether 3  is rational or irrational.
12. Express 2.123  in the form of
p
q
 . 
13. Solve: ( )
2
2 3 4 x y z - +
14. What are the possible expressions for the dimensions of a cuboid whose volume is
2
24 4 8 . Ky ky k - - 15. Write any three Euclid’s postulates.
16. In the figure, BM and DN are both perpendiculars to AC and BM=DN.  Prove that AC
bisects BD.
17. In the given figure, . PO AB ?   IF : : 1:3:5 x y z = , then find the measures of x, y and z.
18. In the figure, line l  is the bisector of . AOB ?  D is a point on l, DL OA ?  and DM OB ? .
Prove that
i. OMD OLD ? ? ?
(ii) DM=DL 
19. On the graph paper, plot a point A(-2,-2).  Reflect point A in x-axis and y-axis.  Let these
points be B and C respectively.  Guess the measure of BAC ? .
20. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an
equilateral triangle of side 8cm.  Find the area of the figure so formed.
SECTION D 
21. If  a =
2 1
2 1
a
+
=
- then find the values of a and b. 
22. Give examples of two irrational numbers whose:-
1. Difference is a rational number.
2. sum is a rational number.
3. product is a rational number.
4. division is a rational number.
Justify also. 
23. If
2
1 x -  is a factor of
2 3 2
, px qx rx sx t + + + +  show that 0 p r t q s + + = + = .
24. Divide polynomial ( )
4 3 2
4 4 3 4 p x x x x x = - + - +  by qx=x-1 and find what should be added
in p(x) so that it is divisible by qx).
25. Simplify:-
( ) ( ) ( )
( ) ( ) ( )
3 3 3
2 2 2 2 2 2
3 3 3
x y y z z x
x y y z z x
- + - + - - + - + - 26. If 3 2 5 5 6 10 15 14 a b c and ab bc ac - + = + - = , find the value of :
3 3 3
27 125 90 8 . a c abc b + + - 27. There is triangular park PQR whose angles P, Q and R are in ratio 2:4:3 respectively.
There friends Rashid, Sita and Geeta go daily on morning walk and walk along these three
side PQ, QR and PR respectively.  Who walks the maximum distance among these three?
Who walks the least?  Why morning walk is necessary for us?
28. Solve the equation 25 40 x + =  and state which axiom you use here.  Also give two more
exioms other than the axiom used in the above situation.
29. In the given figure, line AB and CD intersect each other at O.   Find the value of x, y and z.
30. Prove that the sum of three angles of a triangle is   equal to the sum of two right angles.  If
in a right triangle an acute angle is one-fourth of the other, find the acute angles.
31. The angle of a triangle are ( ) ( )
0 0
40 , 20 x x - -  and
0
10
2
x ? ?
- ? ?
? ?
 .  Find the value of x and the 
angles of the triangle.