Class 9 Maths: CBSE Past Year Paper (SA-1) - 8 PDF Download

 Page 1


Summative Assessment –I
Class – 09 
Mathematics 
Time: 3 hr. Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) There are 31 questions in total divided into 4 sections A, B, C and D. 
Section – A comprises of 4 questions of 1 mark each. 
Section – B comprises of 6 questions of 2 marks each. 
Section – C comprises of 10 questions of 3 marks each. 
Section – D comprises of 11 questions of 4 marks each. 
(iii) There is no overall choice in this question paper. 
(iv) Use of calculators is not permitted. 
Section – A 
Question number 1 to 4 carry one mark each. 
1. find the value of 
3
2
64
25
- ? ?
? ?
? ?
. 
2. Factorise :
2
16 x - .
3. If line l and m are parallel and lines m and n are also parallel, then what can you say
about the lines l and n?.
4. Find the area of a  rhombus whose diagonals are 10 cm and 14 cm.
Section – B 
Question number 5  to 10 carry  two mark each. 
5. Express
4
7
 in decimal form and state the kind of decimal expansion. 
6. Using Remainder theorem, check whether the polynomial
3 2
2 — 2 — 6 6  x ax x a + is a multiple of
x— a.
7. FState any two Euclid's postulates. 2 
8. In the figure, line n intersects two parallel lines I and m such that
0
2 120 . ? = Find the values of  all the
 exterior angles. 
Page 2


Summative Assessment –I
Class – 09 
Mathematics 
Time: 3 hr. Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) There are 31 questions in total divided into 4 sections A, B, C and D. 
Section – A comprises of 4 questions of 1 mark each. 
Section – B comprises of 6 questions of 2 marks each. 
Section – C comprises of 10 questions of 3 marks each. 
Section – D comprises of 11 questions of 4 marks each. 
(iii) There is no overall choice in this question paper. 
(iv) Use of calculators is not permitted. 
Section – A 
Question number 1 to 4 carry one mark each. 
1. find the value of 
3
2
64
25
- ? ?
? ?
? ?
. 
2. Factorise :
2
16 x - .
3. If line l and m are parallel and lines m and n are also parallel, then what can you say
about the lines l and n?.
4. Find the area of a  rhombus whose diagonals are 10 cm and 14 cm.
Section – B 
Question number 5  to 10 carry  two mark each. 
5. Express
4
7
 in decimal form and state the kind of decimal expansion. 
6. Using Remainder theorem, check whether the polynomial
3 2
2 — 2 — 6 6  x ax x a + is a multiple of
x— a.
7. FState any two Euclid's postulates. 2 
8. In the figure, line n intersects two parallel lines I and m such that
0
2 120 . ? = Find the values of  all the
 exterior angles. 
9. Plot reflection of A(3, —6) in x - axis as point B and then plot the reflection of B in y - axis.
10    An advertisement board is of the form of an equilateral triangle of perimeter 240 cm. Find the 2 area of 
the board using Heron's formula 
( )
. 3 1.73 Use =
SECTION-C 
 Question numbers 11 to 20 carry three marks each. 
11. Represent on the number line.
12. Find the values of a and b, if
3 2
2.
3 2
a b
+
= +
- 13. Evaluate 
3
92 , using a suitable identity. 
14. If ( )
2
  3 3 4 f x x x - + - , find ( ) ( ) ( ) 2   — 2  . f f f O + +
15. In the given figure, PO -L AB. If x : y : z=l : 3 : 5, then find the measures of x, y and z,
16. In the figure, if ABIICD, EFLCD and ZGED = 126
0
, find ZAGE, ZGEF and ZFGE.
Page 3


Summative Assessment –I
Class – 09 
Mathematics 
Time: 3 hr. Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) There are 31 questions in total divided into 4 sections A, B, C and D. 
Section – A comprises of 4 questions of 1 mark each. 
Section – B comprises of 6 questions of 2 marks each. 
Section – C comprises of 10 questions of 3 marks each. 
Section – D comprises of 11 questions of 4 marks each. 
(iii) There is no overall choice in this question paper. 
(iv) Use of calculators is not permitted. 
Section – A 
Question number 1 to 4 carry one mark each. 
1. find the value of 
3
2
64
25
- ? ?
? ?
? ?
. 
2. Factorise :
2
16 x - .
3. If line l and m are parallel and lines m and n are also parallel, then what can you say
about the lines l and n?.
4. Find the area of a  rhombus whose diagonals are 10 cm and 14 cm.
Section – B 
Question number 5  to 10 carry  two mark each. 
5. Express
4
7
 in decimal form and state the kind of decimal expansion. 
6. Using Remainder theorem, check whether the polynomial
3 2
2 — 2 — 6 6  x ax x a + is a multiple of
x— a.
7. FState any two Euclid's postulates. 2 
8. In the figure, line n intersects two parallel lines I and m such that
0
2 120 . ? = Find the values of  all the
 exterior angles. 
9. Plot reflection of A(3, —6) in x - axis as point B and then plot the reflection of B in y - axis.
10    An advertisement board is of the form of an equilateral triangle of perimeter 240 cm. Find the 2 area of 
the board using Heron's formula 
( )
. 3 1.73 Use =
SECTION-C 
 Question numbers 11 to 20 carry three marks each. 
11. Represent on the number line.
12. Find the values of a and b, if
3 2
2.
3 2
a b
+
= +
- 13. Evaluate 
3
92 , using a suitable identity. 
14. If ( )
2
  3 3 4 f x x x - + - , find ( ) ( ) ( ) 2   — 2  . f f f O + +
15. In the given figure, PO -L AB. If x : y : z=l : 3 : 5, then find the measures of x, y and z,
16. In the figure, if ABIICD, EFLCD and ZGED = 126
0
, find ZAGE, ZGEF and ZFGE.
17. In the figure, ABC is an isosceles triangle in which AB = AC and LM is parallel to BC. If ZA = 50
0
,
find . LMC ?
18. In an isosceles triangle LMN,    LM = LN and MP and NQ are two medians. Show that
MP=NQ.
19. Plot the points (x, Y) given in the following table on the cartesian plane, choosing suitable units of
distances on the axes:
X 2 4 -4 -2 6 0 
y 5 -3 3 5 -1 2.5 
20. The sides of a quadrilateral taken in order are 9 m, 40 m, 15 m and 28 m. If the angle between first
two  sides is a right angle, find its area.
SECTION-D 
Question numbers 21 to 31 carry four marks each. 
21. If  3 8 x = + , find the value of
2
2
1
x
x
+ . 
22. Simplify :
3 3
3
4 2
81 25 5
16 4 2
- - - ? ?
? ? ? ? ? ?
? ? × ÷
? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
23. Find the value of   'a'   if when
3 2
 3 9 - ax x + and
3
2 5  x x a + - are divided by   x +2   leave the
same remainder.
24. Divide the polynomial
4 3
3 4 3  1 x x x + + +  by x — 1 and find quotient and remainder.
25. Factorise :
2
4 6 x x x - + +
26. It is given that 3a + 2b = 5c, then find the value of
3 3 3
27 8 125 a b c - + if abc = 0.
27. Teacher held two sticks AB and CD of equal length in her hands and marked their mid-points
M and N respectively. She then asked the students whether AM is equal to ND or not.  Arpita
answered yes. Is Arpita correct ? State Euclid's axiom that support her answer. Which characteristics
of Arpita you want to inculcate in your nature?
Page 4


Summative Assessment –I
Class – 09 
Mathematics 
Time: 3 hr. Max. Marks: 90 
General Instructions: 
(i) All questions are compulsory. 
(ii) There are 31 questions in total divided into 4 sections A, B, C and D. 
Section – A comprises of 4 questions of 1 mark each. 
Section – B comprises of 6 questions of 2 marks each. 
Section – C comprises of 10 questions of 3 marks each. 
Section – D comprises of 11 questions of 4 marks each. 
(iii) There is no overall choice in this question paper. 
(iv) Use of calculators is not permitted. 
Section – A 
Question number 1 to 4 carry one mark each. 
1. find the value of 
3
2
64
25
- ? ?
? ?
? ?
. 
2. Factorise :
2
16 x - .
3. If line l and m are parallel and lines m and n are also parallel, then what can you say
about the lines l and n?.
4. Find the area of a  rhombus whose diagonals are 10 cm and 14 cm.
Section – B 
Question number 5  to 10 carry  two mark each. 
5. Express
4
7
 in decimal form and state the kind of decimal expansion. 
6. Using Remainder theorem, check whether the polynomial
3 2
2 — 2 — 6 6  x ax x a + is a multiple of
x— a.
7. FState any two Euclid's postulates. 2 
8. In the figure, line n intersects two parallel lines I and m such that
0
2 120 . ? = Find the values of  all the
 exterior angles. 
9. Plot reflection of A(3, —6) in x - axis as point B and then plot the reflection of B in y - axis.
10    An advertisement board is of the form of an equilateral triangle of perimeter 240 cm. Find the 2 area of 
the board using Heron's formula 
( )
. 3 1.73 Use =
SECTION-C 
 Question numbers 11 to 20 carry three marks each. 
11. Represent on the number line.
12. Find the values of a and b, if
3 2
2.
3 2
a b
+
= +
- 13. Evaluate 
3
92 , using a suitable identity. 
14. If ( )
2
  3 3 4 f x x x - + - , find ( ) ( ) ( ) 2   — 2  . f f f O + +
15. In the given figure, PO -L AB. If x : y : z=l : 3 : 5, then find the measures of x, y and z,
16. In the figure, if ABIICD, EFLCD and ZGED = 126
0
, find ZAGE, ZGEF and ZFGE.
17. In the figure, ABC is an isosceles triangle in which AB = AC and LM is parallel to BC. If ZA = 50
0
,
find . LMC ?
18. In an isosceles triangle LMN,    LM = LN and MP and NQ are two medians. Show that
MP=NQ.
19. Plot the points (x, Y) given in the following table on the cartesian plane, choosing suitable units of
distances on the axes:
X 2 4 -4 -2 6 0 
y 5 -3 3 5 -1 2.5 
20. The sides of a quadrilateral taken in order are 9 m, 40 m, 15 m and 28 m. If the angle between first
two  sides is a right angle, find its area.
SECTION-D 
Question numbers 21 to 31 carry four marks each. 
21. If  3 8 x = + , find the value of
2
2
1
x
x
+ . 
22. Simplify :
3 3
3
4 2
81 25 5
16 4 2
- - - ? ?
? ? ? ? ? ?
? ? × ÷
? ? ? ? ? ?
? ? ? ? ? ? ? ?
? ?
23. Find the value of   'a'   if when
3 2
 3 9 - ax x + and
3
2 5  x x a + - are divided by   x +2   leave the
same remainder.
24. Divide the polynomial
4 3
3 4 3  1 x x x + + +  by x — 1 and find quotient and remainder.
25. Factorise :
2
4 6 x x x - + +
26. It is given that 3a + 2b = 5c, then find the value of
3 3 3
27 8 125 a b c - + if abc = 0.
27. Teacher held two sticks AB and CD of equal length in her hands and marked their mid-points
M and N respectively. She then asked the students whether AM is equal to ND or not.  Arpita
answered yes. Is Arpita correct ? State Euclid's axiom that support her answer. Which characteristics
of Arpita you want to inculcate in your nature?
28. In the given figure, AB =CD, P and Q are points on AB and CD such that
1
3
AP = and
1
.
3
CQ CD = 
Show that AP =CQ. State which Euclid axiom you use here.   Also give two more Euclid axioms other 
than the axiom used in the above situation. 
29. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles  are
parallel, then prove that the two lines are parallel.
30. Prove that the sum of three angles of a triangle is two right angles. If in a right angled triangle  an
acute angle is one-fourth the other, find the acute angles.
31. In the figure, OA = OD And 1  2 ? = ? . Prove that OCB ? is an isosceles triangle.