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# Mathematics Past Year Paper SA-1(Set-5)- 2014, Class 9, CBSE Class 9 Notes | EduRev

## Past Year Papers For Class 9

Created by: Indu Gupta

## Class 9 : Mathematics Past Year Paper SA-1(Set-5)- 2014, Class 9, CBSE Class 9 Notes | EduRev

``` Page 1

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper consists of 31 question divided into four 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 and Section – D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section – A
Question numbers 1 to 4 carry one mark each
1. What can you say about the sum of a rational number and an irrational number?
2. Find the coefficient of
( )
3
2 2
2 x in x +
3. Write the measure of each exterior angle of an equilateral triangle.
4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the
co-ordinates of P?
Section – B

Question numbers 5 to 10 carry two marks each.
5. Rationalize the denominator of
2 3 3
2 2 3 3
- + +

6. If (x+1) is factor of
2
4 3 px px - + what is the value of p?
7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove
that PQ=QR=PR.

8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find
COD ? and reflex COD ? .

Page 2

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper consists of 31 question divided into four 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 and Section – D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section – A
Question numbers 1 to 4 carry one mark each
1. What can you say about the sum of a rational number and an irrational number?
2. Find the coefficient of
( )
3
2 2
2 x in x +
3. Write the measure of each exterior angle of an equilateral triangle.
4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the
co-ordinates of P?
Section – B

Question numbers 5 to 10 carry two marks each.
5. Rationalize the denominator of
2 3 3
2 2 3 3
- + +

6. If (x+1) is factor of
2
4 3 px px - + what is the value of p?
7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove
that PQ=QR=PR.

8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find
COD ? and reflex COD ? .

9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the
triangle. (use 15 3.87 = )
10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals
intersect each other at O. Find the area of the shaded region by using Heron’s formula.

Section – C
Question number 11 to 20 carry three marks each.
11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
12. If
5 2 3
3
7 4 2
a b
+
= +
+
, then find a and b.
13. When the polynomials
3 2
3 13 ax x + - and
3
2 5 x x a - + are divided by (x-2), then remainder is
same. Find the value of a.
14. Factorise:
6 6
a b -
15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is
double the smallest side.
16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that
1
( )
2
DAE C B ? = ? - ? .
17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the
triangle ABC is an isosceles triangle.
18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD

19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that
PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of
the diagonals.
20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest
altitude.

Section – D
Question numbers 21 to 31 carry four marks each.
Page 3

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper consists of 31 question divided into four 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 and Section – D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section – A
Question numbers 1 to 4 carry one mark each
1. What can you say about the sum of a rational number and an irrational number?
2. Find the coefficient of
( )
3
2 2
2 x in x +
3. Write the measure of each exterior angle of an equilateral triangle.
4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the
co-ordinates of P?
Section – B

Question numbers 5 to 10 carry two marks each.
5. Rationalize the denominator of
2 3 3
2 2 3 3
- + +

6. If (x+1) is factor of
2
4 3 px px - + what is the value of p?
7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove
that PQ=QR=PR.

8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find
COD ? and reflex COD ? .

9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the
triangle. (use 15 3.87 = )
10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals
intersect each other at O. Find the area of the shaded region by using Heron’s formula.

Section – C
Question number 11 to 20 carry three marks each.
11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
12. If
5 2 3
3
7 4 2
a b
+
= +
+
, then find a and b.
13. When the polynomials
3 2
3 13 ax x + - and
3
2 5 x x a - + are divided by (x-2), then remainder is
same. Find the value of a.
14. Factorise:
6 6
a b -
15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is
double the smallest side.
16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that
1
( )
2
DAE C B ? = ? - ? .
17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the
triangle ABC is an isosceles triangle.
18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD

19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that
PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of
the diagonals.
20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest
altitude.

Section – D
Question numbers 21 to 31 carry four marks each.

21. If
3 2
3 2
x
- =
+
and
3 2
3 2
y
+
=
- , then show that
2 2
99 x xy y + + = .
22. If (x+1)=3 find the value of
2
1
x
x
? ?
+
? ?
? ?

23. Factorise:
2 2 3 2 2 3 2 2 3
( ) ( ) ( ) a b b c c a - + - + -
24. Simplify and factorise:
2 2 2 2
( ) ( ) 4 4 a b c a b c b c + + - - - + -
25. Without actually calculating the cubes, find the value of
3 3 3
( 12) (7) (5) - + + and
3 3 3
(28) ( 15) ( 13) + - + - . Also write the identify used.
26. Factorise:
3 2
13 32 20 x x x + + +
27. Builder has made a layout of a colony so that lane a is parallel to lane b? he also plans to leave
green areas as shown in the figure. what value is the showing by doing so? If measure of 1 ?
is 120° , find the measure of all other angles.

28. In a right angled triangle XYZ right angled at Z, M is the midpoint of XY. Z is joined to M and
produced to a point P such that PM=ZM. Point P is joined to point Y.
Show that
a) XMZ YMP ? ? ?
b) 90 PYZ ? = °
c) PYZ XZY ? ? ?
d)
1
2
ZM XY =

29. Prove that sum of the angles of a triangle is 180° . If in ABC ? , 120 A B ? + ? = ° and
100 B C ? + ? = ° , then find B ? .
30. In figure, ABC is an isosceles triangle with AB=AC. D is a point in the interior of ABC ? such
that CBD BCD ? = ? . Prove that AD bisects BAC ? of ABC ? .
Page 4

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper consists of 31 question divided into four 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 and Section – D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section – A
Question numbers 1 to 4 carry one mark each
1. What can you say about the sum of a rational number and an irrational number?
2. Find the coefficient of
( )
3
2 2
2 x in x +
3. Write the measure of each exterior angle of an equilateral triangle.
4. P is a point on y-axis at a distance of 6 units from x-axis is lying below x-axis. What will be the
co-ordinates of P?
Section – B

Question numbers 5 to 10 carry two marks each.
5. Rationalize the denominator of
2 3 3
2 2 3 3
- + +

6. If (x+1) is factor of
2
4 3 px px - + what is the value of p?
7. P and Q are centers of the two intersecting circles which intersect at R (see figure). Prove
that PQ=QR=PR.

8. In the figure, AOB is a line. OC and OD are two rays such that 35 AOC DOB ? = ? = ° . Find
COD ? and reflex COD ? .

9. Perimeter of an isosceles triangle is 150 m. if its unequal side is 70 m, find the area of the
triangle. (use 15 3.87 = )
10. In the given figure, ABCD is rectangle in which AB = 8 cm, BC = 6 cm and the diagonals
intersect each other at O. Find the area of the shaded region by using Heron’s formula.

Section – C
Question number 11 to 20 carry three marks each.
11. Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
12. If
5 2 3
3
7 4 2
a b
+
= +
+
, then find a and b.
13. When the polynomials
3 2
3 13 ax x + - and
3
2 5 x x a - + are divided by (x-2), then remainder is
same. Find the value of a.
14. Factorise:
6 6
a b -
15. In a right angled triangle, one acute angel is double the other. Prove that the hypotenuse is
double the smallest side.
16. In figure, in ABC ? , AE is bisector of BAC ? and AD BC ? . Show that
1
( )
2
DAE C B ? = ? - ? .
17. If the bisector of the exterior angle C of a ABC ? is parallel to the side AB, then prove that the
triangle ABC is an isosceles triangle.
18. D is a point on side BC of ABC ? (see figure), such that AD = AC. Show that AB>AD

19. Plot two points P(1, 4) and Q (-5, 4) on the graph paper. Now, plot points R and S so that
PQRS is a rectangle. Draw diagonals and write the coordinates of the point of intersection of
the diagonals.
20. Find the area of a triangle whose sides are 5 cm, 12 cm and 13 cm. Also, find the shortest
altitude.

Section – D
Question numbers 21 to 31 carry four marks each.

21. If
3 2
3 2
x
- =
+
and
3 2
3 2
y
+
=
- , then show that
2 2
99 x xy y + + = .
22. If (x+1)=3 find the value of
2
1
x
x
? ?
+
? ?
? ?

23. Factorise:
2 2 3 2 2 3 2 2 3
( ) ( ) ( ) a b b c c a - + - + -
24. Simplify and factorise:
2 2 2 2
( ) ( ) 4 4 a b c a b c b c + + - - - + -
25. Without actually calculating the cubes, find the value of
3 3 3
( 12) (7) (5) - + + and
3 3 3
(28) ( 15) ( 13) + - + - . Also write the identify used.
26. Factorise:
3 2
13 32 20 x x x + + +
27. Builder has made a layout of a colony so that lane a is parallel to lane b? he also plans to leave
green areas as shown in the figure. what value is the showing by doing so? If measure of 1 ?
is 120° , find the measure of all other angles.

28. In a right angled triangle XYZ right angled at Z, M is the midpoint of XY. Z is joined to M and
produced to a point P such that PM=ZM. Point P is joined to point Y.
Show that
a) XMZ YMP ? ? ?
b) 90 PYZ ? = °
c) PYZ XZY ? ? ?
d)
1
2
ZM XY =

29. Prove that sum of the angles of a triangle is 180° . If in ABC ? , 120 A B ? + ? = ° and
100 B C ? + ? = ° , then find B ? .
30. In figure, ABC is an isosceles triangle with AB=AC. D is a point in the interior of ABC ? such
that CBD BCD ? = ? . Prove that AD bisects BAC ? of ABC ? .

31. Sides BC, CA and BA of a triangle ABC are produced to D, Q, P, respectively as shown in the
figure. If 100 ACD ? = °, 35 QAP ? = ° , find all the angles of the triangle.

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