Mathematics Past Year Paper SA-1(Set-5)- 2014, Class 9, CBSE | Extra Documents & Tests for Class 9 PDF Download

 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.