Mathematics Past Year Paper SA-1(Set-3)- 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 number 1 to 4 carry one marks each 
1. If 
1 1
12 24
49 x = , then find the value of x. 
2. If one zero of the polynomial 
2
13 40 x x - + is 5, which is the other zero? 
3. In the figure, AOB is a straight line. Find the value of x. 
 
4. If the abscissa of a point is x and ordinate is y, then what are the coordinates of the point? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
2 .2
2
p r r p
r p
- - - 
6. What should be subtracted from the polynomial 
2
16 28 x x - + , so that 1 is a zero of the 
polynomial? 
7. In an isosceles triangle, ABC, if AB=BC and AP BC ? , then prove that BAP CAP ? = ? . 
8. State any two Euclid’s axiom. 
9. For a poster completion, students were provided equilateral triangular shaped drawing 
sheets. If the perimeter of the sheet is 90 cm, find the area of the drawing sheet, using 
Heron’s formula. 
10. If coordinates of a point are (3, 10), then write its distances from x-axis and y-axis. 
 
Section – C 
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 number 1 to 4 carry one marks each 
1. If 
1 1
12 24
49 x = , then find the value of x. 
2. If one zero of the polynomial 
2
13 40 x x - + is 5, which is the other zero? 
3. In the figure, AOB is a straight line. Find the value of x. 
 
4. If the abscissa of a point is x and ordinate is y, then what are the coordinates of the point? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
2 .2
2
p r r p
r p
- - - 
6. What should be subtracted from the polynomial 
2
16 28 x x - + , so that 1 is a zero of the 
polynomial? 
7. In an isosceles triangle, ABC, if AB=BC and AP BC ? , then prove that BAP CAP ? = ? . 
8. State any two Euclid’s axiom. 
9. For a poster completion, students were provided equilateral triangular shaped drawing 
sheets. If the perimeter of the sheet is 90 cm, find the area of the drawing sheet, using 
Heron’s formula. 
10. If coordinates of a point are (3, 10), then write its distances from x-axis and y-axis. 
 
Section – C 
 
 
 
 
Question number 11 to 20 carry three marks each. 
11. Find one rational and one irrational number between 2 & 3 . 
12. Find a and b, if 
1 3
3
1 3
a b
- = +
+
. 
13. Evaluate 
2
2
1
x
x
+ , if 
1
6 x
x
+ = . 
14. Factorise: 
8 8
6561 256 a b - . 
15. In figure, AB CD 
 , then find x. 
 
16. In given figure, EAB EBA ? = ? and AC=BD. Prove that AD=BC. 
 
17. In the figure, AB CD 
 , 130 ABE ? = ° and 170 CDE ? = ° . Find BED ? . 
 
18.  In figure D and E are points on base BC of ABC ? such that BD=CE, AD=AE and 
ADE AED ? = ? prove that ABE ACD ? ? 
19. ABCD is a rhombus with each side of length 10 cm and one diagonal of length 10 cm. find the 
area of the rhombus. 
20. A triangular park in a city has dimensions 30 m, 26 m and 28 m. A gardener has to plant 
grass inside it at Rs 1.50 per 
2
m . Find the amount to be paid to the gardener. 
 
Section – D 
Question numbers 21 to 31 carry four marks each. 
21. If 
3 2
3 2
x
- =
+
 and 
3 2
3 2
y
+
=
- , find 
2 2
x y + . 
22. If 2x+3y=12 and xy=6, find the value of 
3 3
8 27 x y + 
23. Express 32.1235 in the form 
m
n
, where m and n are integers and 0 n ? ? 
24. Find ‘a’ and ‘b’, if (x+1) and (x-2) are the factors of 
3 2
2 x ax x b + + + . 
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 number 1 to 4 carry one marks each 
1. If 
1 1
12 24
49 x = , then find the value of x. 
2. If one zero of the polynomial 
2
13 40 x x - + is 5, which is the other zero? 
3. In the figure, AOB is a straight line. Find the value of x. 
 
4. If the abscissa of a point is x and ordinate is y, then what are the coordinates of the point? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
2 .2
2
p r r p
r p
- - - 
6. What should be subtracted from the polynomial 
2
16 28 x x - + , so that 1 is a zero of the 
polynomial? 
7. In an isosceles triangle, ABC, if AB=BC and AP BC ? , then prove that BAP CAP ? = ? . 
8. State any two Euclid’s axiom. 
9. For a poster completion, students were provided equilateral triangular shaped drawing 
sheets. If the perimeter of the sheet is 90 cm, find the area of the drawing sheet, using 
Heron’s formula. 
10. If coordinates of a point are (3, 10), then write its distances from x-axis and y-axis. 
 
Section – C 
 
 
 
 
Question number 11 to 20 carry three marks each. 
11. Find one rational and one irrational number between 2 & 3 . 
12. Find a and b, if 
1 3
3
1 3
a b
- = +
+
. 
13. Evaluate 
2
2
1
x
x
+ , if 
1
6 x
x
+ = . 
14. Factorise: 
8 8
6561 256 a b - . 
15. In figure, AB CD 
 , then find x. 
 
16. In given figure, EAB EBA ? = ? and AC=BD. Prove that AD=BC. 
 
17. In the figure, AB CD 
 , 130 ABE ? = ° and 170 CDE ? = ° . Find BED ? . 
 
18.  In figure D and E are points on base BC of ABC ? such that BD=CE, AD=AE and 
ADE AED ? = ? prove that ABE ACD ? ? 
19. ABCD is a rhombus with each side of length 10 cm and one diagonal of length 10 cm. find the 
area of the rhombus. 
20. A triangular park in a city has dimensions 30 m, 26 m and 28 m. A gardener has to plant 
grass inside it at Rs 1.50 per 
2
m . Find the amount to be paid to the gardener. 
 
Section – D 
Question numbers 21 to 31 carry four marks each. 
21. If 
3 2
3 2
x
- =
+
 and 
3 2
3 2
y
+
=
- , find 
2 2
x y + . 
22. If 2x+3y=12 and xy=6, find the value of 
3 3
8 27 x y + 
23. Express 32.1235 in the form 
m
n
, where m and n are integers and 0 n ? ? 
24. Find ‘a’ and ‘b’, if (x+1) and (x-2) are the factors of 
3 2
2 x ax x b + + + . 
 
 
 
 
25. Show that 2 1 x - is a factor of the polynomial 
3 2
2 2 4 2 2 x x x - - + . Hence factorise the 
polynomial. 
26. Factorise: 
7 6
a ab - 
27. Students in a school are preparing Banner for a rally to make people aware for saving 
electricity. What value are they exhibiting by doing so? 
Parallel line l and m are cut by transversal t, if 4 5, ? = ? and 6 7 ? = ? , what is measure of 
angle 8? 
   
28. ABC ? is an isosceles triangle with AC=BC. Side AC is produced to D so that AC=CD. Prove that 
ABD ? is a right angle. 
 
29. Prove that two triangles are congruent if two angles and the included side of one triangle is 
equal to two angles and the included side of the other triangle. 
30. In figure AC-AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE. 
 
31. Prove that “Angles opposite to equal sides of an isosceles triangle are equal”.