Mathematics Past Year Paper SA-1(Set-6)- 2015, Class 9, CBSE Notes | Study Past Year Papers For Class 9 - Class 9

 Page 1


NAVY CHILDREN SCHOOL, DELHI 
SA-I, 2015-16 
CALSS-IX, MATHEMATICS (041) SET : A 
 Time allowed: 3 hours  Maximum Marks: 90 
General Instructions: 
1. This question are compulsory.
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6
question(2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. No internal choice is provided.
4.Use of calculators is not allowed.
Section A 
Q. 1 Write the distance of a point R (2,4) from x-axis. 
Q. 2 Write a rational number between rational number 1/9 and 2/9 
Q. 3 Check whether (x-2) is a factor of 
3 2
x 3 x 2 x 5 ? ? ? 
Q. 4 In figure -1, find value of x is: 
Section B 
Q. 5 Express 2. 9 3 in the form of p/q where p and q are integers and q 0 ? . 
Q. 6 If x 3 2 2 ? ? then find the value of ? ?
3
x 1 / x ?
Q. 7 In figure-2, lines AC and BD intersect at O. If AOD : D OC 4 : 5 ? ? ? then find C OB ? . 
Q. 8 In fig -3 if PQ||RS then find S OR ?
Page 2


NAVY CHILDREN SCHOOL, DELHI 
SA-I, 2015-16 
CALSS-IX, MATHEMATICS (041) SET : A 
 Time allowed: 3 hours  Maximum Marks: 90 
General Instructions: 
1. This question are compulsory.
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6
question(2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. No internal choice is provided.
4.Use of calculators is not allowed.
Section A 
Q. 1 Write the distance of a point R (2,4) from x-axis. 
Q. 2 Write a rational number between rational number 1/9 and 2/9 
Q. 3 Check whether (x-2) is a factor of 
3 2
x 3 x 2 x 5 ? ? ? 
Q. 4 In figure -1, find value of x is: 
Section B 
Q. 5 Express 2. 9 3 in the form of p/q where p and q are integers and q 0 ? . 
Q. 6 If x 3 2 2 ? ? then find the value of ? ?
3
x 1 / x ?
Q. 7 In figure-2, lines AC and BD intersect at O. If AOD : D OC 4 : 5 ? ? ? then find C OB ? . 
Q. 8 In fig -3 if PQ||RS then find S OR ?
Q. 9 Find the area of a triangle, two sides of which are 18 cm and 10 cm and the perimeter is 42 
cm. 
Q. 10 Write coordinates of two points on x-axis and two points on y- axis which are at equal 
distances from the origin. 
Section C 
Q. 11 Varun was facing some difficulty in simplifying 
1
7 3 ?
. His classmate priya gave him a clue 
to rationalize the denominator for simplification. Varun simplified the expression and 
thanked priya for this goodwill. How Varun simplified
1
7 3 ?
 What value does it indicate? 
Q. 12 A teacher divides a material of volume 
? ?
3 2
x 6 x 12 x 8 ? ? ? cubic units among three stdents
equally. Is it possible to find the quantity of the material each student gets. Which moral values are 
depicted here by the teacher? 
Q. 13  Using suitable identity expand ? ?
2
2 x 3 y 2 z ? ?
Q. 14 Give possible expressions for the length and breadth of rectangle whose area is given by 
2
35 y 13y 12 ? ? . 
Q. 15 A traffic island is a parallelogram with perimeter 84m. One of the sides is 24m and a diagonal 
is 30 m. Find the cost of surfacing at the rate of Rs 200 per sq m. 
Q. 16 In figure -5, If BE is bisector of A BC ? and CE is bisector of AC D ? , then show that 
B E C 1 / 2 B A C ? ? ? . 
Q. 17 Show that in a right angled triangle, the hypotenuse is the longest side. 
Q. 18 In figure- 6, If AB||CD, E F C D ? and 
o
G E D 1 2 6 ? ? then find A G E , G E F ? ? and FG E ? . 
Q. 19 In figure – 7, If PS=PR, TP S Q PR ? ? ? then prove that PT=PQ. 
Q. 20 In the adjoining fig. 8 
Page 3


NAVY CHILDREN SCHOOL, DELHI 
SA-I, 2015-16 
CALSS-IX, MATHEMATICS (041) SET : A 
 Time allowed: 3 hours  Maximum Marks: 90 
General Instructions: 
1. This question are compulsory.
2. The question paper is divided into four sections Section A: 4 question (1mark each) Section B: 6
question(2 marks each) Section C: 10 questions (3 mark each) Section D: 11 questions (4 mark each). 
3. No internal choice is provided.
4.Use of calculators is not allowed.
Section A 
Q. 1 Write the distance of a point R (2,4) from x-axis. 
Q. 2 Write a rational number between rational number 1/9 and 2/9 
Q. 3 Check whether (x-2) is a factor of 
3 2
x 3 x 2 x 5 ? ? ? 
Q. 4 In figure -1, find value of x is: 
Section B 
Q. 5 Express 2. 9 3 in the form of p/q where p and q are integers and q 0 ? . 
Q. 6 If x 3 2 2 ? ? then find the value of ? ?
3
x 1 / x ?
Q. 7 In figure-2, lines AC and BD intersect at O. If AOD : D OC 4 : 5 ? ? ? then find C OB ? . 
Q. 8 In fig -3 if PQ||RS then find S OR ?
Q. 9 Find the area of a triangle, two sides of which are 18 cm and 10 cm and the perimeter is 42 
cm. 
Q. 10 Write coordinates of two points on x-axis and two points on y- axis which are at equal 
distances from the origin. 
Section C 
Q. 11 Varun was facing some difficulty in simplifying 
1
7 3 ?
. His classmate priya gave him a clue 
to rationalize the denominator for simplification. Varun simplified the expression and 
thanked priya for this goodwill. How Varun simplified
1
7 3 ?
 What value does it indicate? 
Q. 12 A teacher divides a material of volume 
? ?
3 2
x 6 x 12 x 8 ? ? ? cubic units among three stdents
equally. Is it possible to find the quantity of the material each student gets. Which moral values are 
depicted here by the teacher? 
Q. 13  Using suitable identity expand ? ?
2
2 x 3 y 2 z ? ?
Q. 14 Give possible expressions for the length and breadth of rectangle whose area is given by 
2
35 y 13y 12 ? ? . 
Q. 15 A traffic island is a parallelogram with perimeter 84m. One of the sides is 24m and a diagonal 
is 30 m. Find the cost of surfacing at the rate of Rs 200 per sq m. 
Q. 16 In figure -5, If BE is bisector of A BC ? and CE is bisector of AC D ? , then show that 
B E C 1 / 2 B A C ? ? ? . 
Q. 17 Show that in a right angled triangle, the hypotenuse is the longest side. 
Q. 18 In figure- 6, If AB||CD, E F C D ? and 
o
G E D 1 2 6 ? ? then find A G E , G E F ? ? and FG E ? . 
Q. 19 In figure – 7, If PS=PR, TP S Q PR ? ? ? then prove that PT=PQ. 
Q. 20 In the adjoining fig. 8 
Suppose this is a chocolate bar & AC = BD, but your teacher divided it into two equal parts 
AB=CD. 
i)State how has she done this and by using which axiom. 
ii) She has also given the third part to one child of LKG. Which moral values of the teacher &
the students are depicted here? 
Section D 
Q. 21 If x y z 1 , x y z 1 ? ? ? ? ? and x y y z x z 1 ? ? ? ? then find the value of 
3 3 3
x y z ? ? 
Q. 22 A child forgot his address but says that his house is in the middle of 5 & 20 . Help him in 
locating his house. Is his address a rational or Irrational number. Represent irrational part of 
address on number line. What type of value is depicted by you if you help the child reach 
home? 
Q. 23 The sides AB and AC of triangle ABC are produced to points E and D respectively. If bisectors 
BO and CO of BC D ? respectively meet at point O, then prove that B O C 9 0 1 / 2 B A C ? ? ? ? . 
Q. 24 By dividing ? ?
3 2
p x 2 x 3x 17 x 30 ? ? ? ? by ? ? g x x 3 ? ? , show that g(x) is a factor of p(x) and
hence factories p(x) completely. 
Q. 25 Find the value of  p and q so that (x+1) and (x-1) are factors of 
4 3 2
x px 3x 2 x q ? ? ? ? . 
Q. 26 Find the value of:
? ? ? ? ? ?
2 3 1
3 4 5
4 1 2
216 256 243
? ? ?
? ?
Q. 27 If two parallel lines are intersected by a transversal, prove that the bisectors of two pairs of 
interior angles encloses a rectangle. 
Q. 28 Sarita made a rectangular chart for the school notice board mentioning the ways by which 
cleanliness can be maintained in one’s surroundings. Write the co-ordinates of the vertices of 
this rectangle if its length and breadth are 12 and 8 respectively, one vertex at the origin, the 
longer side lies on the x- axis and one of the vertices lies in the fourth quadrant. Also find the 
area of chart paper used. What values does Sarita possess? 
Q. 29 In a triangle P Q R , PR PQ ? ? and PS is the bisector of Q PR ? . Prove that PS R PS Q ? ? ? . 
Q. 30 In figure – 9, two sides median AM of A BC ? are respectively equal to sides DE and EF and 
the median DN of D E F ? . Prove that A BC D EF ? ? ? . 
Q. 31 If
13 11 13 11
a b
13 11 13 11
? ?
? ? ?
? ?
Find the value of a and b.