SAMPLE PAPER FOR SESSION ENDING EXAM (2019-20)SUBJECT: MATHEMATICS - Class 9 PDF Download

SAMPLE PAPER FOR SESSION ENDING EXAM (2019-20)
CLASS– IX
SUBJECT: MATHEMATICS
……………………………………………………………………………………………
Time: 3 Hours Marks: 80
INSTRUCTIONS:
1. All questions are compulsory.
2. The Question paper consists of 40 questions divided into four section A,B,C &        D. Section A comprise of 20 questions of 1 mark each. Section B comprises of 6      questions of 2 marks each. Section C comprises of 8 questions of 3 marks each      and Section D comprises of 6 questions of 4 marks each.
3. There is no overall choice.However,an internal choice has been provided in two     questions of 1 markeach,two questions of 2 marks each,three questions of 3           marks each and three questions of 4 marks each.You have to attempt only one       of the alternatives in all suvh questions.
4. Use of calculator is not permitted.
SECTION A
Q.1.√√2234
     (a)2−16 (b)2−6 (c) 216 (d) 26
                                     OR
      6250.16×6250.09=?
     (a)5 (b) 25 (c) 125 (d) 625.25
Q2. If 𝑥𝑦+𝑦𝑥=-1 ,(x,y≠0),the value of x3-y3 is
      (a)-1 (b) 1 (c) 0 (d) 12
Q3. If a+b+c=0 then 𝑎2𝑏𝑐+𝑏2𝑎𝑐+𝑐2𝑎𝑏=?
      (a)1 (b) 0 (c) -1 (d) 3
Q4. The value of 2492-2482 is
      (a)12 (b) 477 (c) 487 (d) 497
Q5. If (2,0) is a solution of the linear equation 2x+3y=k,then the value of k is
      (a)4 (b) 6 (c) 5 (d) 2
Q6.How many linear equations in x and y can be satisfied by x=1 and y=2
      (a)Only one (b) Two (c) Infinitely many (d) Three
Q7.The point whose ordinate is 4 and which lies on y-axis is
      (a)(4,0) (b) (0,4) (c) (1,4) (d) (4,2)
                                      Or
      If P(-1,1) ,Q(3,-4),R(1,-1) ,S(-2,-3) and T(-4,4) are plotted on the graph paper         ,then the points in the fourth quadrant are
      (a)P and T (b) Q and R (c) Only S (d) P and R
Q8.The angles of a triangle are in the ratio 2:4:3.The smallest angle of the                      triangle is
       (a)600 (b) 400 (c) 800 (d) 200
Q9. Two sides of a triangle are of length 5 cm and 1.5 cm .The length of the third           side of the triangle can not be
(a)3.4 cm (b) 3.6 cm (c) 3.8 cm (d) 4.1 cm
Q10.The figure obtained by joining the mid points of the sides of a rhombus taken in order is
(a)A rhombus (b) A rectangle (c) A square (d) Any parallelogram
Fill in the blanks-
Q11- Total surface area of cube-………………
Q12- Mean of first five prime number…………..
Q13- Centre of the circle lies in the ………… part of the circle.
Q14-P (E) +P (notE) =
Q15- sum of the adjacent angles of a parallelogram is ………….
Answer the following-
Q16 if two consecutive angles of a cyclic quadrilateral ar ‘x’ and ‘180 – 2x’ . find other two angles.
Q17- Find median of 10, 11,11,12,12,12,12,13,13,14,15.
Q18- Define linear pair.
Q19- if the exterior angle of a triangle is 1200 and one opposite interior angle is 650. Find the other interior angle.
Q20- if the sides of a triangle are 4cm, 5cm and 6 cm . find the area of the triangle.
SECTION-B
Q.21 Aayush travels regularly in a government bus for school. Today the bus was carrying 70 passengers,
some with 50-paise tickets and the remaining with 1-rupee tickets. The total amount received by the
conductor was Rs. 56.

(i) If there are x number of passengers with 1 rupee ticket, then there will be (70-x) passengers with 50 paise
ticket.(Agree/Disagree)?
(ii) Find the number of passengers with 50 paise ticket and with 1 rupee ticket.
Q22. If two lines intersect each other then prove that vertically opposite angles are equal.
Q23.Find the area of the trapezium whose parallel sides are 14 cm and 10 cm and whose height is 6 cm.
Q24. The perimeter of an isosceles triangle is 32 cm.The ratio of the equal side to it’s base is 3:2 .Find the area
of the triangle.
Q25.The diameter of a roller is 84 cm and it’s length is 120 cm.It takes 500 complete revolutions to move once
cover to level a playground.Find the area of the playground in m2.
Q26 Saina Nehwal and P.V Sindhu are the two gems of Indian badminton, one is the Olympic bronze medalist
and other is the two-time World Championships bronze medalist. One is the badminton queen of India, other is
the Indian teenage badminton sensation.
Saina Nehwal, who is currently the World No. 6 is undoubtedly the more experienced and a better player than
P.V Sindhu, whose ranking is 10, but let’s compare the performance of both the players statistically.
Comparing their performances in 2014

Question 1
Suggest any 2 methods to compare the performance of these two players in 2014?
Question2
How many matches played by Saina Nehwal and P.V Sindhu in 2014?
Question3
Whose probability of winning the game is more and name the title given to the players?
SECTION-C
Q27. If a=2+√3,then find the value of  a¹⁄a
Q28. Prove that- (a+b+c)³- a³ – b³- c³ = 3 ( a+b) ( b+c) ( c+a)
                                 OR
If p=2-a, prove that a²+6ap+p³-8=0
Q29. Refer to the following information:
𝑎 = 1052 + 1.08𝑡
The speed of a sound wave in air depends on the air temperature. The formula above shows the
relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in
degrees Fahrenheit (°F).
Question 1
Which of the following expresses the air temperature in terms of the speed of a sound wave?
A) 𝑡 =
𝑎− 1,052
1.08
B) 𝑡 =
𝑎+ 1,052
1.08
C) 𝑡 =
1,052 –𝑎
1.08
D) 𝑡 =
1.08
𝑎+1,052
Question 2
At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per
second?
A) −46°F
B) −48°F
C) −49°F
D) −50°F
Q30.Three vertices of a rectangle are (3,2),(-4,2) and (-4,5),plot these points on a graph paper and find the
coordinates of the fourth vertex.
Q31.Prove that the sum of three angles of a triangle is 1800.
OR
Q32.The measures of angles of a quadrilateral are (x+20)0,(x-20)0,(2x+5)0 and (2x-5)0.Find the value of x
[Type here]
OR
E is the mid point of the median AD of a triangle ABC and BE is produced to meet AC at F .Show that AF=
1
3
AC
Q33.Prove that the parallelogram on the same base and between the same parallels are equal in area
Or
ABCD is a trapezium in which AB∥DC,DC=30 cm and AB=50 cm .If X and Y are respectively the mid points of
AD and BC ,prove that ar(DCYX)=
7
9
ar(XYBA)
Q34.Prove that equal chords subtend equal angles at centre of circle.
SECTION-D
Q35. Simplify the following- ( 2+ √3) ( 5 - 2√3) – ( 3 - √3) ( √3 – 2)
Q36.Factorise the expression 8x3+27y3+36x2y+54xy2
Q.37 Prove that opposite angles of cyclic quadrilateral are supplementary.
Q38.Construct a triangle XYZ in which ∠Y=600, ∠Z=450,and XY+YZ+ZX=12 cm.
Q39.The radius of a sphere is increased by 10%.Prove that the volume will be increased by
33.1% approximately.
Q40. Health costs of air pollution: Survey
The Global Burden of Disease Study for 2010, published in 2013, had found that outdoor air pollution was the
fifth-largest killer in India and around 620,000 early deaths occurred from air pollution-related diseases in 2010.
According to a WHO study, 13 of the 20 most polluted cities in the world are in India.
Over a million Indians die prematurely every year due to air pollution, according to the non-profit Health Effects
Institute. Over two million children -- half the children in Delhi -- have abnormalities in their lung function,
according to the Delhi Heart and Lung Institute. Over the past decade air pollution has increased in India
significantly. Asthma is the most common health problem faced by Indians and it accounts for more than half of
the health issues caused by air pollution.

Q.1 With reference to the above data, what are the main reasons for concern caused by air pollution? Name threeproblems with the highest percentage of reasons for concern.
Q.2 which reason/reasons for concern have more than 20 % of concern?
Q.3 If the total population of Delhi is 1.9 crores, then how many are the suffers from skin infection and Cancer?
Q.4 Write the steps to prevent air pollution.