cbse cbse class 9 mathematics practice paper sa ii 2015

CBSE Class 9th Practice Paper: Mathematics

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Practice PaperClass IXSA - II

Subject: Mathematics

Section A

Multiple Choice Questions (Carry 1 mark each)

1. ABCD is a parallelogram and DE = EO.The area of the parallelogram ABCD if area of ADE�is 10 cm2 is:

a) 50 cm2

b) 70 cm2

c) 80 cm2

d) 100 cm2

2. In a circle, AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm then find the distance of the chord AB from center of circle.

a) 5.0 cm

b) 8.0 cm

c) 10.0 cm

d) 12.0 cm

3. If mean of 1 2 3, , ,..., nx x x x is x ,then the mean of 1 2 3, , ,..., nax ax ax ax .

a) .a x



b) 2.a x

c) 3.a x

d) .x a

4. The probability of getting a number less than 6, when a dice is rolled:

a) 56

b)16

c) 13

d)23

5. Equation of a line to x-axis and 2 units above the origin is:

a) x = 2

b) x = –2

c) y = 2

d) y = –2

6. Two consecutive angles of a parallelogram are in the ratio 1:3, then the smaller angle is:

a) 50o

b) 90o

c) 60o

d) 45o



7. AD is a diameter of a circle and AB is a chord. If AD = 34 cm and AB = 30 cm, the distance of AB from the center of the circle is:

a) 17 cm

b) 15 cm

c) 4 cm

d) 8 cm

8. If the height and the radius of the cone are doubled, the volume of the cone becomes:

a) 2 time

b) 4 time

c) 6 time

d) 8 time

9. Class mark of a particular class is 6.5 and class size is 3, then class interval is:

a) 5 – 8

b) 6.5 – 9.5

c) 3.5 – 6.5

d) 4.25

10.In a survey of 364 children aged 20 – 40 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chip is:

a) 0.25

b) 0.50

c) 0.75



d) 0.80

11. A triangle and a rhombus are on the same base and between same parallels. Then the ratio of the area of triangle to that of a rhombus is:

a) 1:1

b) 1:2

c) 1:3

d) 1:4

12. In a trapezium ABCD with AB = 20 cm, CD = 10 cm, AB || CD, P and Q are midpoints of ACand BD the length of PQ is:

a) 10 cm

b) 5 cm

c) 2 cm

d) None

Section B

Short Answer Question: (Carry 2 marks each)

1. Find the mode from the following data:

5, 10, 5, 9, 4, 5, 20, 20, 21, 20

2. Explain why it is not possible that all 4 angles of any quadrilateral can not be acute and cannot be obtuse.



3. Mean of salary of 50 employes is 20,000. If one more employee joined this group then mean salary become 21000.

Find salary of the new person joined the group.

4. In figure, ABCD is a parallelogram in which X and Y are the mid-points of the sides DC and AB respectively. Prove that AXCY is a parallelogram

5. In a parallelogram ABCD, bisectors of angles A & B meet at P then find angle APB� .

6. Find the value of K if 3x + ky = 6 meet y-axis at 2 units above x-axis.

7. 4 years ago, age of a mother was 3 times the age of her daughter. Write a linear equation to represent this situation.

8. A hemispherical dome of a building contains4

567

m3 of air. Find the radius of the dome.

9. Find a point on line x + y = 2 which is equidistant from both the coordinate axes.

10. A die is thrown 500 times with frequencies for the outcomes 1,2,3,4,5,6 as given in the following table:



Outcome 1 2 3 4 5 6Frequency 80 75 90 75 85 95

Section C

Short Answer Question: (Carry 3 marks each)

1. A small village, having a population of 5000, requires 75 liters of water per head per day. Thevillage has got an overhead tank of measurement 40 m 25 m 15 m� � . For how many days willthe water of this tank last? (Also write values).

2. A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and the thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are24 cm 12 cm 8 cm� � , how many bricks would be required?

3. In figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that:

(i) ar (||gm PQRS) = ar (||gm ABRS)

4. A dice is tossed 100 times and the data is recorded as below:

Outcome 1 2 3 4 5 6

Frequency 20 15 20 15 20 10



(i) What is the probability that we get an even number in a trial?

(ii) What is the probability of getting a number less than 3?

5. AC and BD are chords of a circle which bisect each other. Prove that:

(i) AC and BD are diameters

(ii) ABCD is a rectangle

6. A school provides milk to the students daily in a cylindrical glass of diameter 7 cm. If theglass is filled with milk up to a height of 12 cm, find how many letters or milk is needed to serve1600 students. (Write your comments)

7. Prove that chord near to center is larger in length than a chord far away from centre.

8. In the figure given below, ABCD is a parallelogram. E is mid point of BC. Then prove that AF= 2AB.



9. Draw the graph of 3x + 2y = 5 and x + y = 2. Find their point of intersection.

10. ABCD issuch a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that:

12

CBD CDB BAD� ��

11. Give geometrical representation of x = 3

(i) In one variable

(ii) In two variable

12. The sum of length, breadth and depth of a cuboid is 19 cm and the length of the diagonal in 11 cm. Find the surface area of the cuboid.

13. The mean marks of 100 students were found to be 40. If by mistake, the tabulator took 45 and 35 instead of correct marks 55 and 45, find the correct mean. Such mistakes do happen in Boards and University’s examinations. Many times, students hurt themselves out of frustration and disappointment. What should be done to stop such mistakes?

14. In the figure, AB is the diameter of the circle with center ‘O’. If o70DAB� � and o30DBC� � , determine ABD� and CDB� .

15. The force exerted to pull a cart is directly proportional to the acceleration produced in thebody. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph. The force required when theacceleration produced is (i) 5 m/sec2, (ii) 6 m/sec2.



Section D

Long Answer Question: (Carry 4 marks each)

1. Construct a Δ with perimeter 10 cm and base angles as 45° and 60°.

2. Express 7x – 21 = 0 as geometrically in (i) one variable and (ii) two variable.

3. Prove that line segment joining the mid-points of diagonals of a trapezium is parallel to parallel sides and half of length of the difference of these parallel sides of trapezium.

4. Two chords AB and CD intersects inside the circle at a point P, prove that AP × BP = CP × DP.

5. On occation of Diwali a charitable trust donated laddoo in a poor society. If diameter of each laddoo is 3 cm and there are 1000 persons , then find quantity of laddoo in kg to give 7 laddoo to each person. (Also write values).

6. A radius of sphere is increased by 10%. Prove that the volume will be increased by 33.1%approximately.

7. A recent survey found that the ages of workers in a factory are distributed as follows:

Age (in years) Number of workers20 – 2930 – 3940 – 4950 – 59

60 and above

382786463

If a person I selected at random, find the probability that the person is:

(i) 40 years or more



(ii) under 40 years

(iii) Having age from 30 to 39 years

(iv) Under 60 but over 39 years

8. In the figure, A, B, C and D, E, F are two sets of collinear points. Prove that AD ||CF.

9. Draw a histogram for the following:

Marks 10 – 15 15 – 20 20 – 25 25 – 30 30 – 40 40 – 60 60 – 80Number ofCandidates 7 9 8 5 12 12 8

10. If the number of hours for which a labourer works is x and y are his wages (in rupees) and y = 2x – 1. Draw the graph of work-wages equation. From the graph, find the wages of the labourer if he works for 6 hours.

11. A dome of a building is in the form of a hemisphere. From inside, it was white washed at thecost of Rs. 498.96. If the cost of white washing is Rs. 2.00 per square metre. Find the:

(i) inside surface area of the dome.

(ii) volume of the air inside the dome.

12. Prove that the angle subtended by an arc at the center is double the angle subtended by it at any point of the remaining part of the circle.



13. In figure two circles with centre at A and B intersect each other at points P and Q. Prove that the line joining the centres AB bisects the common chord PQ at right angles.

14. Find the total number of sample space for given statement: A coin tossed if head turn –up and if tail then a dice is thrown.

15. Construct a ΔABC in which length of altitude AD from A to BC is 4 cm and AB = 5.3 cm, BC= 6 cm.

16. Prove that quadrilateral formed by joining mid-points of consecutive sides of a rhombus is rectangle.

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cbse cbse class 9 mathematics practice paper sa ii 2015

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