# CBSE Board Math Sample Papers for Class 9

Sample Paper
Mathematics  - IX

Time : 3 or 3 ½ hours                                Maximum Marks: 90
General Instructions:
1. All questions are compulsory.
2. The question paper consists of 34 questions divided  into four sections -  A, B, C  and D.Section - A
contains  8  questions of  1  mark  each, Section  B  is of  6   questions of  2 marks  each, Section is of
10 questions of 3 marks each  and  section  D is  of  10 questions of4 marks each.
3. In questionon construction, the drawing shouldbe neatand exactly as per the given measurements.
4. Use of calculator is not permitted..

SECTION  – A

1. Given a cuboid of dimensions l = 6 cm, b=5 cm and h= 4 cm. How many cubes, each of side 2 cm
can be cut out from it ?
i. 6 ii.    15 iii.   30 iv. None of these

2. Given figure A and figure B such that ar(A) = 20 units 2 and ar ( B ) = 20 units 2 . Then
i. Fig. A and B are congruent  iii.  Fig. A and B are not congruent
ii. Fig. A and B may be or may not be  congruent

3. A data is such that its minimum value is 86 and range is 22. Then the maximum value is:
i. 54 ii. 811  iii.  118 iv. 181

4. The region between a chord and either of the arcs is called:
i. An arc   ii. A sector   iii. A segment  iv. A semicircle.

5. If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4, then
ABCD is  i. Trapezium ii. Rhombus iii. Parallelogram   iv. Kite.

6. In an experiment, probability of an event is better approximated, when an experiment is performed :
i. 10 times ii. 20 times iii.  Large number of times iv. 30 times.

7. A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup, then radius of
cone is : i. 14 cm ii.  7 cm  iii. 12.12 cm iv. None of the above.

8. The equation 2x + 5y = 7 has unique solution, if x and y are :
i. Natural number ii. Positive real number      iii. Real number iv. Rational number

SECTION  – B

9. Ten observation 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in an ascending order. The
median of the data is 24. Find the value of x.

10. Show that the points A(1,2 ), B(-1,-16) and C(0,-7) lie on the graph of the linear equation y = 9x – 7.

11. Three cubes each of side 6 cm are joined end to end. Find the surface area of the resulting cuboid.

12. If x = 3, y = - 2 is a solution of the linear equation  3x – ky = 1, then find the value of k.

13. The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m. Find its area.

14. In the given, AB is the chord of a circle with centre O.
AB is produced to C such that BC = OB, CO is joined
and produced to meet the circle in D. If ACD = y and
AOD = x, prove that x = 3y.SECTION  – C

15. Construct a right 
le
in which one side is 3.5 cm and sum of the other side and hypotenuse is 5.5 cm.

16. The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank
contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the
volume of water pumped into the tank.

17.  ABC and  DBC are on the same base BC with vertices A and D on opposite sides of BC such
that area of ABC = area of  DBC. Show that BC bisects AD.

18. Ram is half of his father’s age. Twenty years ago the age of father was six times age  of Ram. Find
the age of Ram and his father.

19. Draw a histogram and a frequency polygon from the following data :
Class Interval 21 - 25 26 – 30  31 – 35  36 – 40  41 – 45  46 – 50  51 – 55  55- 60
Frequency 21 22 50 110 87 51 18 23

20. A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.

21. Two coins are tossed simultaneously 100 times and we get the following outcomes :
Find the probability of each event.

22. The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to
intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal areas.

23. A conical tent is 10 m high and the radius of its base is 24 m. Calculate its slant height and cost of
canvas required to make it at the rate of Rs. 70 per meter square.

24. In the given figure, O is the centre and AE is the diameter of the semicircle
ABCDE. If AB = BC and AEC = 50, then find
(a) CBE (b) CDE (c) AOB. Prove that BO||CE.

SECTION  – D

25. Prove that the angle subtended at any point on the arc of a circle is half the angle subtended at the
centre of a circle.

26. Water flows in a tank 150 m X 100 m at the base through a pipe whose cross section is 2 dm by
1.5 dm at the speed of 15 km/hr. In what time will the water be 3 m deep ?

27. The force exerted to pull a cart is directly proportional to the acceleration produced in the body.
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 the acceleration
produced is (a) 5 m/sec 2
(b) 6 m/sec 2

28. How much steel was actually used, if of the steel actually used was wasted in making the closed circular tank whose diameter is 4.2 m and length is 4.5 m.

29. Construct a triangle with perimeter 10 cm and base angles 60 and 45.

30. The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the
mean marks of all the students in that examination are 71, find the ratio of the number of boys to the
number of girls.

31. “Two years later a father will be 8 years more than three times the age of the son” taking the present
age of father and son as x and y respectively. Write a linear equation for the above and draw its
graph. From the graph, find the age of the father when the son’s age is 10 years.

32. E and F are respectively the mid  – points of the non – parallel sides AD and BC of a trapezium
ABCD. Prove that EF||AB and EF = ½ (AB + CD).

33. Prove that, if two triangles are on the same base and between the same parallel lines then their areas
are equal.

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