Mathematics is all about practice, the more you practice the more you reach towards perfect. CBSE Mathematics sample papers for class IX are drafted in such a way that it cover maximums syllabus and complete pattern of marks. By solving such papers students can get clear idea about difficulty level of sums and the amount of accuracy they need to develop. Following is the Mathematics sample paper which can improvise your sums solving skill:
TIME: 3 hours – 3½ hours, Maximum Marks: 80
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections – A, B, C and D. Section A comprises of 10 questions of 1mark each, Section B comprises of 8 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and section D comprises of 6 questions of 4 marks each.
(iii) Question numbers 1 to 10in section A are multiple choice question where you are to select one correct option out of the given options.
(iv) There is no overall choice. However, internal choice has been provided in 1question of 2 marks, 3 questions of 3 marks each and 2 questions of 4 mark each. You have to attempt only one of the alternatives in all such question.
(v) Use of calculator is not permitted.
(a) 900 (b) 1800 (c) 2700 (d) 3600
2. Curved surface Area of Cylinder is
(a) ?r2 (b) 2?rl (c) 2?rh (d) ?rl
3. CSA of Dome (hemisphere) is
(a)2?r2 (b) 4?rl (c) 3?r2 (d) ?rl
4. Mode of 14, 15, 15, 18, 20, 21,21,21,25 is
(a)18(b)19 (c) 20 (d) 21
5. Find angle ?DCP
(a)1400 (b) 1100 (c) 700 (d) 600
6. The mean of 16 numbers is 8. If 2 is multiply to every number, what will be the new mean.
(a) 16 (b) 12 (c) 10(d) 8
7. 1m3 =……..cm3
(a) 1000(b) 10000 (c) 100000(d) 1000000
8. In a cyclic quadrilateral one angle is 600 then exterior angle will be
(a) 1020 (b) 600 (c) 3600(d) None of these
9. Height of cone is equal to
(a) ?rl (b) r2+h2 (c) ?l2-r2 (d) ? r2+h2
10. Surface area of circle = …?….. Surface area of Sphere
(a) 1/2 (b) 1/3 (c) 1/4 (d) 1/5
11. Find the mean of 13, 19, 25, 60, 49, 36, 30, 32, and 56? And if 13 is misread by 31, what will be the new mean?
14. Two coins are tossed simultaneously. The outcomes of getting tails are recorded.
Number of tails 0 1 2
Outcomes 22 16 12
Calculate the probability of getting (a) exactly 1 tail (b) no tail (c) at least 1 tail
15. How many liters of milk can a hemispherical bowl of diameter 10.5cm hold?
16. A conical tent is 10m high and the radius of its base is 24m. Find area of cloth used.
Construct a triangle in which QR = 5cm, ? Q= 750 and PR-PQ= 2.5 cm.
17. Find the value of a and b such that the following equations may have (5, -3) as a solution 5x + ay = -2 7x+by = 4b
18. If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of a?
Draw the graph of the equation 2x + y = 4. From the graph
19. Write the four solutions for the equation x=4y-1
In Fig. , AB is a diameter of the circle; CD is a chord equal to the radius of the circle. AC and BD when extended intersect at a point E, Prove that ? AEB = 600
22. Draw the graph of the equation 2x – 3y =5. From the graph, find the value of x when (i) y = 1 and (ii) y = 3
23. If E, F, G, H are respectively the mid points of the sides of a parallelogram ABCD, show that ar (EFGH) = ½ (ABCD).
24. Here is a linier equation that converts Fahrenheit to Celsius:
(i) if the temperature is 950F, What is the temperature in Celsius?
(ii) Is there temperature which is numerically the same in both Fahrenheit and Celsius if yes, find it?
25. A bag contains 5 red, 3 green and 2 blue marbles. A marble is selected at random from the bag. Calculate the probability of getting (a) a red ball (b) a blue ball (c) not a blue ball.
Construct a triangle with base of length 5cm, sum of two sides 7.7cm and one of the angles of the base as 750.
26. If the mean of the following distribution is 21, find the value of x
x: 10 15 20 25 30
f: 6 10 x 10 8
If the mean of five observations, x, x+2, x+4, x+6 and x+8 is 11. Find the mean of the first three observations
27. ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) =ar (ACY).
28. Show that the bisectors of angles of a parallelogram form a rectangle.
29. If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body. Express this in the form of an equation into variable and draw the graph of the same by taking the constant force as 5 units. Also from the graph the work done when the distance travelled by the body is
(1). 2 units (2). 0 units
30. Construct a triangle XYZ, in which ?X=450, ?Y=600 and XY+YZ+ZX=10.5cm
31. 2000 families with 3 children were selected at random and the following data is recorded
Girl child in family
No. of families
a) probability of family having 0 girl
b) probability of family having 1 girl
c) probability of family having 2 girl
d) probability of family having more than 1 girl
e) probability of family at least 1 girl
32. In figure ABCD is a parallelogram and E, F is the midpoints of sides AB and CD respectively. Show that quadrilateral AECF is a parallelogram.
A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other, Find the length of the string of each phone.
33. It costs Rs.2200 to paint the inner curved surface of a cylindrical vessel 10m deep. If the cost of painting is at the rate or Rs. 20 per m2,find the
(i) Inner curved surface area of the vessel.
(ii) Radius of the base.
(iii) Capacity of the vessel.
In fig., you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height 30 cm. A margin of 2.5cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
34. A random survey of the number of children of various age groups playing in a park are found as follows:
Age in years No.of children
Draw a histogram to represent the above data.