cbse.nic.in : Class IX Mathematics Question Paper Sample Central Board Of Secondary Education

Board : Central Board Of Secondary Education
Exam : Class IX
Subject : Mathematics.
Document Type : Sample Paper
Website : cbse.nic.in

Download Model/Sample Question Paper : https://www.pdfquestion.in/uploads/cbse.nic.in/7042-SA-II%20_IX_%20final%20maths.pdf

CBSE Mathematics Sample Question Paper SA-II

Class IX :
(Section-A)
TIME : 3 HRS.
M.M.:90

Related : Central Board Of Secondary Education Class X Mathematics Question Paper Sample : www.pdfquestion.in/7040.html

Question numbers 1 to 8 carry 1mark each. For each question, four alternative choices have been provided of which only one is correct. You have to select the correct choice.
1. Equation of x-axis is
(A) x = 0 (B) x = y (C) y = 0 (D) x + y = 0
2. The median of a triangle divides it into two
(A) triangles of equal area (B) equilateral triangles
(C) right triangles (D) isosceles triangles

3. In Fig.1, AOB is a diameter of the circle and AC = BC, then ??CAB is equal to
(A) 30o (B) 45o (C) 90o (D) 60o
4. Linear equation of the type has
(A) infinitely many solutions (B) a unique solution
(C) only solution x = 0, y = 0 (D) solution m = 0.

5. In a frequency distribution, the mid-value of a class is 20 and the width of the class is 8. then the lower limit of the class is
(A) 12 (B) 24 (C) 28 (D) 16

6. If the volume of a sphere is numerically equal to its surface area, then radius of the sphere is
(A) 1 unit (B) 3 units (C) 2 units (D) 6 units
7. Which of the following cannot be empirical probability of an event?
(A) 4/5 (B) 1 (C) 0 (D) 5/4

SECTION-B :
Question numbers 9 to 14 carry 2 marks each.
10. An edge of a cube is increased by 10%. Find the percentage by which the surface area of the cube has increased.
11. Find the mode of the following data:
5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.
12. In a cricket match, a batsman hits a boundary 4 times out of 30 balls, he plays. Find the probability that he did not hit a boundary.
13. Prove that equal chords of a circle subtend equal angles at the centre.
14. If the arithmetic mean of 25, 30, 32, x, 43 is 34, then find the value of x.

SECTION-C :
Question numbers 15 to 24 carry 3 marks each. :
15. Find three different solutions for the equation 3x – 8y = 27

16. Prove that a diagonal of a parallelogram divides it into two congruent triangles.
17. Draw a line segment AB = 5cm. From the point A, draw a line segment AD = 6cm making DAB = 60o. Draw the perpendicular bisector of AD. Does it pass through B? (Use ruler and compass only).

18. A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7mm and the diameter of the graphite is 1mm. If the length of the pencil is 14cm, find the volume of the wood. (use ?? = 22/7)
OR
A heap of wheat is in the form of a cone, the diameter of whose base is 14m and height is 3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

19. Find mean of the following data:
Marks: 10 11 12 13 14 15
Number of students: 6 3 4 5 7 5
OR
The points scored by a basket-ball team in a series of matches are as follows
17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10
Find mean, median and mode for the data.

20. Give the geometrical representation of x = -3 as an equation
(i) in one variable (ii) in two variables.
OR
Solve the equation 2x+1 = x–3 and represent the solution(s)
(i) on the number line
(ii) in the Cartesian plane.

21. The radius of a spherical balloon increases from 7cm to 14cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
22. In Fig.3, ABCD is a parallelogram and E is the mid point of AD.DL??BE meets AB produced at F. Prove that B is the midpoint of AF and EB =LF. Fig. 3
23. In Fig.4, ABCD is a trapezium in which AB??DC. O is the mid point of BC. Through the point O, a line PQ??AD has been drawn which intersects AB at Q and DC produced at P. Prove that ar (ABCD) = ar (AQPD).
24. A die is thrown 400 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table.
Find the probability of
(i) getting a number less than 3.
(ii) getting an outcome 6.
(iii) getting a number more than 4.

SECTION-D :
Question numbers 25 to 34 carry 4 marks each.
25. Show that the line segments joining the mid points of the opposite sides of a quadrilateral bisect each other.
26. Construct a triangle ABC in which BC = 8cm, ??B = 30o and AB – AC = 3.5cm