**CBSE Sample Paper IX Mathematics**

*(Sample Paper / CBSE Guess Paper - 1 | NCERT Practice Paper)***Class IX, CBSE Mathematics (SA 2 - Term II)**

**Time: 3 hours**

**M.M.: 80**

**Instructions**

1. All questions are compulsory.

2. The question paper has 34 questions divided into Sections A, B, C and D.

3. Section - A contains 12 MCQs first 8 of 1 mark each and the next 4 of 2 marks each.

Section – B contains 7 questions of 2 marks each.

Section – C contains 10 questions of 3 marks each.

Section – D contains 5 questions of 4 marks each.

4. Use of calculator not permitted.

**Section - A**

1. The value of π is

(a) 3.24 (b) 3.242 (c) 3.15 (d) 3.14159265….

2. Between two irrational numbers √2 and √3, there be

(a) No irrational number (b) No rational number

(c) Infinite irrational number (d) Only one irrational number.

3. To determine a line, the number of points required is

(a) 1 (b) 2 (c) 3 (d) Infinite.

4. If the sides of a triangle are produced in order, then the sum of the exterior angles so formed is equal to

(a) 90

^{O}(b) 180^{O}(c) 270^{O}(d) 360^{O}
5. In figure (1), PM ┴ OA and PN ┴ OB. If

__/__AOB = 50^{O}then__/__MPN equals
(a) 40

^{O}(b) 90^{O}(c) 100^{O}(d) 130^{O}
6. If the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is –

(a) Rectangle (b) Parallelogram (c) Rhombus (d) Square

7. In figure (2) OM ┴ to the chord AB of the circle with center O. If OA = 13 cm and AB = 24 cm then OM equals –

(a) 3 cm (b) 4 cm (c) 5 cm (d) √4.7 cm

8. A ΔABC is inscribed in a circle with center O. If

__/__AOB = 140^{O}and__/__BOC = 100^{O}then__/__ABC equals
(a) 60

^{O}(b) 100^{O}(c) 120^{O}(d) 150^{O}
9. If √3 = 1.732 and √2 = 1.414 the value of

10. The expansion of (a – 2b – 3c)

^{2}is –
(a) a

^{2}+ 2b^{2}+ 3c^{2}+ 4ab + 12bc + 6ac (b) a^{2}+ 4b^{2}+ 9c^{2}+ 2ab + 2bc + 2ca
(c) a

^{2}– 4b^{2}– 9c^{2}– 4ab + 12bc – 6ac (d) a^{2}+ 4b^{2}+ 9c^{2}– 4ab + 12bc – 6ac
11. In fig (3) Δ ABC, E is the mid-point of the median AD, then area of Δ BED equals

(a) ar (Δ ABC) (b) ½ ar (Δ ABC) (c) 1/3 ar (Δ ABC) (d) ¼ ar (Δ ABC)

12. The average age of a family of 5 members is 30 years. The average age of the same family after 5 years will be

(a) 30 years (b) 25 years (c) 35 years (d) 55 years

**Section – B**

13. Divide (√3 + √7) by (√3 – √7).

14. In fig (4) AB || CD,

__/__APQ = 50^{O }and__/__PRD = 120^{O}. Find x and y.
15. In fig (5) ABCD, is a quadrilateral in which AB = CD and AC bisects angle A. Show that BC = DC.

16. In fig (6) ABCD is a quadrilateral in which AB = AD and AC bisects angle A. Show that BC = DC.

17. The angles of a quadrilateral are in the ratio 3:4:5:6. Find al the angles of the quadrilateral.

18. Find the lateral surface area of a solid cylinder having diameter as 50 cm and height 3.5 cm.

19. The mean f 20 observations is 50. If the observation 50 is replaced by 140, what will be the resulting mean?

**Section – C**

20. Factorize : (x – y)

^{3}+ (y – z)^{3}+ (z – x)^{3}
21. Write (2x – 3y – 4z)

^{2}in expanded form.
22. In a Δ ABC,

__/__A +__/__B = 100^{O}, and__/__B +__/__C = 140^{O}. Find the measure of each of the angles of the triangle.
23. Prove that the diagonal divides a parallelogram into two congruent triangles.

24. ABCD is a rhombus show that the diagonal AC bisects

__/__A as well as__/__C.
25. In fig (7) ABCD is a parallelogram in which DE ┴ AB and BF ┴ AD. If AB = 12 cm, DE = 6 cm and AD = 9 cm, find BF.

26. In fig (8) A, B, C and D are four points on a circle. AC and BD intersect at a point E such that

__/__BEC = 130^{O}and__/__ECD = 20^{O}. Find__/__BAC.
27. The pillars of a temple are in the shape of a cylinder. If each pillar has a base radius 20 cm and height 10 cm, find the volume of concrete required to build 7 such pillars.

29. Find the curved surface area of a cone whose base diameter is 10.5 cm and slant height is 10 cm.

**Section – D**

30. If x + y + z = 0 show that x

^{3}+ y^{3}+ z^{3}= 3xyz.
31. Triangle ABC and DBC are on the same base line BC, with A and D on opposite sides of the line BC such that ar (Δ ABC) = ar (Δ DBC). Show that BC bisects AD.

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

33. Find the volume of a sphere whose surface area is 154 cm

^{2}.
34. Marks secured by 15 students in a class are as below: 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 52, 60, 30. Find the mean and median of the data.

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