# CBSE Sample Paper 2014 – Mathematics – class ix

**Sample Paper – 2014 **

**Class – IX **

**Subject – Mathematics **

*General instructions: *

1. All questions are compulsory.

2. The question paper consists of 34 questions divide into four sections A, B, C and D.

3. (i) Section A contains 8 questions of 1 mark each.

(ii) Section B contains 6 questions of 2 marks each

(iii) Section C contains 10 questions of 3 marks each

(iv) Section D contains 10 questions of 4 marks each

*Section A *

**1. **Which of the following is a rational number?

(a) √3

(b) √4

(c) √0.9

(d) None of these

**2. **When x25 + 2 is divided by (x + 1), the remainder is

(a) 1

(b) 2

(c) 25

(d) None of these

**3. **The coefficient of x2 in the expansion of (x + 10)2 is

(a) 2

(b) 4

(c) 10

(d) None of these

**4. **Which of the following need a proof

(a) Theorem

(b) Axiom

(c) Postulate

(d) None of these

**5. **Find the value of x, If AB is parallel to CD and ‘T’ is a transversal.

(a) 120o

(b) 60o

(c) 30o

(d) None of these

**6. **If X > 0 and y < 0, the point (x, y) lies in which quadrant (a) I

(b) II

(c) III

(d) IV

**7. **In the given figure, if l is parallel to m then value of x is (a) 40o

(b) 20o

(c) 30o

(d) None of these

**8. **If a + b = -1, then the value of a3 + b3 – 3 a b is

(a) 26

(b) 1

(c) -1

(d) None of these

*Section B *

**9. **Give an example of two irrational numbers whose product is

(a) A rational number

(b) An irrational number

**10. **Expand (1/2 x + 2y –c)2

**11. **Represent √5.2 on the number line.

**12. **Plot the points A (4, 0) and B (0, 4). Join A, B to the origin O. fined the area of the triangle AOB.

**13. **Simplify (2x + a + b)2 – (2x – a + b)2

**14. **Find two irrational numbers between √2 and √5.

**Or **

Represent √5 on a number line.

*Section c *

**15. **Write any three Euclid’s postulate.

**16. **factorize x2 + 1/x2 + 2 – 2x – 2/x

**17. **Express 0.0010101…. in the form of p/q, where p and q are integers and q ≠ 0.

**18. **Find the values of a and b, if a + b √35 = (√7 + √5) / (√7 – √5) **Or **

Factorize x2 + 3 √3 x – 30

**19. **If x, y, z are real numbers, show that √(x-1 y) √(y-1 z) √(z-1 x) = 1

**20. **Plot the following points and write the name of the figure thus obtained: A (2, 0), B (4, 0), C (4, 2)

and D (2, 2)

**21. **If a = 6 + 2√3, find the value of a – 1/a.

**Or **

Factorize 2 x2 – 7x – 15

**22. **Simplify 128-2/7 – (625-3)-1/4 + 14 (2401)-1/4

**23. **If x – y = 5 and x y = 84, find the value of x3 – y3.

**Or **

If x + y + z = 10 and x2 + y2 + z2 = 40, find the value of x y + y z + z x.

**24. **In the given figure, DE is parallel to QR and AP and BP are bisectors of angle EAB angle RBA respectively. Find angle APB.

*Section D*

**25. **In the given figure bisector of angle B and D of a quadrilateral ABCD meet CD and AB

produced at P and Q respectively. Prove that angle P + angle Q = ½ (ABC + ADC).

**26. **S is a point on side QR of a ∆PQR. Show that: PQ + QR + RP > 2 PS.

**27. **If the bisector of an angle of a triangle bisects the opposite side at 90o; prove that the triangle is an isosceles.

**28. **If each side of a triangle is doubled, then find the ratio of area of new triangle thus formed and the given triangle.

**29. **If x = 7 + √40, find the value of √x + 1/√x.

**Or **

Factorize (x2 – 2x)2 – 23 (x2 – 2x) + 120.

[(√ (a + 2b) + √ (a – 2b)]

**30. **If x =

[(√ (a + 2b) - √ (a – 2b)]

Then show that bx2 – a x + b = 0

**31. **Prove that angles opposite to two equal sides of a triangle are equal.

**32. **In the given figure, the side BC of a ∆ABC is produced, such that D is on ray BC. The bisector of angle A meets BC in L. Prove that angle ABC + angle ACD = 2 angle ALC.

**33. **Factorize x6 – 64

**34. **A field is in the shape of a trapezium, its parallel sides are 25m and 10 m and non-parallel sides are 14 m and 13 m. find the area of the trapezium.

**Or **

In triangle ABC, the sides AB and AC of ∆ABC are produced to points E and D respectively. If bisectors of BO and CO of angle CBE and angle BCD respectively meet at a point O. then prove that angle BOC = 90o – ½ angle A.

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