CBSE Board Class 9 Math Sample Papers 2010

Sample Paper – 2010
Class – IX
Subject – Maths  

General Instructions:
(i)All questions are compulsory.
(ii)The question paper consists of 30 questions divided into four sections – A, B, C and D. Section A contains 10 questions of 1mark each, Section B contains 5 questions of 2 marks each, Section C contains 10 questions of 3 marks each and section D contains 5 questions of 6 marks each.
(iii)There is no overall choice. However, internal choice has been provided.
(iv)Use of calculator is not permitted.

SECTION A

1.Find the Value of a if (2y+3) is a factor of 2y3 + 9y2 – y – a.

2.The measure of an angle is four times the measures of its supplementary angles .Find the angles.

3.Factorize: x2 – 2x + 7/16.

4.The length of a diagonal of a square is 20 cm. Find its area.

5.The C.S.A. of a Cylinder is 4620 cm2. Find its radius if height is 35 cm.

6.Find the length of a chord which is at a distance of 5 cm from the centre of a circle whose radius is 10 cm.

7.Find p(–3) , if p(x) = x4 + 3x3 + 11x2 + 4x – 6

8.The value of K is when x–1 is factor of 4x3 + 3x2 – 4x – K is
(a) 3  (b) 0        (c) –1   (d) –3

9.Every square is a rhombus. True or False.

10.Define Zeros of polynomial.

SECTION B

11.Factorise a6–1

12.∆ABC is an isosceles triangle in which AB = AC. D, E and F are the midpoints of the sides BC, AC and AB respectively, prove that DE=DF.

13.Write two solution of equation 5x – 4y = 9

14.If ∠AOC + ∠BOD= 240°, find all  the  angles:

15.Curved surface area of a right circular cylindrical is 4.4m2. If the radius of the base of the cylinder is 0.7m. Find its height.

SECTION C

16.“Lines which are parallel to same line are parallel to each other.” Prove.
OR
∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that BCD is a right angle.

17.We know that force applied on a body is directly proportional to the acceleration produced in the body. Express this using equation in two variables taking the constant as 4.5 units. Also, draw the graph for the equation.

18.Factorise (y2 – 5y)2–2(y2 – 5y) – 24 

19.If x = 2 – √3   Find x2 + 1
  2  +√3                   x2

20.If E and F are midpoints of sides AC and AB respectively. G is a point of intersection of BE and CF, prove that ar(quad.AEGF) = ar(∆GBC)

21.Without actual multiplication evaluate (a) (99.7)2  (b) 100.4 × 99.6

OR

Simplify:  (a) (a + b – c)2  + (a – b – c)2    (b) (2x+ 3p)3 +(2x – 3p)3

22.In the figure AD and BE are medians ∆ABC and BE||DF, prove that CF = ¼AC.

23.If p + q + r = 0, show that p3 + q3 + r3 = 3pqr

24.Represent √5.6 on a number line.

25.A park, in the shape of a quadrilateral ABCD, has C = 900, A=9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

OR

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26cm, 28cm, 30cm and the parallelogram stands on the base 28cm find the height of the parallelogram.

SECTION D

26.ABCD is a trapezium such that CD||AB, if E and F are midpoints of AD and BC, prove that

a) EF||CD||AB
b) EF= ½ (AB + CD)

OR

Prove that the quadrilateral formed by joining the midpoints of sides of square is square.

27.If a diagonal of a parallelogram bisect one of the angles of the parallelogram. Prove that its two diagonals are perpendicular bisector of each other.

28.Construct a triangle PQR such that PQ=QR, ∠P=50° and perimeter is 12cm.

29.“The sides opposite to equal angle of a triangle are equal.” Prove
Prove that CP =BP, if in the figure below AD bisects ∠CPB and ∠CAB.

30.A closed box is made of wood which is 1cm thick. The external dimensions of the box are 1.5m, 1.08m and 0.72m, find the

a)Volume of the wood used in making the box.
b)Capacity of the box

OR

A conical tent is 12m high and 14m in diameter.
c) Find the area of canvas required to make it.
d) Suppose if a person requires 5m2 space on ground and 12m3 in air, how many person such tent can accommodate.