Sample Paper – 2009
Class – IX
Subject – Mathematics
(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, an internal choice has
been Provided in one question of two marks each, three
questions of three marks each and two questions of six
(iv) Use of calculator is not permitted.
SECTION A (10 x 1 = 10 marks)
Q.1 Two unbiased coins are tossed once. What is the probability
of getting exactly one head?
Q.2 Express 1.324 in the form p/q.
Q.3 Find the remainder when x3 – ax2 + 6x – a is divided by
x – a.
Q.4 The angles of a quadrilateral are in the ratio 2 : 4 : 5 : 7.
Find all the angles.
Q.5 In which quadrant do these points (-2,4), (3,-1), (-3, 8),
(4, -5) lie?
Q.6 Factorize: 5x2+16x+3
Q.7 Find the volume of a right circular cylinder which has a
height of 21cm and base radius 5cm.
Q.8 If x + y + z = 0, show that x3 + y3 + z3 = 3xyz .
Q.9 Find the arithmetic mean of first 10 natural numbers.
Q.10 Three angles of a quadrilateral measure 560, 1150 and 840.
Find the measure of the fourth angle.
SECTION – B (5 x 2 = 10 marks)
√5 + √3
√5 ─ √3
Q.12 A metallic sphere of radius 10.5 cm is melted and then recast
into smaller cones, each of radius 3.5cm and height 3cm. How
many cones are obtained?
Q.13 curved surface area of a right circular cylindrical is 4.4
m2. If the radius of the base of the cylinder is 0.7m,
Find its height.
Q.14 Prove that if a side of a triangle is produced, then the exterior
angle so formed is equal to the sum of the two interior
A sphere of diameter 15.6cm, is melted and cast into a right
circular cone of height 31.2 cm. Find
the diameter of the base
of the cone.
Q.15 A bag contains 4 red, 5 black and 6 white balls. A ball `
is drawn from the bag at random. Find the probability
that the ball drawn is;
a. either red or white b. neither black nor red
c. Red and white d. Red or white or black
SECTION – C (10 x 3= 30 marks)
Q.16 Simplify: (a) (x+ y+ z)2 + (x + y- z)2 (b) (2 x+ 3p)3 +(2x-3p)3
Factorise by using factor theorem.
(i) x3 – 2x2 – x + 2 (ii) x3 – 3x2 – 9x –5
Q.17 A solid composed of a cylinder with hemi spherical ends.The
whole height of the solid is 19cm and the radius of the
Cylinder is 3.5cm.Find the weight of the solid if 1cm3 of the
metal weighs 4.5g.
Q.18 Three unbiased coins are tossed. What is the probability of
getting a) two heads b) at least two heads c) at most two
heads d) one head or 2 heads.
Q.19 ∆ABC is an isosceles triangle in which AB = AC. Side BA is
produced to D such that AD = AB. Show that ÐBCD is a right
Q.20 Find the median.
Q.21 Prove that angles opposite to equal sides of an isosceles
triangle are equal.
In the given figure, Ð B < Ð A and Ð C < Ð D. Show that AD <
Q.22 Show that the each angle of a equilateral triangle is 600 .
Q.23 Draw the graph of the equation 2x + y = 6. Find the
coordinates of the point where the graph cuts the x- axis.
Q.24 A park, in the shape of a quadrilateral ABCD, has ÐC = 900, A=9
m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it
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.
Q.25 ABC is a right angle triangle in which ÐA = 900 and AB = AC.
Find ÐB and ÐC.
SECTION – D (5 x 6 = 30 marks)
Q.26 From a solid right circular cylindrical with height 10 cm and
radius of the base 6 cm, a right circular cone of the same
height band base is removed. Find the volume of the
Q.27 A right triangle ABC with sides 5cm,12cm,13cm is revolved
about the side 12cm.Find the volume of the solid so obtained.
If the triangle is revolved about side 5cm find volume of the
solid so obtained. Also find the ratio of both the volumes.
Show that the line segments joining the mid – points of two
sides of a triangle is parallel to the third side and half of it.
Q.28 Prove that sum of three angles of a triangle is 180º.
find the value of 'x' if three angles of the triangle are
(2x-7)º, (x+25)º, (3x+12)º.
A hemispherical bowl of internal radius 9cm contains a liquid.
The liquid is to be filled in to cylindrical shaped small bottles of
diameter 3 cm and height 4 cm. how many bottles arte
required to empty the bowl?
Q.29 A metal pipe is77 cm long. The inner diameter of a cross
section is 4 cm, the outer diameter 4.4 cm. Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
Q.30 Find the missing frequencies in the following distribution.
It is given that mean of the Frequency distribution is 50.
Also find mode.
0 – 20
20 – 40
60 – 80
80 – 100