# CBSE Class 9 Mathematics Sample Paper 2017 (12)

CBSE Class 9 Mathematics Sample Paper 2017 (12). It’s always recommended to practice as mane sample papers as possible before the examinations. Students can download the sample papers and also question papers of previous years to practice and score better marks in examinations. Refer to other links too for more sample papers.

• Use of calculators is not permitted.

SECTION – A

(Question numbers 1 to 4 carry 1 mark each)

Q.1 Write the rationalising factor or conjugate factor of 7 + 2.

Q.2 Write an example of a binomial of degree 35.

Q.3 Can a triangle have two obtuse angles? Give reason for your answer.

Q.4 How many axes and quadrants are there in a Cartesian plane?

SECTION – B

(Question numbers 5 to 10 carry 2 marks each)

Q.5

Write two rational numbers between

3

2

and

3

5

.

Q.6 Find the remainder when x4 + x3 – 2x2 + x + 1 is divided by x – 1.

Q.7 If B lies between A and C, AC = 15 cm and BC = 9 cm. What is ?

Q.8 In the given figure, can we say l || m, state with

reasons?

Q.9 In the given figure, DPQR is an equilateral triangle

with coordinates of Q and R as (-2, 0) and (2, 0)

respectively. Find the coordinates of the vertex P.

Q.10 What will be the semi perimeter of an equilateral triangle of side ‘a’? Show your work.

SECTION – C

(Question numbers 11 to 20 carry 3 marks each)

Q.11 Locate 5 on number line.

Q.12 In a survey, it was found that 9 out of every 11 households are donating some amount of their

income to an orphanage or old age homes or institutions for physically handicaps. What

fraction of households are not donating? Write it in decimal form and find what kind of decimal

expansion it has. What values of society are depicted here?

Q.13 Find the value of k, if x – 1 is a factor of 4x3 + 3x2 – 4x + k.

Q.14 Factorise : 2y3 + y2 – 2y – 1.

Q.15 A point C lies between two points A and B such that AC = BC. Using Euclid’s axiom, show

that AC =

2

1

AB.

Q.16 In figure, AB || CD and CD || EF. Also EA ⊥ AB. If ÐBEF = 55°,

find the values of x, y and z.

Q.17 Prove that the sum of all the interior angles of a triangle is 180 .

Q.18 E and F are respectively the mid-points of equal sides AB and

AC of Δ ABC. Show that BF = CE.

Q.19 Locate the points (5, 0), (0, 5), (–3, 5), (–3, –5), (5, –3) and (6, 1) in the Cartesian plane.

Q.20 Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

SECTION – D

(Question numbers 21 to 31 carry 4 marks each)

Q.21 Find the value of a and b: 5

3 5

7 3 5

3 5

7 3 5

=a + b

+

+

.

Q.22 Prove that:

nl

l

mn n

n

lm m

m

l

x

x

x

x

x

x

1 1 1

= 1.

Q.23 Find the possible expressions for the dimensions of a cuboid whose volume is

x3 – 23x2 + 142x – 120 cubic units.

Q.24 Find the following products using appropriate identities:

(i) (x + 3) (x + 3) (ii) (x – 3) (x + 5)

Q.25 Evaluate the following products without multiplying directly:

(i) 103 × 107 (ii) 104 × 96

Q.26 If p(x) = x3 – 4x2 + x+ 6, then show that p(3) = 0 and hence factorise p(x).

Q.27 In figure, the side QR of Δ PQR is produced to a point S.

If the bisectors of ÐPQR and ÐPRS meet at point T, then

prove that ÐQTR =

2

1

ÐQPR.

Q.28 Line-segment AB is parallel to another line-segment CD.

O is the mid-point of AD. Show that

i) DAOB ≅ DDOC

ii) O is also the mid-point of BC.

Q.29 In an isosceles triangle ABC with AB = AC, D and E are

points on BC such that BE = CD. Show that AD = AE.

Q.30 In the figure, AB is a line-segment. P and Q are points on

opposite sides of AB such that each of them is equidistant

from the points A and B. Show that the line PQ is the

perpendicular bisector of AB.

Q.31 AB and CD are respectively the smallest and longest sides of

a quadrilateral ABCD. Show that ÐA > ÐC and ÐB > ÐD.

D

A

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