# Time: 3 to 3 ½ hours M.M.:90

Sample Question Paper
Mathematics
First Term (SA - I)
Class IX
Time: 3 to 3 ½ hours
M.M.:90
General Instructions
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section A
comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks each,
section C comprises of 10 questions of 3 marks each and section D comprises of 10 questions of 4
marks each.
(iii) Question numbers 1 to 8 in section A are multiple choice questions where you have to select one
correct option out of the given four.
(iv) There is no overall choice. However, internal choice has been provided in 1 question of two
marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt
only one of the alternatives in all such questions.
SECTION A
Question numbers 1 to 8 carry 1 mark each. For each question, four alternative choices have been
provided of which only one is correct. You have to select the correct choice
Q .1
Solution
Ans : [A]
Q .2
Which of the following expressions is a polynomial?
Ans: [C]
Q .3
If a + b + c = 0, then
(A) 0
Solution
Ans: [D]
(B) abc
(C) 2abc
(D) 3abc
Q .4.
The maximum number of terms in a polynomial of degree 10 is :
(A) 9
(B) 10
Solution
Ans: [C]
Q .5
In the given figure, if
Solution:
(C) 11
(D) 1
Q .6
Solution
The two triangles will be congruent by SAS axiom if AC = DE
Ans : [D]
Q. 7
Area of an equilateral triangle of side ‘a ’ units can be calculated by using the formula :
Solution
Side of an equilateral triangle = a units
Ans : [D]
Q. 8
The area of
in which AB = BC = 4 cm and
Solution
Ans : [B]
SECTION – B
Question numbers 9 to 14 carry two marks each
Q. 9
Solution
Q. 10
Find the value of k, if
Solution:
Q. 11
Solution:
Q. 12
In the given figure,
a and b
Solution
, then find the value of
Q. 13
In the given figure,
and
OR
In the figure given below AC > AB and AD is the bisector of
Solution
In the given figure,
OR
Q. 14
Plot the point which lies on y axis and at a distance of 4 units in the negative direction of y axis. Also
find its coordinates
Solution
The coordinates of the point are
SECTION – C
Question numbers 15 to 24 carry three marks each
Q. 15
Prove that
Solution
Q. 16
OR
Visualise 3.765 on the number line, using successive magnification
Solution
OR
Q. 17
OR
What are the possible expressions for the dimensions of a cuboid whose volume is given below?
Solution
OR
Factorising the expression given for volume, we get
Q. 18
Solution
Q. 19
OR
In the given figure, bisectors of
at P and Q respectively.
Prove:
Solution
OR
In parallelogram ABCD
Q. 20
In the given figure,
Find the value of x
Solution
Q. 21
In the given figure, AB = AC, D is the point in the interior of
.
Solution
Q. 22
In the given figure, AB = BC and AE = CD
Prove that BD = BE
Solution
Q. 23
In the given figure, if
Solution
Q. 24
The perimeter of a triangular field is 300 cm and its sides are in the ratio 5 : 12 : 13. Find the length of
the perpendicular from the opposite vertex to the side whose length is 130 cm
Solution:
Ratio of the sides of the triangular field = 5 : 12 : 13
Let the sides be 5x cm, 12x cm and 13x cm
Perimeter of the triangular field = 300 cm
Let AD be the perpendicular from the opposite vertex to the side of length 130 cm
SECTION – D
Question numbers 25 to 34 carry four marks each.
Q. 25
Rationalise the denominator of
OR
Solution
OR
(Student can use any one of the following methods)
Method 1:
Method 2:
Q. 26
Solution
Q. 27
Verify that
Solution
Q. 28
If
the values of m and n.
Solution
as a factor, and leaves a remainder n when divided by
find
Q. 29
(i) Expand:
(ii) Evaluate
by using suitable identity
OR
Factorise :
Solution
OR
Q. 30
Prove that the sum of all sides of a quadrilateral is greater than the sum of its diagonals
Solution:
Given : A quadrilateral ABCD with diagonals AC and BD
To prove : AB + BC + CD + DA > AC + BD
Proof : In a triangle sum of any two sides is greater than the third side
Q. 31
Plot the following points and check whether they are collinear or not :
(1, 1) (2, − 3) (−1, −2)
Solution:
Given points do not lie on a single straight line.
Hence, they are not collinear.
Q. 32
ABC is a triangle with
Prove that
Solution:
is a point on BC such that AD bisects
Q. 33
In the given figure, if AD is the bisector of
(i) AB > BD
(ii) AC > CD
Solution:
then prove that :
Q. 34
BE and CF are two equal altitudes of a triangle ABC. Prove that the triangle ABC is isosceles
Solution