Class 9 Math: Sample Question Paper Term I- 5 (With Solutions) | Mathematics (Maths) Class 9 PDF Download

Class 09 Mathematics

Max. Marks: 40

General Instructions :

1. The question paper contains three parts A, B and C
2. Section A consists of 20 questions of 1 mark each. Attempt any 16 questions
3. Section B consists of 20 questions of 1 mark each. Attempt any 16 questions.
4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions.
5. There is no negative marking.

Q.1: Which of the following is not a rational number?
(a) √2
(b) √4
(c) √25
(d) √9

Correct Answer is Option (a)
√4 = 2
√9 = 3
√25 = 5
√2 = 1.4142135.......Hence, it is an irrational number.

Q.2: The graph of a linear equation x - 5y + 3 = 0 cuts the x-axis at the point
(a) (-5, 0)
(b) (5, 0)
(c) (-3, 0)
(d) (3, 0)

Correct Answer is Option (c)
Then a line cuts x -axis in that case y co-ordinate is 0, so to find the co-ordinate of x we put y = 0 in given equation.
x – 5y + 3 = 0
At y = 0
x - 5 x 0 + 3 = 0
x + 3 = 0
x = -3
So the co-ordinate are (-3, 0)

Q.3: Given that lines l₁, l₂ and l₃ in figure are parallel. The value of x is:

(a) 140°
(b) 40°
(c) 50°

(d) 80°
Correct Answer is Option (a)

In the given figure
40° + ∠a = 180° (linear - pair)
Therefore ∠a = 180° - 40° = 140°
Now ∠a = ∠b (corresponding - angles)
Similarly ∠b = ∠x = 140°
Therefore ∠x = 140°

Q.4: Each of the two equal sides of an isosceles right triangle is 10 cm long. Its area is
(a) 50 cm²
(b) 75 cm²
(c) 10√3cm²
(d) 5√10cm²

Correct Answer is Option (a)
Here, the base and height of the triangle are 10 cm and 10 cm, respectively.
Thus, we have
Area of triangle = 1/2 x Base x Height
= 1/2 x 10 x 10
= 50 cm²

Q.5: If x = 2 + √3, then x + 1/x =
(a) 4
(b) -5
(c) -4
(d) 5

Correct Answer is Option (a)

→
now, put x = 2 + √3

we have,
→
→
→
= 4

Q.6: Which one of the options is true, and why? y = 3x + 5 has
(a) only two solutions
(b) infinitely many solutions
(c) a unique solution
(d) None of these

Correct Answer is Option (b)

Equation y = 3x + 5 is a linear equation in two variables.
This means that we can put any value of x and in return, we will get some other value of y.
For example, at x = 0, y = 3 x 0 + 5, y = 5 at x = 1000, y = 3 x 1000 + 5, y = 3005 we can put infinitely many values of x and we will get infinitely many solutions for y.
Thus there are infinite solutions for the equation. Graphically: When plotted graphically, it will give a straight line extending to infinity and thus will give infinite solutions.

Q.7: In the adjoining figure, if AB ║ DE, then the measure of ∠ACD is :-

(a) 90°
(b) 100°
(c) 80°
(d) 70°

Correct Answer is Option (b)

x + 110° = 180° (Supplimentary angles)
x = 70°y + 150° = 180° (Supplimentary angles)
y = 30°
ACD = 70° + 30° = 100°

Q.8: In fig, in ΔABC, AB = AC, then the value of x is:

(a) 120°
(b) 100°
(c) 130°
(d) 80°

Correct Answer is Option (c)

Triangle ABC is an iscosceles triangle and hence in the triangle other two angles are 50 and 50
Therefore,
X = 180 - 50 = 130

Q.9: Which of the following numbers is irrational?
(a)
(b)
(c)
(d) √8

Correct Answer is Option (d)
√8 =

Q.10: If  are the means of n groups with n1, n2, ..., nn number of observations respectively, then the mean  of all the groups taken together is:
(a)
(b)
(c)
(d)

Correct Answer is Option (c)
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

Q.11: In the adjoining figure, m  n, if ∠1 = 50°, then ∠2 is equal to -

(a) 50°
(b) 40°
(c) 130°
(d) 120°

Correct Answer is Option (c)
∠2 = 180°- ∠1
∠2 = 180° - 50° = 130°

Q.12: If 9^x+2 = 240 + 9^x, then x =
(a) 0.5
(b) 0.2
(c) 0.4
(d) 0.1

Correct Answer is Option (a)

9^x+2 = 240 + 9^x
9^x+2 - 9^x = 240
9^x . 9² - 9^x = 240
9^x(9² - 1) = 240
9^x(81 - 1) = 240
9x x 80 = 240
9x = 240/80
(3²)^x = 3¹
3^2x = 3¹
x = 1  x = 1/2 = 0.5

Q.13: The simplest form of is 
(a) 125
(b) 5
(c) 25

(d) none of these
Correct Answer is Option (b)

=
=

Q.14: A, B, C are the three angles of a triangle. If A - B = 15o and B - C = 30o, then angles A, B, C are respectively:
(a) 35^o, 65^o, 80^o
(b) 65^o, 80^o, 35^o
(c) 80^o, 35^o, 65^o
(d) 80^o, 65^o, 35^o

Correct Answer is Option (d)

Since ABC is a triangle
A + B + C = 180^o  (Angle sum property)....(i)
A - B = 15^o
A = 15o + B ....(ii)
B - C = 30^o 
C = B - 30^o ....(iii)
From (i) equation
15o + B + B + B - 30^o = 180^o
B = 65o
From equation (ii) and (iii)
A = 15^o + B = 15^o + 65^o = 80^o
C = B - 30^o = 65^o - 30^o = 35^o

Q.15: x = 2, y = -1 is a solution of the linear equation
(a) 2x + y = 0
(b) x + 2y = 0
(c) x + 2y = 4
(d) 2x + y = 5

Correct Answer is Option (b)
2 + 2(-1) = 2 - 2 = 0

Q.16: A die is thrown 1000 times and the outcomes were recorded as follows :

find probability of 2?
(a) 9/50
(b) 4/25
(c) 7/25
(d) 3/20

Correct Answer is Option (d)
150/1000 = 3/20

Q.17: The sides of a triangle are 4 cm, 8 cm and 6 cm. The length of the perpendicular from the opposite vertex to the longest side is :
(a)
(b)
(c)
(d)

Correct Answer is Option (c)
s =  = 9 cm
Area of triangle =
=
=
= 3√15 sq. cm
Area of triangle taking base as longest side = 1/2 x 8 x h
⇒ 1/2 x 8 x h = 3√15
⇒ h =

Q.18: The difference between the highest and lowest values of the observations is called
(a) range
(b) frequency
(c) mean
(d) class-intervals

Correct Answer is Option (a)
The difference between the highest and lowest value of observations is called 'Range' of observations.

Q.19: The smallest rational number by which1/3should be multiplied so that its decimal expansion terminates after one place of decimal, is
(a) 1/10
(b) 30
(c) 3/10
(d) 3

Correct Answer is Option (c)
The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal, is 3/10
Since, 1/3 x 3/10 = 1/10 = 0.1
Since, among them 3/10 is the only number which when multiplied, then its decimal expansion terminates after one place of decimal.

Q.20: In the figure if m  n and ∠1 : ∠2 = 1 : 2, then the measure of ∠8 is

(a) 30°
(b) 120°
(c) 60°
(d) 45°

Correct Answer is Option (b)

let the common ratio be x
Therefore ∠1 = 1x and ∠2 = 2x
∠1 + ∠2 = 180° (linear pair)
x + 2x = 180°
3x = 180°
x = 180°/3 = 60°
Therefore ∠1 = 60° and ∠2 = 2 x 60° = 120°
∠2 = ∠6 (corresponding angles)
and ∠6 = ∠8 (Vertically Opposite Angles)
⇒ ∠2 = ∠8 = 120°

Q.21: The taxi fare in a city is as follows: For the first kilometer, the fare is ₹8 and for the subsequent distance it is ₹5 per kilometer. Taking the distance covered as x km and total fare as ₹y, write a linear equation for this information.
(a) y = 5x + 3
(b) y = 5x – 3
(c) x = 5y – 3
(d) x = 5y + 3

Correct Answer is Option (a)

Taxi fare for first kilometer = ₹8
Taxi fare for subsequent distance = ₹5
Total distance covered = x
Total fare = y
Since the fare for first kilometer = ₹8
According to problem, Fare for (x - 1) kilometer = 5(x - 1)
So, the total fare y = 5(x - 1) + 8
⇒ y = 5(x - 1) + 8
⇒ y = 5x – 5 + 8
⇒ y = 5x + 3
Hence, y = 5x + 3 is the required linear equation.

Q.22: The base of an isosceles triangle is 6 cm and each of its equal sides is 5 cm. The height of the triangle is
(a) √11 cm
(b) 8 cm
(c) √30 cm
(d) 4 cm

Correct Answer is Option (d)
Height of isosceles triangle =
=   (a = 5 cm and b = 6 cm)
=
=
= 1/2 x 8
= 4 cm

Q.23: x – 4 is the equation of
(a) a line parallel to x-axis
(b) y-axis
(c) a line parallel to y-axis

(d) x-axis

Correct Answer is Option (c)

We know that the line parallel to y axis is given by x = a
x - 4 = 0
x = 4
So it is a line parallel to y-axis, at a distance of 4 units from it, to the right.

Q.24: In the adjoining figure, AB ║ CD and AB ║ EF. If EA ⊥ BA and ∠BEF = 55°, then the values of x, y and z :-

(a) 125°, 125°, 35°
(b) 60°, 60°, 60°
(c) 120°, 130°, 25°
(d) 35°, 125°, 120°

Correct Answer is Option (a)

x + 55 = 180° (Sum of supplementary angles or co-interior angles)
x = 125°
x = y = 125° (Corresponding angles)
z + ∠EAB = y (Exterior angle property)
z = 125° - 90° = 35°

Q.25: If x^1/12 = 49^1/24 , then the value of x is
(a) 7
(b) 12
(c) 49
(d) 2

Correct Answer is Option (a)

⇒
Equating both, x = 7

Q.26: An isosceles triangle has perimeter 30cm and each of equal sides is 12cm. Find the area of the triangle in cm²
(a) 12√15
(b) 9√15
(c) 17√15
(d) 6√15

Correct Answer is Option (b)

a = 12 cm
b = 12 cm
Perimeter = 30 cm

⇒ a + b + c = 30
⇒ 12 + 12 + c = 30
⇒ 24 + c = 30
⇒ c = 30 - 24
⇒  c = 6 cm
s = 30/2 = 15cm
∴ Area of the triangle =
=
=
=

Q.27: The mean of the below frequency distribution is 3.5, then the value of x is

(a) 3
(b) 4
(c) 5
(d) 2

Correct Answer is Option (a)
from the given frequency distribution table:
3.5 =
3.5 =
70 = 4x + 58
4x = 12
x = 3

Q.28: Which of the following numbers can be represented as non-terminating, repeating decimals
(a) 137/25
(b) 3/16
(c) 39/24
(d) 3/11

Correct Answer is Option (d)
Since, decimal expansion  of 3/11 = 0.27272727... which is a non - terminating repeating decimal.

Q.29: In the adjoining figure, the three lines AB, CD and EF all pass through the point O. If ∠EOB = 90° and x:y = 2:1 then ∠BOD and ∠COE:-

(a) 60°, 60°
(b) 30°, 60°
(c) 80°, 20°
(d) 45°, 45°

Correct Answer is Option (b)
x + y + 90° = 180° (Linear Pair)
2a + a + 90° = 180° (Since, x:y = 2:1)
a =  30°
x = 2a = ∠COE = 60° (Vertically opposite angles)
y = ∠BOD = 30° (Vertically opposite angles)

Q.30: The range of the data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is
(a) 18
(b) 26
(c) 10
(d) 15

Correct Answer is Option (b)
Range = 32 - 6 = 26

Q.31: The area of a triangle is 150 cm² and its sides are in the ratio 3 : 4 : 5. What is its perimeter?
(a) 60 cm
(b) 70 cm
(c) 40 cm
(d) 50 cm

Correct Answer is Option (a)
60 cm

Q.32: The positive square root of 7 + √48 , is
(a) 3 + √2
(b) 7 + √3
(c) 2 + √3
(d) 7 + 2√3

Correct Answer is Option (c)

=
=
=
=
=
=

Q.33: In the adjoining figure, AC = BD. If ∠CAB = ∠DBA, then ∠ACB is equal to

(a) ∠ABC
(b) ∠BDA
(c) ∠ABD

(d) ∠BAD

Correct Answer is Option (b)

In Triangle CAB and traingle DBA,
AC = BD and ∠CAB = ∠DBA (Given)
AB (Common)
Therefore, Triangle CAB and traingle DBA are congruent by SAS criteria
Therefore, ∠ACB = ∠BDA (by CPCT)

Q.34: A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class interval is constructed for the following data :
268, 220, 368, 258, 242, 310, 272, 342, 310, 290, 300, 320, 319, 304, 402, 318, 406, 292, 354, 278, 210, 240, 330, 316, 406, 215, 258, 236. The frequency of the class 310 - 330 is:
(a) 4
(b) 7
(c) 5
(d) 6

Correct Answer is Option (d)

The class interval is 250 - 270, 270 not included.
means that the class is continuous.
Also, the data can be tabulated as follows:

Thus, frequency of the class 310 - 330 is 6 as can be seen from the table.

Q.35: The difference between two complementary angles is 40^o.The angles are
(a) 70°, 110°
(b) 65°, 25°
(c) 65°, 35°
(d) 70°, 30°

Correct Answer is Option (b)
We know that the sum of two complementary angles is 90°
Let the two angles be x and y
x + y = 90° (1)
We also know that the difference of the angles is 40°
Therefore  x - y = 40° (2)
Combining (1) and (2)
We have
x + y = 90°
x - y = 40°
Solving as simultaneous equations we get
2x = 130°
Hence x = 65°
Substituting this value of x in either one of the equations (1) or (2)
We get y = 25°

Q.36: The graph of a linear equation  cuts the y-axis at the point
(a) (0 , 32)
(b) (-32 , 0)
(c) (0 , -32)
(d) (32 , 0)

Correct Answer is Option (a)
when the graph cut at y axis in that case the value of x- coordinate is 0


y = 32
so the co-ordinates are (32,0)

Q.37: D is a point on the side BC of a ΔABC such that AD bisects ∠BAC then:
(a) BD = CD
(b) BA >BD
(c) CD > CA
(d) BD > BA

Correct Answer is Option (b)

Since, ∠BAC is bisected by AD, then ∠BAD is  less than ∠ABC  ,hence the side opposite ∠ABC, i.e. BA  is greater than the side opposite to ∠BAD  i.e.BD

Q.38: If a = -2, b = -1, then a^b - b^a is equal to
(a) -1
(b) 0.5
(c) -2
(d) -1.5

Correct Answer is Option (d)
a^b - b^a
(-2)^-1 - (-1)^-2
=
=
= -3/2
= -1.5

Q.39: The minimum value of a data is 82 and range is 38, then the maximum value is
(a) 76
(b) 120
(c) 82
(d) 60

Correct Answer is Option (b)

The difference between the maximum and minimum value of the observation is called a range.
Let the maximum value be x.
So,
x - 82 = 38
x = 82 + 38
x = 120

Q.40: The empirical relation between mean, mode and median is:
(a) Mode = 3 Mean - 2 Median
(b) Mode = 3 Median + 2 Mean
(c) Mode = 3 Median - 2 Mean
(d) Mode = 2 Median - 3 Mean

Correct Answer is Option (c)

For frequency distribution: mean, mode & median connected by the relation
mean - mode = 3(mean - median)
Thus,

mode = 3 median - 2 mean

Question No. 41 to 45 are based on the given text. Read the text carefully and answer the questions:
Maths teacher draws a straight line AB shown on the blackboard as per the following figure.

i. Now he told Raju to draw another line CD as in the figure
ii. The teacher told Ajay to mark AOD  as 2z
iii. Suraj was told to mark AOC as 4y
iv. Clive Made and angle COE = 60°
v. Peter marked BOE and BOD as y and x respectively

Q.41: What is the value of x?
(a) 100°
(b) 120°
(c) 96°
(d) 48°

Correct Answer is Option (c)
96°

Q.42: What is the value of y?
(a) 96°
(b) 48°
(c) 100°
(d) 24°

Correct Answer is Option (d)
24°

Q.43: What is the value of z?
(a) 42°
(b) 120°
(c) 96°

(d) 48°

Correct Answer is Option (a)
42°

Q.44: What should be the value of x + 2z?
(a) 148°
(b) 360°
(c) 180°
(d) 120°

Correct Answer is Option (c)
180°

Q.45: What is the relation between y and z?
(a) 4y + 2z = 120°
(b) 2y + z = 90°
(c) 2y + z = 180°
(d) y = 2z

Correct Answer is Option (b)
2y + z = 90°

Question No. 46 to 50 are based on the given text. Read the text carefully and answer the questions:
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop student's knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one-to-one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in 2015, the following distribution of ages (in years) of primary school teachers in a district was collected to evaluate the teacher on the above-mentioned criterion.

Q.46: Write the lower limit of the first-class interval.
(a) 17.5
(b) 15
(c) 20
(d) 5

Correct Answer is Option (b)
15

Q.47: Determine the class limits of the fourth class interval.
(a) 25 - 30
(b) 30 - 35
(c) 45 - 50
(d) 40 - 45

Correct Answer is Option (b)
30 - 35

Q.48: Find the class mark of class 45 – 50.
(a) 45.5
(b) 54.5
(c) 55.5
(d) 47.5

Correct Answer is Option (d)
47.5

Q.49: Determine the class size.
(a) 5
(b) 5.5
(c) 6
(d) 4

Correct Answer is Option (a)
5

Q.50: Facts or figures collected with a definite purpose are called ________.
(a) Statistics
(b) Data
(c) Sample
(d) Information

Correct Answer is Option (b)
Data