Class 9 Question Paper 2022-23 Maths (Half Yearly)

HALF YEARLY EXAMINATION

Question Paper
2022-23

NCERT BASED SYLLABUS
FOR CBSE AND STATE BOARD
FOLLOWING NCERT

QUESTION PAPER
PT-
PT-2/HALF YEARLY EXAMINATION, 2022-
2022-23
MATHEMATICS
Time - 7:15 AM to 10:20 AM Class - IX M.M. : 80
Date – 09.09.2022 (Friday)
Name of the student _________________________________________________ Section _____

General Instructions –
 The question paper consists of 26 questions divided into
4 sections A, B, C& D
 All questions are compulsory.
 Section A comprises of 11 questions of 2 marks each.
Internal choice has been provided in two questions. It
contains two case study-based questions of 5 marks each.
 Section B comprises of 7 questions of 3 marks each.
Internal choice has been provided in two questions.
 Section C comprises of 3 questions of 4 marks each.
Internal choice has been provided in two questions.
 Section D comprises of 3 questions of 5 marks each.
Internal choice has been provided in two questions.

SECTION - A (2x11=22 marks)


Q1 A rational number between and is:
 


 
(a) (b) (c) (d)

 

 


Q2 √√
is equal to:
√ √


(a) 2 (b) 4 (c) 8 (d) 20
Q3 Points (1, -2), (1, -3), (-4, 5), (0, 0), (3, -3)
(a) Lie in III quadrant (b) Lie in II quadrant
(c) Lie in IV quadrant (d) Do not lie in the same quadrant
OR
The co-ordinates of the points X, Y, Z and W from the figure.

(a) X(4,3), Y(4,3), Z( 2,0), W(-2,4) (b) X(4,0), Y(4,3), W(-2,4), Z(-2,0)
(c) X (0,0), Y(4,4), Z( 3,8), W ( 0 4 ) (d) X(3,3), Y(4,3), Z( 1,0), W(-2,4)
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Q4 If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the
perpendicular lies on the negative direction of x-axis, then the point P has:
(a) y-coordinate = 7 or –7 only (b) y-coordinate = 7 only
(c) y-coordinate = –7 only (d) x-coordinate = –7 only
Q5 Point (3, 4) lies on the graph of the equation 3y = kx + 7. The value of k is:
(a) 4/3 (b) 5/3 (c) 3 (d) 7/3
OR
The graph of linear equation x+2y = 2, cuts the y-axis at:
(a) (2,0) (b) (0,2) (c) (0,1) (d) (1,1)
4
Q6 The supplement of of right angle is equal to:
3
(a) 60° (b) 100° (c) 110° (d) 70°
Q7 If the perimeter of an equilateral triangle is 60 cm, then what is its area?
(a) 200√2 cm2 (b) 100√2 cm2 (c) 100√3 cm2 (d) 200√3 cm2
Q8 The sides of a triangle are in the ratio of 3 : 4: 5. If its perimeter is 36 cm, then what is its
area?
(a) 32 cm2 (b) 54 cm2 (c) 67 cm2 (d) 72 cm2
Q9 The sides of a triangle are 3 cm, 5 cm and 6 cm. What is its area?
(a) 2√3cm2 (b) 2√14 cm2 (c) 5√12 cm2 (d) 2√5 cm2
Q10 An isosceles right triangle has an area of 8 cm². The length of its hypotenuse is:
(a) √32 cm (b) √16 cm (c) √48 cm (d) √24 cm
Q11 The value of y at x = −1 in the equation 5y = 2 is
 
(a) (b) (c) 0 (d) 10
 

Q12 CASE– STUDY BASED QUESTION-1 (1× )
Two classmates, Salma and Anil simplified two different expressions during the revision
hour and explained to each other their simplifications.
√
Salma explains simplification of by rationalising the denominator and Anil
√√
explains simplification of √2 + √3(√2 − √3) by using the identity (a+b) (a–b).
Based on the above information, answer the following questions.
(i) What is the conjugate of √5 + √3 ?

√
(a) √5 + √3 (b) √5 − √3 (c) √5 × √3 (d)
√

√
(ii) By rationalising the denominator of Salma got the answer:
√√

√ √(√) √(√)
(a) (b) (c) √5 − √3 (d)
√√  

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(iii) Anil applied …………………….. identity to solve √2 + √3 √2 − √3
(a) ( + )( −  ) (b) ( +  )( + ) (c) ( − )( −  ) (d) ( +  )( + )
(iv) √2 + √3 √2 − √3 is equal to:
(a) −1 (b) 3 (c) 5 (d) −5
(v) Addition of √2 + √3 and √2 − √3 is equal to:
(a) a rational number (b) an Irrational number (c) an Integer (d) a whole number
Q13 CASE-STUDY BASED QUESTON-2 (1× )
There is a slide in a park. One of its side walls has been painted in some colour with a
message “KEEP THE PARK GREEN AND CLEAN”. The sides of the wall are 15 m, 11 m and
6 m.

Based on the above information, answer the following questions:
(i) The semi perimeter of the triangle is.
(a) 30 m (b) 16 m (c) 32 m (d) 15 m
(ii) If  ,  ,  are the lengths of the three sides of a triangle then the formula to find
the perimeter of the triangle is:
!"
(a) (b)  +  +  (c) 3 (d) 2( +  + )


(iii) Area of the triangle is:

(a) 15 m2 (b) 30 m2 (c) 20√2 m2 (d) 20√3 m2
(iv) Formula to find area of the sidewall is:

(a) #(# − )(# − )(# − ) (b) #(# + )(# + )(# + )

(c) #(# + )(# − )(# − ) (d) #(# + )(# − )(# + )
(v) Perimeter of the triangle is:
(a) 35 m (b) 16 m (c) 32 m (d) 15m

Section - B (3 x7=21 marks)
%
Q14 Find three different irrational numbers between the rational numbers $$ and $$.
(
Q15 Express 2.4178' in the form of ) where p and q are integers and q≠ 0

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Q16 Find the value of k, if x = 2, y = 1 is a solution of the equation 5x + 4y = k.
Q17 If an angle is half of its complementary angle, then find its degree measure.
OR
An angle is 14° more than its complement. What is its measure?
Q18 In the given figure, OD bisects ‘ -./ , OE bisects ‘ 0./ and OD ⊥ OE. Show that
points A, O and B are collinear.

Q19 Write any three Euclid’s Axioms.
OR
Write any three Euclid’s Postulates.
Q20 If a point C lies between two points A and B such that AC = BC, then prove that AC =
AB,

explain by drawing the figure.

Section - C (4x3=12 marks)
Q21 Find the value of  and b by rationalising the denominator of the following:
3 2
+ = √5 + √3
4√5 − √3 4√5 + √3
Q22 If (5)6 × (3)6 = 225, then find the value of .
OR
Show that : ( ! ) ! ( !" )!" ( " )" = 1
Q23 In the given figure, triangle AOB with coordinates of A and O as
(4,0) and (0,0) , AB=5 units , find the coordinates of B. Also, find
the area of ∆ AOB.

OR
In the given figure, ∆ ABC is an equilateral triangle with coordinates of B and C as
B (1,0) and C (5,0). Find the coordinates of vertex A. Also, find the area of the triangle
ABC.

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Section (5x3=15 marks)
Section-D
Q24 The force exerted to pull a cart is directly proportional to the acceleration produced in
the body. Express the statement as a linear equation in two variables by taking the
constant mass equal to 6 kg. Write the equation in standard form and also write the
values of a , b and c.
OR
If the work done by a body on application of a constant force is directly proportional to
the distance travelled by the body, express this in the form of an equation in two
variables by taking the constant force as 3 units. Also write the equation in stand
standard
form and write the values of a, b and c.
Q25 In the given figure, POQ is a line. Ray OR is perpendicular to line PQ.. OS is another ray
1
lying between rays OP and OR. Prove that ∠ ROS = (∠QOS – ∠POS)
2

OR
It is given that ∠XYZ
XYZ = 64° and XY is produced to point P. Draw a figure from the given
information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.
Q26 In the given figure, lines XY and MN intersect at O. If ∠POY
POY = 90°, and a : b = 2 : 3 , then
find c.

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