- ·- - - - - - - - KOcnt- 682019

Toe H PUBLIC Sc• aoOL' VYTT

•
ILA
'
- July;2023 ,, •·
y~

1 Per1odic--Examination
st

· Time : 1 Hr.· )
. Subject: Mathematics Max. Marks : 20- -
IX
\ Standard :--
"- -- -- -- -_ :_ ________ ~----~~

General Instructions - A, B, C, D
questions divided into 4 sections
► The question paper consists of 17
ns of 0.5 mark each.
► Section A comprises of 1Oquestio
ns of 1 ½ marks each
► Section B comprises of 3 questio
ns of 2 ½ marks each
► Section C comprises of 3 questio
n of 3 marks
► Section D comprises of 1 questio
► All questions are compulsory.

[10x½=5J
SECTION A
S
I. MULTIPLE CHOICE QUESTION

decimal
number if and only if its
I. A num ber is an irrational
representation is
g
b) Non terminating and repeatin
a) Non terminating g
d) Termin atin
c) Non terminating
and Non repe atin g
~
C:
• 2. JITf x ../f s is equal to :
CJ
i c).. .fis d) 10. ./fs
C
a) 6{ 5 b) S../ 6

)= 2x + 1 is
3. The zero of the polynomial P(x
-1
1 c)2- d) 1
a)- b) 2
2

tional number?
4. Which of the following is an irra

c) J7
a) ,ft b) v'i2
v'3
d)v 'BI

-¾
5. (625) is ....................... .
1 d) 25
b) 625 c)-
a) 125 125

II. MATCH THE FOLLOWING

6. A B
a) 7 1)
Rationalising factor of 3~ is I

7. The degree of the polynomial

b) v'2
3
P(x) = 3x + 6x + 5x - 7 is
4

2 c) 4
8. The coefficient of x in
2
x(-3 x + 4x + 2) is
Pg 1 of 2
9. (2x + 5) is a d) Quadratic Polynomial

10. The value of P(x) =3x2 - 4x at x =-1 is e) -3

f) Linear Polynomial

SECTION B (3 xl½ = 4½)

1 l. •. - p
Express 23.47 in the form - where p and q are integers and q -=I= o.
q

12. Simplify : (5 + {7) (2 + ~)

13. Check whether (x+ I) is a factor of P(x) = 3x3 - 2x 2 - x + 4.

SECTION C [3 X 21/2 =7½]

14. 350 +349 -924
99
Prove that
348 .+347 +923
=-
13

15. If P(x) = x 2 -4x + 3, then evaluate P(2) - P(-1) + P(1/2t).

16.
5+2'13
Find the value of a and b if
7+4v.:)
r;; =a - b"'3°.,

SECTIOND (3xl =3)

17. Factorise : P(x) =x3 - 6x 2 + I Ix - 6.

***************

,I
 GE1'ERAL INSTRUCTIONS:
► This Question Paper has 5 Sections A-E
► Section A has 20 MCQs carrying 1 mark each
► Section B has 5 questions carrying 02 marks each
► Section C has 6 questions carrying 03 marks each
► Section D has 4 questions carrying 05 marks each
► Section E has 3 case base integrated units of assessment (04 marks each) with subparts of
the values of 1, 1 and 2 marks each respectively
► All questions are compulsory, However, an internal choice in 2 Questions of 5 marks, 2
Questions of 3 marks and 2 questions of 2 marks has been provided. An internal choice has
been provided in the 2 marks questions of Section E

SECTION A
Section A consists of 20 questions of 1 mark each
S. NO. MARKS
1. ln between any l\\,'O rational numbers, there are: 1
a) Only one rational number b) Two rational numbers
c) lnfinite rational n.umbers d) No rational number
2. (x+ I) is a factor of the polynomial: 1
I
) "I
a) x -rx--x + I b) X J + X 2 + X + l
c)x~-Jx 1 +3.r 2 +.r+ I d) X 4 + X J + X 2 + l

3.
l Any solution of the linear equation 2 x + 0y + 9 = 0 in two variables is of
lhe fonn:
-9 -9
1

-9
a) <z• m) b) (-9. 0) c) (0,
2) d) (n,
2)
7. jThe abscissa of a point ~ the distance of the point from: 1

a) y - axis b) origin c) x - axis d) quadrant

-- 1
5. The things which coincide with one another are:

I
~
1
I a) Equal to one another
c) Double of same things
b) Unequal
d) Triple of same things

6. If two acute angles of a right triangle are e~ual, then each acute angle is 1
equal to:
a) 60° b) 30° c) 45° d) 90°

Two lines are said to be parallel if they have: 1

7.
a) One point in common b) Two points in common
c) No point io common d) None of these
- - 1n a continuous frequency distribution, class mark of a class is 85 and 1
8
lo~r:r Ji1n1t is 83, then its upper limit is:
b) 84 c) 83 d) 87
I :s) 86

IX I Pg 1 o17
 . . 16 13 cm2 then the side of the I
9. The area of an equilaternl tnangle 15 '
triangle is:
a) 16cm b) 8cm c) 4cm d) ...f3 cm
1
10. For a given data, the difference between the maximum and minimum
observation is known as its:
c) Class Mark d) Class Limit
a) Class b) Range
1
11. The Simplest fonn of 1.6 is:
s b) ! ) !! d) 1s
a) 3 4 C 9 13

12. In 6 ABC, AB= AC and LB = 50°, then LC is equal to:

a) 40° b) 50° c) 80° d) 180°
1
13. The base of a right triangle is 16cm and hypotenuse is 34cm. Its area will

- be:
a) 240cm
2
b) 180cm
2
c) 160cm
2 d) 150cm
2

l
14. In the given figure, the value of x is:
C
E
X
75°
_, I
,, .,

A 200 0 B
('
D

a) 85° b) 60° c) 55° d) 50°

15. Given the class intervals 0-10, 10, -20, 20-30... then 20 is considered in I
class:
a) 10-20 b) 20-30 c) I 0-30 d) 15-25
16. If two supplementary angles differ by 28°, then the angles are: 1
a) 100°, 80° b) 78°, 102° c) 76°, 104° d) 80°, 105°

17. On dividing 6-127 by 2-/3, we get: 1

a) 3v6 b) 6 c) 9 d) None of these

,, 18. The number of lines that can pass through a given point is:
a)Two
c) Infinitely many
b) Only one
d) None
1

Direction: In the question number 19 and 20, a statement of assertion (A)

is followed by a statement of Reason (R).
Choose the correct option:
19. Assertion (A) : In quadrilateral ABCD, AC=AD and AB bisects LA then 1
b..ABC~6 ABD.
C

D
 Reason (R): By AAS congruence rule.
(a) Both assertion (A) and reason (R) are true and reas .
explanation of assertion (A) on (R) 1s the correct

(b) Both assertion (A) and reason (R) are true and reason (R) is n t th
correct explanation of assertion (A) •0 e
(c) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

20. Assel'tion (A) : The value of x in the given figure is Is0.
I

0 B
Reason (R) : The sum of angles on the·same side of a line is 180°.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A)

(b) Both assertion (A) and reason (R) are true and reason (R) is not the
correct explanation of assertion (A)

( c) Assertion (A) is true but reason (R) is false.

( d) Assertion {A) is false but reason (R) is true.

SECTION B
Section B consists of 5 questions of 2 marks each
21. Find the area of a triangle whose sides are 8cm and 11 cm and the
2
perimeter is 32cm?
22. Find the value of the polynomial 3x 3 - 4x 2 + ?x - 5, when x = 3 and also
2
whenx =-3?
OR
If x = - i is a zero of the polynomial P(x) = 8x 3 - k, then find the value of
2
k.
23. In the given figure, LACD = 120° and LAPB = 100°, find x and y. 2
A

I
8 P' C D
l 0_._ _ _ _--.1..-_ _2_ __..
2-t:·_~I_:F~in::d~an~y_:fi~our~d~i~f£~er~e:nt~s:o:::lu::.:t1::·o::n:_s.:.of=-t=h:.:. e. :. .e2.qu:.:. :a:. .:.:ti. .:.o_n_2_x_5.:....y__
20
25. In the given figure, if LA = 40° and LB = 70°, then find LBCE. 2
A

D
B C

OR
In the given figure, for what value of x, will the lines l and m be parallel to 2
each other?

(3x+13)0

SECTIONC f
Section C consists of 6 questions of 3 marks each
26. Find the value of a and b if, 3
7 + 3{5 7- 3/5 _ r;:S b
- ----- -a+v:,
3+ -./5 3-/s
27. a. Simplify: (x + 2)3 + (x - 2)3 3
b. Factorise : 3x 2 - 12x + 9
28. The sides of a triangular field are 41m, 40m and 9m. Find the number of 3
rose beds that can be prepared in the field, if each rose bed, on an average
needs 900 cm2 space. •
OR
The sides of a triangular park are of the ratio 3:5:7 and the perimeter is
300m. Find its area and the length of the perpendicular drawn to the
biggest side.
29. Factorise: x 3 + 2x 2 - 13x + 10 3
3 3 3
30. If a + b + c = 6, abc = 6 and ab + be + ca = 11 find the value of a + b + c 3
OR
Use suitable identify and
a. Evaluate (103)3
3 3
b. Factorise: 343a - 729b
31. ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. 3
Prove that AB = AD and CB = CD.
D C

IV / O,.. ,1 ,..f 7
 SECTIOND
Section D consists of 4 questions of S marks each
32. Prove that angles opposite to equal sides of an isosceles triangle are equal. 5
Al~o, show that in an isosceles triangle ABC with AB = AC, D and E are
pomts on BC such that BE = CD. Show that AD = AE.
A

B • D E C
OR
In the given figure, OA = OB and OP= OQ. Prove that
(i) PX=QX
(ii) AX=BX
8

0 p A
33. , a) Without actually calculating the cubes, find the value of 5
(¾)3 + (¾)3 _(:2)3
\I 3 1 9X 2 X
b) Factorise: 27x -27y3 -
- - -y-+ y2
;

34. Plot the following points and write the name of the· figure thus obtained: 5
P(-3, 2), Q(-7, -3), R(6, -3), S(2, 2). Also, find its area?
OR
Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot these points
and find. the coordinates of the fourth vertex. Also, find its area.
35. Consid,.,the marks, out of 100, obtained by 51 students of a class in a test, 5
give~n table below. Draw a histogram and frequency polygon for the
giy,,en data.
,r
1; Marks Number of Students
0-10 5 .
10-20 10 ' .
20- 30 4
30-40 6
40-50 7
50-60 3
60-70 2
70-80 2
80-90 3
I 90- 100 9
I Total 51
I
IX/ Pg 5 of 7
 SECTIONE
36. THE CLASS - ROOM BUDDIES
Manik and Dhruv are bench - mates in the class. In the mathematics class,
Manik was finding that it was difficult to simplify ("5~ \12)' His bench -
mate Dhruv gave him a clue to rationalize the denominator by taking the
conjugate of ( vs' - ..fi). Manik simplified the expression and thanked
Dhruv for the help. Dhruv also gave him the approximate value of -Is' =
2.236 and -Jz = 1.414 to find the approximate value of the expression.

...._, ,

Based on the above information answer the following questions:

a) What is the conjugate of ( vs' - ft)?
b) Where should we multiply the conjugate of VS - ../2. to rationalize? 1
c) "
What is the simplified form of the expression that Manilc found out? 2
OR
d) What is the approximate value of the expression did Manik find after
putting the values ../2. = 1.414 and {s' = 2.236?
37. ANGLE INFORMATION
Leaming by doing' has great impact in teaching of Maths. Students also
enjoy mathematics by activity method. Mr. Paul, a Mathematics teacher
has explained the topic of Lines and Angles' by taking a very thin steel
wire. He used steel wire and made some shapes at some specific angles
and'Tuown to students and asked questions.
/

8
F. D A
;1' •
I '
I .•••'
I

/ I
I

•''
'
~.I ''
•••'
I

E D B
Fig(i) Fig(ii)

Based on the above infonnation.ailswer the following questions:

a) What is the measure of Ll on figure (i) where AB 11 EF 11 DC? 1

6) ·what is measure of LBOD in figure (ii)? 1

c) What is the measure of Lx and L2 in figure (i) where AB II EF II DC? 2

·,
OR

d) What is the ·measure of Ly and'·f~-flex LAOC in figure· (ii)1 ; _.;-,-~... •

-~ ' f "'
 38. THE RIDERS CLUB
The Biker's Club of a city organised a trip to a destination which is famous
for its forts and delicious cuisine. A total of 24 Riders participated in the
trip. The Captain of the team wanted to gather some data of the journey for
analysis for future trips. Every Rider note down the distance travelled by
them in the first 2 Hrs. and reported the same to the Captain. After getting
the raw data, captain converted them into the exclusive frequency
distribution as shown below:

Distance Covered (in km) Frequency

60-75 2
75-90 4
90- 105 6
105 - 120 2
120- 135 6
135 - 150 4

Based on the above information and the given data and table, answer the
following questions:
a. How many riders covered less than 90km? i/ 1
b. What are the suitable graphical representation for the above data? / 1
C. What percentage of riders travelled I 05km or more but less than l 50km? 2

OR
d. How many riders travelled 135km or more but less than 150km and how
many travelled 90km or less but more than 60km.

***************
 GENERAL INSTRUCTIONS:
....
❖ This Question Paper has 5 Sections A, B, C, D and E
❖ Section A has 20 Multiple Choice Questions (MC(?~ carrying 1 mark each.
<· Section
~· ❖ Section
B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
♦ Section D has 4 Long Answer (LA) type questions carrying 5 Marks each
❖ Section E has 3 Case Based integrated units of assessment (4 marks each) with
sub-parts of the values of 1, 1 and 2 marks each respectively.
~(t
<• All questions are compulsory. However, an internal choice in 2 Qs of 5 marks,
~
2 Qs of 3 marks and 2 Qs of 2 Marks has been provided. ·An internaJ choice has
' been provided· in the 2 marks questions of Section E.
Draw neat figures wherever required.

SECTION A
S.NO. Section A consists of 20 questions of 1 mark each MARKS

If equals are subtracted from equals, the r~mainders are 1

m
....
go (a) equal b) not equal
tll
0••♦.
c) proportional d) none of these
so
i
) :
•f!'

2. The graph of y = 6 is a line 1

- f
.-1!
;;:c
~ a) Parallel to x-axis at a distance 6 units from the origin
~ b) Making an intercept 6 on the x-axis
"i-:
~
c) Making an intercept 6 on both the axes
-
ci:

d) Parallel to y-axis at a distance 6 units from the origin

I
1
Signs of the abscissa and ordinate of a point in the second quadrant are
respectively
b) (+, -) c) (+, +) d)(-,-)
I/
a) (-, +)
I 1
/

- V If a point C lies between A and B, then

b)AC+BC=AB
a) AB+BC=AC
c) AB+AC-BC d) AC=2AB
1

1/ If (2,0) is a solution of the linear equation 2x + 3y = k, then the value of

k is
c) 4 d) 6
a) 2
y The things which are double of the same things are
a) equal b) halves of the same thing
1

c) unequal d) double of the same thing

1
In the figure, POQ, is a line. The value ofx is

0 ,-.
,.~,)
,
~ 0 0

a) 25° b) 30° c) 20° d) 35°

8. If a diagonal AC and BD of a quadrilateral ABCD bisect each other a! i 1

y
then ABCD is a
a) Parallelogram b) Rhombus
c) Rectangle d) Triangle
1 2
9. If 10x-4x -3, then the value of p(O) + p(l) is 1
'/ a) -3 b) 0 c) 3 d) 1

I 0. / The cost of a notebook is twice the cost of a pen. The equation to 1

•/ represent this statement is
a) 2x = 3y b) x = 3y c) none of these d) x-2y = 0

11 / In 6ABC, E is the mid-point of median AD such that BE producted 1

meets AC at F. If AC = 10.5cm, then AF=
- a) 2.5. cm b). 5 cm c) 3 cm d) 3.5 cm

l/i2 "D and E are the mid-points of the sides AB and AC of 6ABC and O is 1
\ any point on the side BC, 0 is joined to A. If P and Qare the mid-points
of OB and OC, Then DEQP is

a) A Triangle b) A Rectangle

c) ARhombus d) A Parallelogram

In a figure, 0 is the centre of the circle with AB and diameter. If LAOC 1

13
✓ = 40°, the value ofx is equal to

J'\

}t -
\ C

a) 80° b) 5if c) 70° d) 60°

1( The value of J.9999 ........... in the fonn;, where 'p' and 'q' are
1

integers and q -:f. 0, 1s .

a)
1999
b) ~ c) 2
1000 10

(Pg. 2/7 of Std. IX)

 ...
• "'.._.._ , ..,,..,,r•- - .,. • .. -,.- ••--..,
- .
15 / The radius of a sphere is 2r, then its volume is 1

V a) -
4
m-3 b) 41rr3 c)
enr3
3
32
d)-1rr3
3 3

A rational number between [2 andJ'3 is 1

V a) ..fi.+ ../3
2
b) 1.5 c
) -
2
..fi. .../3
d) 1.8

17 1o., qraw a histogram to represent the following frequency distribtuion: 1

V Class interval 5-10 10-15 15-25 25-45 45-75

Frequency 6 12 10 8 15

The adjusted frequency for the class 25 - 45 is

a) 6 b) 5 c) 2 d) 3

18 2
The area of an equilateral triangJe is 16 ,tim . Its perimeter (in metres) is
1
,1

a) 12 b) 48 c) 24 d) 306
/"
19 / Assertion (A) : The sides of a triangle are 3cm, 4cm and 5cm. Its area 1
2
\r is 6cm •
Reason (R) : If 2s = (a + b + c), where a, b, c, are the sides of a triangle,
then area= J(s - a)(s - b)(s - c).
a) Both A and Rare true and R is the correct explQ'Y\.Obon DF A
b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

20 Assertion (A): The equation of 2x + 5 = 0 and 3x + y = 5 both have 1

✓ degree 1.
Reason (R) : The degree
.. ... , ...
of
..
a linear equation in two varibles is 2.
~ ,:

a) Both A and R ~e true and R is the correct eJ..Plo..-na.non oF A

b) Both A and R are true but R is not the correct explanation of A
c) A is true but R is false
d) A is false but R is true

SECTION B

Section B consists of 5 questions of 2 marks each

2
21 / There ia a slide in a park. One of its side walls has be,~n painted in some
'/ : colour with a message, "KEEP THE PARK CLEAN . If the side of the
wall are 15m, l l m and 6m, find the area painted in colour.
(Use '12. = 1.4) \\
\
,.f KEEP \01
._, THE PARK\~
CLEAN \

15m
L-------~
_ _ _ _ _ _-----1-------
~~
,'d]
L___ _L_ _ _ _ _ _ _~.:,:__
.-----,..-------------121
22/ Find angles marked as x and y in given figure where O is the centre of
\ \

V the circle

23 2
A hemispherical bowl made of brass has inner diameter l 0.5cm. Find
2
the cost of tit\-l)latihg •it oh the inside at the rate of Rs. 32 per 100 cm

ABCD is a rhombus. Find the values of x and y. Also, find all the 2
angles of rhombus.
0..,-------..c

OR

If angles A, B, C and D of quadrilateral ABCD, taken in order, are in

the ratio 3 : 7 :•6 : 4, find the angles. What type of a quadrilateral is
ABCD?

25/ Fi~d the solution of the linear equation x + 2y = 8 which represents a 2

·{ pomton

1. The x-axis
11. The y-axis

[OR]

Find whether (4, 0) is the solution of the equation x - 2y = 4 or not?

Give two more solutions for the given equation.

SECTIONC

Section C consists of 6 questions of 3 marks each

26 i) .
Fmd
. (2)x (3)
x,- 1f -3 ix ·.-81
- =- 3
• - 2 16

1 1 1

ii) Simplify gi x16 3 x(25) 1.

(32) 3

21 Factorise 3

i) 12x2 - 1Ox + 2

ii) 4x2 + 9y2 + z2 + 12xy + 4xz + 6yz

 28
Plot the points A(-5 .
1 , 3), B(3, 3), C(3, 0) and D(-5, 0) m the cartesian
~e. ~am.e the figure ABCD. Find the ratio of ~eas of two parts of 3
CD in the I quadrant and II quadrant.

OR
\, ~ee vertices of square PQRS are P(-4, 0), Q(l, 0) R(l, -5). Plot the
points. Also find the coordinates of vertex S and area of PQRS.
29
\ -In the adjoining figure, sides AB and DC of a cyclic quadrilateral
3
ABCD are produced to meet at E. Sides AD and BC are
produced to meet at F. If LADC = 80° and LBEC = 50°, fincl
LBAD and LCFD. ~'

_,,---D /~
I \'
80'
C
A ,.....__ I '\
• .....___ !i()•
B -~
E

~O P is the mid-point of the side CD of a parallelogram ABCD. A line

through C parallel to PA intersects AB at Q and DA produced at R. 3
Prove that DA=AR and CQ=QR.

[OR]

Show that the quadrilateral formed by joining the mid-points the sides
of a rhombus, taken in order, form a rectangle.

Find the area of a triangle whose perimeter is 180cm and two of its
3
sides are 80cm and 18cm. Also find the altitude of the triangle
corresponding to the longest side as the base.

SECTIOND

Section D consists of 4 Questions of 5 marks each

r

o/ i) Find the values of a and b if

. 7+3.,/s
7 3
7-3.,/s
.. .,fs - 7+ .Js
3
rr:
= a+ bv 5
5

ii) Find two irrational numbers between 3 and 5.

(OR}

i) If a= v'T+i and b =Ii-: , then find the value of a 2 +b 2 - 4ab

../2-1 '12+1

ii) Represent -J's on a number line

33 s
i) In the adjoining figure, in parallelogram ABCD, AP and DP
are bisectors of LA and LD respectively, find the measure of
LAPD D -------· ---·- ···- •••••, C
('' i
~ !
I
/·
A
L_ _ _ ------~!
■ (Pg.5/7 of Std. IXJ
 ii) In the adjoining figure, BM and DN are perpendiculars to AC
such that BM= DN. Prove that AC bisects BD.
o~-----~C

34 i) In the figure given below, AB II CD. Find the value ofx. s

\

ii) The diameter of the moon is approximately one-fourth of the

diameter of the earth. What fraction of the volume of the
earth is the volume of the moon?
OR
i) In the figure given below, AB II CD. Find the value ofx

lD
ii) Radius and slant height of a solid right circular cone are in
the ratio 3:5. If the curved surface area is 60,r cm2, then find
its volume.

he given frequency table show the rate at which the heart beats of an 5
athelete running on a tread mill at a constant speed:

Time (in seconds) 0-60 60- 120 120- 180 180-24 0 240-30 0

Heart Beat Rate 85 100 120 110 110

Draw a histo gram and a frequency polygon.

SECTIONE

Case study based questions are compulsory

Read the text carefully and answer the question:
Sanjay and his mother visited a mall. He observes that three shops are
situated at P,Q,R as shown in the figure from where they have to
purchase things according to their need. Distance between shop P and Q
is 8 m ,nd between shop P and R is 6m.
1,1
vJ ~d the Measure of LQPR jii) Find radi~t the circle
2
'iQIFind the Measure of LQSR. _ Find the area of ~PQR

t'""'-" '' • 7
' ,
.
j I! ~,,
,j

. , , -

/1\.
-.,.,
r ....
 Read the text carefully and answer the questions:
Once upon a time in Ghaziabad was a com cob seller. During
the
lockdown period in the year 2020, his business was almost lost.
So, he started selling com grains online through Amazon and Flipca
rt.
Just to understand how many grains he will have from one com
cob, he
started counting them.
Being a student of mathematics let's calculate it mathematically
. Let's
assume that one com cob (see Fig.) shaped somewhat like a cone,
has
the radius of its broadest end at 8 cm and length as 15 cm

i) Find the slant height of the cone cob?

ii) What is the curved surface area of a cob? 1
2
i w If each 1cm of the surface of the cob carries an average of 1
four g.rains, find how many grains yo_u would find 011 th~
entire cob Ca..pp-zr o ~ i ma. te. \~ ) 1
.,
• OR
J
,find
J
the volume of a cone cob? 2
Read the text carefully and answer the questions:
Haresh and Deep ~ere trying to prove a theorem. For this they did
the
following
A

Draw a triangle ABC

D and E are found as the mid points of AB and AC
DE was joined and DE was extended to F so DE= EF
FC was joined

I
/
W, .6AD E and .6EFC are congruent by which criteria?
1
(ii) Show that CF II AB
1
(iii) Show that CF = BD
OR 2
Show that DF = BC and OF II BC
 Toe H PUBLIC SCHOOL VYTTILA, Kochi - 682019

SECOND PERIODIC TEST -Augu st 2023

Subject : Mathematics Time: 1 Hr

Standard : IX Max. Marks: 20

Genera l Instructions:
s - A, B, C, D
• The question paper consists of 17 questions divided into 4 section
• Section A comprises l 0 questions of 0.5 marks each.
• Section B comprises 3 questions of 1.5 marks each.
• Section C comprises 3 questions of 2.5 marks each.
• Section D comprises I question of 3 marks
• All questions are compulsory.

SECTION A

Choose the correct answer:

(
1. If the coordinates of a point are ( -3, 4 ), then it lies in :

(a) I quadrant (b) II quadrant

(c) III quadrant (d) IV quadrant

2. Ordinate of all points on the X axis is: ,,,,, ,/

(a) -1 (b) 0 (c.) l (d) any number J'{
are : /
3. If the ratio between two complementary angles is 2 : 3 , the angles

(b) 120°, 240° (c) 36°, 54° (d) 30°, 60° /

(a) 144°, 216°
/
4. How many solutions does the equation 2x + Sy= 8 have? /

(a) one (b) two (c) no solutions (d) infinitely many soluti ons/

( 5.x 3 -y3 - (x-y) ( _ _ _ _ _ _ _~

2
(a) x 2 + xy + y
2 (b) x2+ xy - y
2
(c) x2 - xy + y
2 (d) x2 - xy - y

Fill in the blanks :

6. ( a - b + c )2 = -------------------------------
---- units
7., The pe'rpendicular distance of the point P ( 4,5) from Y axis is------
so formed is-------------- ;-~"'
8. If a ray stands on a line, then the sum of the two adjacent angles

9. If ( 2, O) is a solution of the linear equation 2x + 3y = k, then the value

ofk is------------ ✓_,,.,--
Io. If a transversal intersects two parallel lines, then each pair of corresp
onding angles ✓
lS -----------
(10 X Q.5 = 5)
 •

SECTION B
\
11. \Vithout actually calculating the cubes evaluate :
(-24)3+ 11 3 + 13 3

12. In the given figure, find the value of x .

B X + 15
0
13.Write any two solutions of the equation 2x - y =
7

(3 X }.5 = 4.5)

SECT ION C
14. Let the cost of a book and a pen be x and y respec
tively. A -girl pays Rs. 190 for 3
books and 2 pens. Write the given data in the form of
a linear equation in two variables.
Also find:

\ (i) the cost of a book if a pen costs Rs. 20

(ii) the cost of a pen if a book costs Rs. 60.

15. In the figure AB I CE, CD I EF_ Find the value of

x.
/ __/
B E ;--+
----------. F

L:

D
-•
~
.\
A . ,.
-✓()v "- ....
......
........

16. Using a suitable ide:tity : ) . ./ " - r v

Jr'
(i) Expand : (
3X - Y 3
a2 ·bi ab a
(ii) Factorise : - + - + l- - b+
16 4 4 2

SECTION D

,.,,.,,,,.-

. . .
!'
17. Plot the points A ( -3, 2 ) , B ( -S, -4 C ( -2, -4 , D r h a t figure do you get
)
on J01t11ng the po1·nts in order ? Also find its are~. ,
• J , . ~
(l x 3 == 3)
I , I
., I

f I
J -:
~1 GENERAL INSTRUCTIONS:
Toe Question Paper consists of 17 Questions divided into 4 Secti
ons : A,B, c, n
❖ Section A consists of 12 questions of 0.5 mark each .
❖ Section B consists of 2 questions of 2 marks each.
❖ Section C consists of 2 questions of 3 marks each.
❖ Section D consists of 1 question of 4 mark each
.
❖ All Questions are compulsory

I
SECTION A
S.NO. Choose the Correct Answer form the Options
MARKS
/1. Which of the following is an irrational number?
{1 ~~1' 2.~~ .5
(a) 3.14 b) 3.141414 ......
✓) f--l.~ h ~ c) 3.144444 ....... . d), 3.14114111411114 ......
/2. A rational numb er between ff and ff is : .5
a) ,/2+ ./3 b) 5 ./3 c) l.5
,
~ 2 2 d) 1.8
31- J.
- ~- Simplified ~alue of ( )4
16
-1
X ~ IS : .5
a) 16 b) 4• c) 1 d) 0
~

4. lfx = 2 + ./3 then.!. is equal to: .5

J a) 2 + -J3
1
b)
X

i c) !. +'13 dl 2 - "\13
2-\13 2

l. ,..rr_
-->
\
'l\~ Js. u
e of the polynomial 4x4 + Ox3 + Qx5 + 5x + 7 is : .5
I
~
I
"- } ~ b)J5 c) 3 d) 7 -
!
:c
~
1-~
---- I 6.
~

(5 + ..Ja) + (3 - .fl.) - ('12. - 6) when simplified is

.5
\ a) Positive and irrational b) Negative and irrational
' c) Positive and rational d) Negative and rational . . _ '
If ( x - 2) is a factor of 5x 2
/7. - kx- 18 the value ofk is .5
a) -1 b} 1 c) 0 d) 5
Jg. Zero of the polynomial p(x) =ex + dis: .5
d -d
a) -d b) -c c) - d) - ,
C C

/. 2
If (23) = 4x, then.__value of xis : L "',..

~J
'l__ . '- .5

a) fr>
~ - 2-
b) 3 , ) c) 2 d) 1

(Pg. 1/2 of Std. IX)

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