KENDRIYA VIDYALAYA SANGATHAN, KOLKATA
SESSION ENDING EXAMINATION 2022-23
CLASS IX
MATHEMATICS
FOR PRACTICE
TIME: 3 HRS M.M. 80
General Instructions: -
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment (04 marks each) with subparts of the
values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks
and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks
questions of Section E
8. Draw neat figures wherever required. Take π =22/7 wherever required if not stated.
SECTION A
Section A consists of 20 questions of 1 mark each.
SL NO. MARKS
1. An irrational number between 2/5 and 3/5 is 1
(a) 7.2 (b) 0.252525… (c) 0.720304….. (d) 1.020304
2. The value of 322/5 is 1
(a) 4 (b) 6 (c) 8 (d) 16
3. 3 2
Find the value of k, if x – 1 is a factor of 4x + 3x – 4x + k. 1
(a) -5 (b) 5 (c) -3 (d) 3
4. The zero of the polynomial p(x) = 3x - 15 is 1
(a) -5/4 (b) 5/2 (c) 5 (d) – 5
5. If the point (2,-3) lies on the graph of 2y = 5 - ax then the value of a is 1
(a) 2/5 (b) -11/2 (c) 3/5 (d) 11/2
6. What value of x will make angle AOB a right angle ? 1
(a) 18.5 o (b) 40.5 o (c) 20.5 o (d) 27.5 o
7. Supplement of an angle is one fourth of itself. The measure of the angle is 1
(a) 18 o (b) 36 o (c) 144 o (d) 72 o
8. In a Δ ABC , AB=AC and angle B = 500 then measure of angle C will be 1
(a) 50o (b) 40o (c) 80o (d) 120o
9. In the given figure, if AOB is a diameter of the circle and AC = BC, then ∠CAB is 1
equal to
(a) 30o (b) 60o (c) 90o (d) 45o
10. o
ABCD is a rhombus such that ACB = 40 , then ∠ADB is 1
(a) 40o (b) 45o (c) 50o (d) 60o.
11. In figure if ∠ ABC = 69°, ∠ ACB = 31°, then ∠ BDC will be 1
a) 30o (b) 80o (c) 50o (d) 100o.
12. The area of an equilateral triangle with side 6√3 cm is 1
(a) 27 cm2 (b) 27√3 cm2 (c) 18√3 cm2 (d) 54√3 cm2.
13. The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is 1
(a) 12√5 cm2 (b) 12√3 cm2 (c) 24√5 cm2 (d) 63 cm2.
14. If the slant height of a right circular cone is 10cm and its curved surface area is 220 1
cm2, then the diameter of its base is
(a) 14 cm (b) 8 cm (c) 12 cm (d) 16 cm
15. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being 1
pumped into it. Then the ratio of surface areas of the balloon in the two cases S1 :
S2 will be
(a) 1:2 (b) 1:4 (c) 1:5 (d) 1:3
16. If the volume of the right circular cone of height 15cm is 80π cm3,then the 1
diameter of the base will be
(a) 10 cm (b) 8 cm (c) 9 cm (d) 27 cm
17. The class size of the class interval 115-145 is 1
(a) 45 (b) 35 (c) 30 (d) 20
18. 2
An isosceles right triangle has area 32 cm . The length of its equal side is 1
(a) 6cm (b) 4cm (c) 16cm (d) 8cm
19. Assertion (A):- The number 5.236256246266276…….……………….. is an 1
irrational number.
Reason(R):- An irrational number are non-repeating and terminating decimal.
a) Both Assertion (A) and reason (R) are true and reason (R) is correct explanation
for assertion (A).
b) Both Assertion (A) and reason (R) are true but reason(R) is not correct
explanation for Assertion (A).
c) Assertion (A) is true but reason (R) is false.
d) Assertion (A) is false but reason (R) is true.
20. Assertion (A):- In an isosceles triangle PQR , PM is the altitude. If QR = 10 cm, PQ = 1
PR = 13 cm, then QM = 5 cm.
Reason (R):- In an isosceles triangle, the altitude from the vertex bisects the base.
a) Both Assertion (A) and reason (R) are true and reason (R) is correct explanation
for assertion (A).
b) Both Assertion (A) and reason (R) are true but reason(R) is not correct
explanation for 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.
SL MARKS
NO.
21. ̅̅̅̅ in the form p/q, where p and q are integers and q ≠ 0
Express 2.015 2
1
22. If x = 3 + 2√2 , then find the value of x + 𝑥 . 2
23. ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show 2
that BD = CE.
OR
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule,
prove that the triangle ABC is isosceles.
24. In the given figure, two circles intersect at P and Q. 2
If A = 80o and ∠D=84o. Calculate ∠QBC and ∠BCP.
25. Expand (2x – 3y +z )2 by using suitable identity. 2
SECTION C
Section C consists of 6 questions of 3 marks each.
SL MARKS
NO.
26. Factorise:- 2x3 -3x2 -17x +30 3
OR
(a)Evaluate by using a suitable identity:- (102)3
(b) Factorise 27x3 – 8y3
27. How many metres of cloth, 5 m wide, will be required to make a conical tent, the 3
radius of whose base is 7 m and height is 24 m.
OR
The height of a cone is 15 cm. If its volume is 1570 cm3, find its slant height. (use
π=3.14).
28. Prove that the figure formed by joining the mid-point of the adjacent sides of a 3
quadrilateral is a parallelogram.
OR
Diagonal AC of a parallelogram ABCD bisects ∠ A . Show that ABCD is a rhombus.
29. 4+3√5
If a and b are rational numbers and 4−3√5 = a + b√5 , find the values of a and b. 3
30. In the given figure, if AC = BD, then prove that AB = CD. 3
31 2𝑥 3 +2𝑥+3 7 2 3
For the polynomial − 2 𝑥 2 − 3 𝑥 6 , write
5
(a) the degree of the polynomial (b) the coefficient of x3
(c) the constant term.
SECTION D
Section D consists of 4 questions of 5 marks each.
SL MARKS
NO.
32. In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = 5
BQ.
Show that:
(i) Δ APD ≅ Δ CQB
(ii) AP = CQ
(iii) Δ AQB ≅ Δ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram
OR
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse
AB and parallel to BC intersects AC at D.
Show that
(i) D is the mid-point of AC
(ii) MD ⊥ AC
1
(iii) CM = MA = 2 𝐴𝐵
33. a)Prove that the angle subtended by an arc at the centre is double the angle 5
subtended by it at any point on the remaining part of the circle .
(b) Using the above theorem find reflex ∠ POR if ∠ PQR = 100°, where P, Q and R are
points on a circle with centre O.
34. The lifetimes of 400 neon lamps in hours is noted, and the obtained data is 5
represented in the following table:-
Lifetime in 300- 400- 500- 600- 700- 800- 900-
hours 400 500 600 700 800 900 1000
No. of lamps 14 56 60 86 74 62 48
(i) Draw a histogram to represent the given data.
(ii) How many lamps have a lifetime of 700 or more hours?
35. If x + y + z = 0, show that x3 + y3 + z3 = 3xyz. Also, find the value of (-12)3 + (7)3 + 5
(5)3 without actual calculation.
SECTION E
Case study based questions are compulsory
SL. MARKS
NO.
36. Students of a school are standing in rows and columns in their playground for a 4
drill practices. A, B, C and D are positions of four students as shown in figure.
Now, answer any four question on this information.
(a) What are the Co-ordinate positions of A and B?
(b) Find the coordinate of teacher.
(c) Find the distance CD .
OR
If we draw a perpendicular from B to Y axis, then find its coordinate.
37. Mathematics teacher of a school took her 9th standard students to show Red fort. 4
It was a part of their educational trip. The teacher had interest in history as well.
She narrated the facts of Red fort to students. Then the teacher said in this
monument, one can find combination of solid figures. There are 2 pillars which are
cylindrical in shape. Also 2 domes at the corners which are hemispherical. 7 smaller
domes at the centre. Flag hoisting ceremony on Independence Day takes place near
these domes.
Now, answer following questions
(a) How much is the volume of a hemisphere if the radius of the base is 3.5 m?
(b) What is the circumference of the base of the hemisphere ?
(c) How much cloth material will be required to cover 2 big domes each of radius
2.8 metre?
OR
What will be the ratio of the volume of one dome (hemispherical shape) of base
radius 1m to the volume of sphere of radius 2m.
38. In the below given layout, the design and the measurements have been made 4
such that area of two bedrooms and kitchen together is 95 sq m.
(a)Find the area of the two bedrooms and the kitchen in terms of the given
variables .
(b)Find the length of the outer boundary of the layout.
( c)Find the area of each bedroom.
OR
Find the area of the living room.
