PRACTICE PAPER

Class 09 - Mathematics
Time Allowed: 3 hours Maximum Marks: 80

General Instructions:

Read the following instructions carefully and follow them:

1. This question paper contains 38 questions.

2. This Question Paper is divided into 5 Sections A, B, C, D and E.

3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19 and 20 are Assertion-

Reason based questions of 1 mark each.

4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks each.

5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.

7. In Section E, Questions no. 36-38 are case study-based questions carrying 4 marks each with sub-parts of the

values of 1,1 and 2 marks each respectively.

8. All Questions are compulsory. However, an internal choice in 2 Questions of Section B, 2 Questions of Section

C and 2 Questions of Section D has been provided. An internal choice has been provided in all the 2 marks
questions of Section E.

9. Draw neat and clean figures wherever required.

10. Take π = 22/7 wherever required if not stated.

11. Use of calculators is not allowed.

Section A
−− −
−
−−
1.
4
√√2
3
2
is equal to [1]

a) 2−6
b) −
2 6

c) 2 6
d) 6
2

2. The equation 2x + 5y = 7 has a unique solution, if x, y are : [1]

a) Rational numbers b) Real numbers

c) Natural numbers d) Positive real numbers

3. A point of the form (0, b) lies on: [1]

a) x- axis b) quadrant I

c) quadrant III d) y- axis

4. In a histogram, which of the following is proportional to the frequency of the corresponding class? [1]

a) Width of the rectangle b) Length of the rectangle

c) Perimeter of the rectangle d) Area of the rectangle

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 5. Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form [1]

a) (− 9
, m) b) (-9 , 0)
2

c) (0, − 9
) d) (n, −
9
)
2 2

6. The number of end points a line has: [1]

a) 1 b) 0

c) 2 d) 3
7. In the given figure, the value of x which makes POQ a straight line is: [1]

a) 40° b) 30°

c) 35° d) 25°
8. Given Rectangle ABCD and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. If [1]
length of a diagonal of Rectangle is 8 cm, then the quadrilateral PQRS is a

a) Parallelogram with one side 4 cm b) Rectangle with one side 4 cm

c) Square with each side 4 cm d) Rhombus with each side 4 cm

–
9. If x = 2 -√3 then the value of x2
+
1
2
x
and x 2
−
1
2
x
respectively, are ________. [1]
– –
a) 14, 8√3 b) −14, 8√3

– –
c) 14, −8√3 d) −14, −8√3

10. The linear equation 2x – 5y = 7 has [1]

a) No solution b) Infinitely many solutions

c) A unique solution d) Two solutions

11. In the adjoining fig. AB = AC. If ∠C = 50 , then the value of x and y are:
∘
[1]

a) x = 80o and y = 50o b) x = 70o and y = 60o

c) x = 50o and y = 80o d) x = 60o and y = 70o

12. Diagonals of a quadrilateral ABCD bisect each other. If ∠ A = 45o, then ∠ B = [1]

a) 125o b) 115o

c) 120o d) 135o

13. In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB [1]
such that ∠ ADC = 95° and ∠ ECF = 20°. Then, ∠ BAD = ?

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 a) 85° b) 75°

c) 105° d) 95°
14. An irrational number between 2 and 2.5 is [1]
– −−
a) √5 b) √11

−
− −
− −−−
−
c) √22.5 d) √12.5

15. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]

a) y = 9x - 7 b) 9x - y + 7 = 0

c) x - 9y = 7 d) x = 9y - 7
16. The side BC of △ABC is produced to a point D. The bisector of ∠ A meets side in L. If ∠ ABC = 30° and [1]
∠ ACD = 115°, then ∠ ALC =

a) 85° b) 115°
∘
c) 145° d) 72
1

17. If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e, then [1]

a) a + c + e = b + d b) a + b + c = d + e

c) b + c + d = a + e d) a + b + e = c + d
18. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of [1]
the cone so formed is

a) 12π cm3 b) 20π cm3

c) 16π cm3 d) 15π cm3

19. Assertion (A): The side of an equilateral triangle is 6 cm then the height of the triangle is 9 cm. [1]
√3
Reason (R): The height of an equilateral triangle is 2
a.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

20. Assertion (A): There are infinite number of lines which passes through (2, 14). [1]
Reason (R): A linear equation in two variables has infinitely many solutions.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

Section B
21. In the given figure, O is the centre of the circle and ∠ AOB = 70°. Calculate the values of (i) ∠ OCA, (ii) ∠ OAC. [2]

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22. The perimeter of an equilateral triangle is 60 cm. Find its area. [2]
23. In the given figure, sides AD and AB of cyclic quadrilateral ABCD are produced to E and F respectively. If [2]
∠ CBF = 130° and ∠ CDE = x°, find the value of x.

24. If O is the centre of the circle, find the value of x in given figure: [2]

OR
If O is the centre of below circle, find the value of x in given figure:

25. Solve the equation for x: 5(4x + 3) = 3(x - 2) [2]

OR
Find whether the given equation have x = 2, y = 1 as a solution:
2x – 3y + 7 = 8
Section C
2
−1 −
1

4
[3]
26. Simplify {[625 2
] }

27. Factorize: x 3
+ 13x
2
+ 32x + 20 [3]
28. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m [3]

and 15 m. The advertisements yield an earning of Rs2000 per m2 a year. A company hired one of its walls for 6
months. How much rent did it pay?
OR

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 Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs7 per m2.
29. The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per [3]

cm3?
30. AB is a line segment and P is the mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ [3]
ABE and ∠ EPA = ∠ DPB. Show that:
i. ΔDAP ≅ ΔEBP
ii. AD = BE (See figure)

OR
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O.
Show that OB = OC and AO bisects ∠ A.
31. In fig find the vertices' co-ordinates of △ABC [3]

Section D
[5]
5−√3 5+√3 10√3
32. If x = 5+√3
and y = 5−√3
,show that x − y = −
11
.
OR
– 3
If x = 2 - , find the value of (x − .
1
√3 )
x

33. In the adjoining figure, name: [5]

i. Six points
ii. Five line segments
iii. Four rays
iv. Four lines
v. Four collinear points

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34. In each of the figures given below, AB || CD. Find the value of x ∘
[5]

OR
In the given figure, AB || CD. Prove that p + q - r = 180.

35. Draw a histogram for the frequency distribution of the following data: [5]

Class interval 8-13 13-18 18-23 23-28 28-33 33-38 38-43

Frequency 320 780 160 540 260 100 80

Section E
36. Read the following text carefully and answer the questions that follow: [4]
Once upon a time in Ghaziabad was a corn cob seller. During the lockdown period in the year 2020, his business
was almost lost.
So, he started selling corn grains online through Amazon and Flipcart. Just to understand how many grains he
will have from one corn cob, he started counting them.
Being a student of mathematics let's calculate it mathematically. Let's assume that one corn cob (see Fig.),
shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm.

i. Find the curved surface area of the corn cub. (1)

ii. What is the volume of the corn cub? (1)

iii. If each 1 cm2 of the surface of the cob carries an average of four grains, find how many grains you would
find on the entire cob? (2)

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 OR
How many such cubs can be stored in a cartoon of size 20 cm × 25 cm × 20 cm. (2)
37. Read the following text carefully and answer the questions that follow: [4]
Ajay lives in Delhi, The city of Ajay's father in laws residence is at Jaipur is 600 km from Delhi. Ajay used to
travel this 600 km partly by train and partly by car.
He used to buy cheap items from Delhi and sale at Jaipur and also buying cheap items from Jaipur and sale at
Delhi.
Once From Delhi to Jaipur in forward journey he covered 2x km by train and the rest y km by taxi.
But, while returning he did not get a reservation from Jaipur in the train. So first 2y km he had to travel by taxi
and the rest x km by Train. From Delhi to Jaipur he took 8 hrs but in returning it took 10 hrs.

i. Write the above information in terms of equation. (1)

ii. Find the value of x and y? (1)
iii. Find the speed of Taxi? (2)
OR
Find the speed of Train? (2)
38. Read the following text carefully and answer the questions that follow: [4]
Harish makes a poster in the shape of a parallelogram on the topic SAVE ELECTRICITY for an inter-school
competition as shown in the follow figure.

i. If ∠ A = (4x + 3)o and ∠ D = (5x - 3)o, then find the measure of ∠ B. (1)
ii. If ∠ B = (2y)o and ∠ D = (3y - 6)o, then find the value of y. (1)
iii. If ∠ A = (2x - 3)o and ∠ C = (4y + 2)o, then find how x and y relate. (2)
OR
If AB = (2y - 3) and CD = 5 cm then what is the value of y? (2)

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