Stepping Stones Sr. Sec.

School
Sector 37D, Chandigarh

CLASS 9 RETEST EXAM

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. The signs of abscissa and ordinate of a point in quadrant III are [1]

a) (−, −) b) (−, +)

c) (+, +) d) (+, −)

2. Each side of an equilateral triangle measures 10 cm. Then the area of the triangle is [1]

a) 43.2 cm2 b) 43.4 cm2

c) 43.1 cm2 d) 43.3 cm2

3. If one zero of a quadratic polynomial kx2 + 4x + k is 1, then the value of k is: [1]

a) -4 b) 4

c) -2 d) 2
4. In the adjoining figure, the rule by which △ABC ≅ △ADC [1]

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 a) SAS b) SSS

c) AAS d) RHS
1
1
[1]
5. The value of [(81) is
2
2 ]

a) -3 b) 9

c) 1

3
d) 3
6. In △ABC, if AB = AC and ∠AC D = 120
0
= , find ∠ A [1]

a) 50 0
b) 80o

c) 70 0
d) 60
0

7. How many lines pass through two points? [1]

a) many b) three

c) two d) only one

8. (x2 - 4x - 21) = ? [1]

a) (x - 7) (x + 3) b) ( x - 7) ( x - 3)

c) (x + 7) (x + 3) d) (x + 7) (x - 3)
– –
9. On simplification (3 + √3)(3 − √3) gives [1]
–
a) 0 b) −2√3

c) 16 d) 6
10. In the given figure, AOB is a straight line. The value of x is [1]

a) 12 b) 20

c) 15 d) 25
11. Express 7

8
in the decimal form. [1]

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 a) 0.8 b) 20

c) 0.67 d) 0.875
12. If x = 3 and y = -2 satisfies 5x - y = k, then the value of k is [1]

a) 3 b) 17

c) 12 d) -2
13. In the given figure, AOB is a straight line. If ∠AOC = 4x
∘
and ∠BOC = 5x
∘
then ∠AOC = ? [1]

a) 60° b) 40°

c) 100° d) 80°
−− – −− –
14. Which of the following is the value ( √11 − √7)( √11 + √7)? [1]
–
a) √7 b) 4
−−
c) √11 d) -4
15. Area of the given triangle is [1]

a) 60 cm2 b) 32.5 cm2

c) 78 cm2 d) 30 cm2

16. Points (1, 0) and (-1, 0) lies on [1]

a) line x + y = 0 b) y-axis

c) x-axis d) line x - y = 0
17. The cost of a notebook is twice the cost of a pen. The equation to represent this statement is [1]

a) 2x = 3y b) x = 3y

c) x + 2y = 0 d) x - 2y = 0
18. The degree of a biquadratic polynomial is [1]

a) 2 b) 4

c) 3 d) 1
19. Assertion (A): Two adjacent angles always form a linear pair. [1]
Reason (R): In a linear pair of angles two non-common arms are opposite rays.

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

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 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): If √2 = 1.414, √3 = 1.732, then √5 = √2 + √3 . [1]
Reason (R): Square root of a positive real number always exists.

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. If a point C lies between two points A and B such that AC = BC, then prove that AC = 1

2
AB. Explain by [2]
drawing the figure.
22. Why is axiom 5, in the list of Euclid's axioms, considered as a 'universal truth'? [2]
OR
In fig., if AC = BD, then prove that AB = CD

23. Name the quadrant in which the following points lie: (i) A(2, 9) (ii) B(–3, 5) (iii) C(–4, –7) (iv) D(3, –2) [2]
– – – –
24. Simplify: (3√5 − 5√2)(4√5 + 3√2) [2]
OR
Find five rational numbers between and .
3 4

5 5

25. Two supplementary angles differ by 48°. Find the angles. [2]
OR
In Fig., find the value of x.

Section C
26. You know that 1

7
¯
¯¯¯¯¯¯¯¯¯¯¯¯¯
= 0. 142857
¯
. Can you predict what the decimal expansions of 2

7
,
3

7
,
4

7
,
5

7
,
6

7
are, without [3]
actually doing the long division? If so, how?
27. The following data shows the average age of men in various countries in a certain year: [3]

Country India Nepal China Pakistan U.K. U.S.A.

Average age
55 52 60 50 70 75
(in years)

Represent the above information by a bar graph.

28. In the given figure, ABC and DBC are two triangles on the same base BC such that AB = AC and DB = DC. [3]
Prove that ∠ ABD = ∠ ACD,

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29. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any [3]
common such solution for equations 9x + 7y = 63 and x + y = 10
OR
Find four solutions for the following equation :12x + 5y = 0
30. The following table gives the marks scored by 100 students in an entrance examination. [3]

Mark: 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80

No. of Students
4 10 16 22 20 18 8 2
(Frequency):

Represent this data in the form of a histogram.

31. Evaluate the product without multiplying directly: 103 × 107 [3]
Section D

32. In figure, ∠ ABC = 65o, ∠ BCE = 30o, ∠ DCE = 35o and ∠ CFE = 145o. Prove that AB || EF. [5]

OR
In each of the figures given below, AB ∥ CD. Find the value of x in each other case.
∘

33. The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs.58 per hectare is [5]
Rs.783, find its base and height.
34. The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 150 m. Find the area of the triangle. [5]
OR
Two sides of a triangular field are 85 m and 154 m in length and its perimeter is 324 m. Find the area of the field.
35. Verify that x3
+ y
3
+ z
3
− 3xyz =
1

2
(x + y + z) [(x − y)
2
+ (y − z)
2 2
+ (z − x) ] [5]
Section E
36. Read the following text carefully and answer the questions that follow: [4]
Reeta was studying in the class 9th C of St. Surya Public school, Mehrauli, New Delhi-110030
Once Ranjeet and his daughter Reeta were returning after attending teachers' parent meeting at Reeta's school.
As the home of Ranjeet was close to the school so they were coming by walking.
Reeta asked her father, "Daddy how old are you?"

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 Ranjeet said, "Sum of ages of both of us is 55 years, After 10 years my age will be double of you.

i. What is the second equation formed? (1)

ii. What is the present age of Reeta in years? (1)
iii. What is the present age of Ranjeet in years? (2)
OR
If the ratio of age of Reeta and her mother is 3 : 7 then what is the age of Reeta's mother in years? (2)
37. Read the following text carefully and answer the questions that follow: [4]
As shown In the village of Surya there was a big pole PC. This pole was tied with a strong wire of 10 m length.
Once there was a big spark on this pole, thus wires got damaged very badly. Any small fault was usually
repaired with the help of a rope which normal board electricians were carrying on bicycles.
This time electricians need a staircase of 10 m so that it can reach at point P on the pole and this should make

60o with line AC.

i. Show that △APC and △BPC are congruent. (1)

ii. Find the value of ∠ x. (1)
iii. Find the value of ∠ y. (2)
OR
What is the value of ∠ PBC? (2)
38. Read the following text carefully and answer the questions that follow: [4]
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

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collected to evaluate the teacher on the above-mentioned criterion.

i. What is the total no of teachers? (1)

ii. Find the class mark of class 15 - 20, 25 - 30 and 45 - 50? (1)
iii. What is the no of teachers of age range 25 - 40 years? (2)
OR
Which classes are having same no. of teachers? (2)

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