KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32

SAMPLE PAPER 02 FOR SESSION ENDING EXAM (2020-21)

SUBJECT: MATHEMATICS(041)

BLUE PRINT : CLASS IX

Case
VSA SA – I SA – II LA
Chapter Study Total
(1 mark) (2 marks) (3 marks) (5 marks)
Questions

Number Systems 1(1)* -- 2(1)* -- 5(1) 8(3)

1(1)*
Polynomials -- 2(1) -- 5(1) 9(4)
1(1)
Linear Equations in two 1(1)*
4(1)# 2(1) -- -- 8(4)
variables 1(1)

Coordinate Geometry -- 4(1)# -- -- -- 4(4)

Lines and Angles 2(2) -- 2(1) 3(1)* -- 7(4)

Triangles 1(1)* -- -- 6(2) -- 7(3)

Quadrilaterals 1(1) -- -- -- 5(1)* 6(2)

Circles 2(2) -- -- 3(1)* -- 5(3)

Constructions -- -- -- 3(1) -- 3(1)

Heron’s Formula 2(2) 4(1)# -- -- -- 6(4)

Surface Areas and 1(1)* 2(1)*

-- -- -- 7(4)
Volumes 2(2) 2(1)

Statistics -- 4(1)# -- 3(1) -- 7(2)

Probability -- -- -- 3(1) -- 3(1)

Total 16(16) 16(4) 12(6) 21(7) 15(3) 80(36)

Note: * - Internal Choice Questions and Yellow shaded with # - Case study questions
attempt 4 questions out of 5 questions

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KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32
SAMPLE PAPER 02 FOR SESSION ENDING EXAM (2020-21)

SUBJECT: MATHEMATICS MAX. MARKS : 80

CLASS : IX DURATION : 3 HRS
General Instruction:
1. This question paper contains two parts A and B.
2. Both Part A and Part B have internal choices.
Part – A:
1. It consists two sections- I and II.
2. Section I has 16 questions of 1 mark each. Internal choice is provided in 5 questions.
3. Section II has 4 questions on case study. Each case study has 5 case-based sub-parts. An
examinee is to attempt any 4 out of 5 sub-parts.
Part – B:
1. Question No 21 to 26 are Very short answer Type questions of 2 mark each,
2. Question No 27 to 33 are Short Answer Type questions of 3 marks each
3. Question No 34 to 36 are Long Answer Type questions of 5 marks each.
4. Internal choice is provided in 2 questions of 2 marks, 2 questions of 3 marks and 1 question of 5
marks.

PART - A
SECTION-I
Questions 1 to 16 carry 1 mark each.
1. In a triangle ABC, if A + B = 650 and B + C = 1400, then find the measure of B.
OR
ABC is a right angled triangle in which ∠ A = 90° and AB = AC. Find ∠ B and ∠ C.

2. Find the value of p(y) = 5y2 – 3y + 7 at y = – 1

OR
Find the value of k, if – 1 is a zero of the polynomial x2 + 8x + k?

3. Find the zero of the polynomial p(x) = 3x + 4.

4. The radius of the circle is 5 cm and distance of the chord from the centre of the circle is 4 cm.
Find the length of the chord.
5. In the given figure, O is the centre of the circle and AB is a chord of the circle. If AOB = 110°,
find APB.

6. At what point the graph of the linear equation 2x – 3y = – 15 cuts the x-axis?

7. Find the area of triangle whose sides are 13 cm, 14 cm and 15 cm.
8. Three angles of quadrilateral are 75°, 90°, 75°. Find the fourth angle.

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9. The surface area of two hemispheres are in the ratio 25 : 49. Find the ratio of their radii.

3 2
10. Rationalize the denominator of .
3 2
OR
1
3
Find the value of 125 .

11. In the below left figure, find the ∠x.

12. Find the area of an equilateral triangle with side 2√3cm.

13. In the below figure, ∠EBC = 115° and ∠DAB = 100°. Find ∠ACB.

14. The perimeter of floor of rectangular hall is 250m. The cost of the white washing its four walls
is Rs. 15000 at the rate of Rs. 10 per m2. Find the height of the room.

15. Express 2x = 5y in the form ax + by + c = 0

OR
Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k.

16. Find the height of cone, if its slant height is 34 cm and base diameter is 32 cm.
OR
Find the curved surface area of a hemisphere of radius 21 cm.

SECTION-II
Case study-based questions are compulsory. Attempt any four sub parts of each
question. Each subpart carries 1 mark

17. Triangles are used to make bridges because a triangle is an undeformable shape, as considered
in the civil engineering field. it can hold the most force when applied to it, compared to
quadrilaterals and arches. Isosceles triangles were used to construct a bridge in which the base
(unequal side) of an isosceles triangle is 4 m and its perimeter is 20 m.

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 (a) What is the length of equal sides ?
(i) 2 m (ii) 3 m (iii) 8 m (iv) 10 m

(b) What is the Heron's formula for a triangle ?

(i) s  s  a  s – b  s – c  (ii) s  s  a  s  b  s  c 
(iii) s  s – a  s – b  s – c  (iv) s  s.a  s.b  s.c 

(c) What is the semi perimeter of the highlighted triangle ?

(i) 30 m (ii) 40 m (iii) 10 m (iv) 50 m

(d) What is the area of highlighted triangle ?

(i) 4√15 m2 (ii) 4 m2 (iii) √15 m2 (iv) 20 m2

(e) If the sides of a triangle are in the ratio 3 : 5 : 7 and its perimeter is 300 m. Find its area.
(i) 100√2 (ii) 500√3 (iii) 1500√2 (iv) 200√3

18. Students of class IX are on visit of Sansad Bhawan. Teacher assign them the activity to observe
and take some pictures to analyses the seating arrangement between various MP and speaker
based on coordinate geometry. The staff tour guide explained various facts related to Math's of
Sansad Bhawan to the students, students were surprised when teacher ask them you need to
apply coordinate geometry on the seating arrangement of MP's and speaker.
Calculate the following refer to the below image and graph. Answer the following questions:

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 Answer the following refer to the above image and graph:
(i) What are the coordinates of position ‘F’?
(a) (3, 4) (b) (4, 3) (c) (-3, 4) (d) (-4, 3)

(ii) What are the coordinates of position ‘D’?

(a) (3, 2) (b) (-3, -2) (c) (-3, 2) (d) (3, -2)

(iii) What are the coordinates of position ‘H’?

(a) (8, 5) (b) (8, 4.5) (c) (8, 4) (d) (8, 5.5)

(iv) In which quadrant, the point ‘C’ lie?

(a) I (b) II (c) III (d) IV

(v) Find the perpendicular distance of the point E from the y-axis.
(a) 13 units (b) 10 units (c) 11 units (d) 3 units

19. The COVID-19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic of
coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus
2 (SARS-CoV-2). It was first identified in December 2019 in Wuhan, China.
During survey, the ages of 80 patients infected by COVID and admitted in the one of the City
hospital were recorded and the collected data is represented in the less than cumulative
frequency distribution table.

Age(in yrs) No. of patients

5 – 15 6
15 – 25 11
25 – 35 21
35 – 45 23
45 – 55 14
55 – 65 5

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 Based on the information, answer the following questions :
(a) The class interval with highest frequency is :
(i) 45-55 (ii) 35-45 (iii) 25-35 (iv) 15-25

(b) Which age group was affected the least?

(i) 35-45 (ii) 25-35
(iii) 55-65 (iv) 45-55

(c) What is the class mark of the class interval which was affected the most?
(i) 30 (ii) 40 (iii) 50 (iv) 60

(d) How many patients of the age 45 years and above were admitted?
(i) 61 (ii) 19 (iii) 14 (iv) 23

(e) How many patients of the age 35 years and less were admitted?
(i) 17 (ii) 38 (iii) 61 (iv) 41

20. On his birthday, Manoj planned that this time he celebrates his birthday in a small orphanage
centre. He bought apples to give to children and adults working there. Manoj donated 2 apples
to each children and 3 apples to each adult working there along with Birthday cake. He
distributed 60 total apples.

(a) How to represent the above situation in linear equations in two variables by taking the
number of children as ‘x’ and the number of adults as ‘y’?
(i) 2x + y = 60 (iii) 2x + 3y = 60
(ii) 3x + 2y = 60 (iv) 3x + y = 60

(b) If the number of children is 15, then find the number of adults?
(i) 10 (iii) 15
(ii) 25 (iv) 20

(c) If the number of adults is 12, then find the number of children?
(i) 12 (iii) 15
(ii) 14 (iv) 18

(d) Find the value of b, if x = 5, y = 0 is a solution of the equation 3x + 5y = b.

(i) 12 (iii) 15
(ii) 14 (iv) 18

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 (e) Which is the standard form of linear equations in two variables: y – x = 5 ?
(i) 1.y – 1.x – 5 = 0 (ii) 1.x – 1.y + 5 = 0
(iii) 1.x + 0.y + 5 = 0 (iv) 1.x – 1.y – 5 = 0

PART – B
(Question No 21 to 26 are Very short answer Type questions of 2 mark each)

4 5 4 5
21. Simplify  by rationalizing the denominator.
4 5 4 5
OR
0.16 0.09
Find the value of (81) × (81) .
1 9 1
22. Factorise: 27 x 3   x2  x
216 2 4

23. A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find
the area of the sheet required to make 10 such caps.
OR
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it.
Find the ratio of surface areas of the balloon in the two cases.

24. The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of
the cone.

25. Find two solutions for the equation 4x + 3y = 24. How many solutions of this equation are
possible?

26. In the below figure, if AB || CD, ∠ APQ = 50° and ∠ PRD = 127°, find x and y.

(Question no 27 to 33 are Short Answer Type questions of 3 marks each)

27. 1500 families with 2 children were selected randomly, and the following data were recorded:
Number of girls in a family 0 1 2
Number of families 475 814 211
Compute the probability of a family, chosen at random, having
(i) 2 girls (ii) 1 girl (iii) No girl

28. A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are
sitting at equal distance on its boundary each having a toy telephone in his hands to talk each
other. Find the length of the string of each phone.
OR
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a
point on the minor arc and also at a point on the major arc.

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29. Line l is the bisector of an angle A and B is any point on l. BP and BQ are perpendiculars
from B to the arms of A (see the below figure). Show that:
(i)APB AQB (ii) BP = BQ or B is equidistant from the arms of A.

30. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that
BAD = ABE and EPA = DPB (see the below figure). Show that (i) DAP EBP (ii)
AD = BE

31. Construct a triangle PQR in which QR = 6cm, ∠Q = 60° and PR – PQ = 2cm.

32. The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data
is represented in the following table:

Length (in mm) 118 – 126 127 – 135 136 – 144 145 – 153 154 – 162 163 – 171 172 – 180
Number of leaves 3 5 9 12 5 4 2

Draw a histogram to represent the given data.

33. In the adjoining figure, PQ and RS are two mirrors placed parallel to each other. An incident ray
AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror
RS at C and again reflects back along CD. Prove that AB || CD.

(Question no 34 to 36 are Long Answer Type questions of 5 marks each.)

34. Verify: (i) x3 + y3 = (x + y) (x2 – xy + y2) (ii) x3 – y3 = (x – y) (x2 + xy + y2)

35. Represent the real number 2, 3, 5 on a single number line.

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36. P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a
quadrilateral ABCD such that AC  BD. Prove that PQRS is a rectangle.
OR
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see
the below figure). Show that:
(i) Δ APD ≅ Δ CQB
(ii) AP = CQ
(iii) Δ AQB ≅ Δ CPD
(iv) AQ = CP
(v) APCQ is a parallelogram

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