Karnataka SSLC Question Paper 2022 Mathematics

Question Paper
2022
docs.

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Question Paper Serial No.
Jlflo »⁄flfl¶√}⁄ Æ⁄‚¥lV⁄◊⁄ —⁄MSÊ¿ : 16 ]
Total No. of Printed Pages : 16 ]
Jlflo Æ⁄√ÀÊ-V⁄◊⁄ —⁄MSÊ¿ : 38 ] CCE RF
Total No. of Questions : 38 ] CCE RR
—⁄MOÊfi}⁄ —⁄MSÊ¿ : 81-E

101
Code No. : 81-E
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Subject : MATHEMATICS

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Æ⁄√ÀÊ-Æ⁄~√OÊæ⁄fl´⁄fl-}Ê¡Êæ⁄flƒfl B∆« O⁄}⁄°¬“
¶´¤MO⁄ : 04. 04. 2022 ] [ Date : 04. 04. 2022
—⁄»⁄flæ⁄fl : ∑Ê◊⁄VÊX 10-30 ¬M•⁄ »⁄fl®¤¿‘⁄-1-45 ¡⁄»⁄¡ÊVÊ ] [ Time : 10-30 A.M. to 1-45 P.M.
V⁄¬Œ⁄r @MO⁄V⁄◊⁄fl : 80 ] [ Max. Marks : 80

General Instructions to the Candidate :
1. This question paper consists of objective and subjective types of
38 questions.
2. This question paper has been sealed by reverse jacket. You have to cut
on the right side to open the paper at the time of commencement of the
examination. Check whether all the pages of the question paper are
intact.
3. Follow the instructions given against both the objective and subjective
types of questions.
4. Figures in the right hand margin indicate maximum marks for the
questions.
5. The maximum time to answer the paper is given at the top of the
question paper. It includes 15 minutes for reading the question paper.
Tear here

101 RF/RR (A)-(200)-9020 [ Turn over

81-E 2 CCE RF & RR

I. Four alternatives are given for each of the following questions /

incomplete statements. Choose the correct alternative and write the

complete answer along with its letter of alphabet. 8×1=8

1. The graphical representation of the pair of lines x + 2y – 4 = 0 and

2x + 4y – 12 = 0 is

(A) intersecting lines

(B) parallel lines

(C) coincident lines

(D) perpendicular lines.

2. The common difference of the Arithmetic progression 8, 5, 2, – 1, ...

is

(A) –3

(B) –2

(C) 3

(D) 8.

RF/RR (A)-(200)-9020

CCE RF & RR 3 81-E

3. The standard form of 2x 2 = x − 7 is

(A) 2x 2 − x = − 7

(B) 2x 2 + x − 7 = 0

(C) 2x 2 − x + 7 = 0

(D) 2x 2 + x + 7 = 0 .

4. The value of cos ( 90° – 30° ) is

(A) –1

1
(B)
2

(C) 0

(D) 1.

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81-E 4 CCE RF & RR

5. The distance of the point P ( x, y ) from the origin is

(A) x2 + y2

(B) x2 + y2

(C) x2 − y2

(D) x2 − y2 .

6. In a circle, the angle between the tangent and the radius at the point

of contact is

(A) 30°

(B) 60°

(C) 90°

(D) 180°.

RF/RR (A)-(200)-9020

CCE RF & RR 5 81-E

7. In the given figure, the volume of the frustum of a cone is

(A) π ( r1 + r 2 )l

(B) π ( r1 − r 2 )l

1
(C) π h ( r12 − r2 2 − r 1 r 2 )
3

1
(D) π h ( r12 + r2 2 + r 1 r 2 )
3

8. Surface area of a sphere of radius ‘r’ unit is

(A) π r 2 sq.units (B) 2 π r 2 sq.units

(C) 3 π r 2 sq.units (D) 4 π r 2 sq.units.

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81-E 6 CCE RF & RR

II. Answer the following questions : 8×1=8

9. If the pair of linear equations in two variables are inconsistent, then

how many solutions do they have ?

10. In an Arithmetic progression if ‘a’ is the first term and ‘d’ is the

common difference, then write its n th term.

11. Write the standard form of quadratic equation.

sin 18 o
12. Write the value of .
cos 72o

13. Write the distance of the point ( 4, 3 ) from x-axis.

14. Find the median of the scores 6, 4, 2, 10 and 7.

15. Write the statement of “Basic Proportionality” theorem ( Thales

theorem ).

RF/RR (A)-(200)-9020

CCE RF & RR 7 81-E

16. In the given figure, write the formula used to find the curved surface

area of the cone.

III. Answer the following questions : 8 × 2 = 16

17. Solve the given pair of linear equations by Elimination method :

2x + y = 8

x – y = 1

18. Find the 30th term of the arithmetic progression 5, 8, 11, ..... by

using formula.

RF/RR (A)-(200)-9020 [ Turn over

81-E 8 CCE RF & RR

19. Find the sum of first 20 terms of the Arithmetic progression

10, 15, 20, .......... by using formula.

OR

Find the sum of first 20 positive integers using formula.

20. Find the roots of x 2 + 5x + 2 = 0 by using quadratic formula.

21. Find the value of the discriminant and hence write the nature of

roots of the quadratic equation x 2 + 4x + 4 = 0.

22. Find the distance between the points A ( 2, 6 ) and B (5, 10 ) by

using distance formula.

OR

Find the coordinates of the mid-point of the line segment joining the

points P ( 3, 4 ) and Q ( 5, 6 ) by using ‘mid-point’ formula.

RF/RR (A)-(200)-9020

CCE RF & RR 9 81-E

23. Draw a line segment of length 10 cm and divide it in the ratio 2 : 3

by geometric construction.

24. In the given figure find the values of

i) sin θ

ii) tan α.

IV. Answer the following questions : 9 × 3 = 27

25. The sum of first 9 terms of an Arithmetic progression is 144 and its

9th term is 28. Then find the first term and common difference of the

Arithmetic progression.

RF/RR (A)-(200)-9020 [ Turn over

81-E 10 CCE RF & RR

26. The diagonal of a rectangular field is 60 m more than its shorter

side. If the longer side is 30 m more than the shorter side, then find

the sides of the field.

OR

In a right angled triangle, the length of the hypotenuse is 13 cm.

Among the remaining two sides, the length of one side is 7 cm more

than the other side. Find the sides of the triangle.

27. Prove that

( sin A + cosec A ) 2 + ( cos A + sec A ) 2 = 7 + tan 2 A + cot 2 A.

OR

Prove that sec θ ( 1 – sin θ ) ( sec θ + tan θ ) = 1.

RF/RR (A)-(200)-9020

CCE RF & RR 11 81-E

28. Find the coordinates of the point on the line segment joining the

points A ( – 1, 7 ) and B ( 4, – 3 ) which divides AB internally in the

ratio 2 : 3.

OR

Find the area of triangle PQR with vertices P ( 0, 4 ), Q ( 3, 0 )

and R ( 3, 5 ).

29. Find the mean for the following grouped data by Direct method :

Class-interval Frequency

10 — 20 2

20 — 30 3

30 — 40 5

40 — 50 7

50 — 60 3

OR

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81-E 12 CCE RF & RR

Find the mode for the following grouped data :

Class-interval Frequency

5 — 15 3

15 — 25 4

25 — 35 8

35 — 45 7

45 — 55 3

30. During a medical check-up of 50 students of a class, their heights

were recorded as follows :

Draw “less than type” ogive for the given data :

Height in cm Number of students

( Cumulative frequency )

Less than 140 5

Less than 145 10

Less than 150 15

Less than 155 25

Less than 160 40

Less than 165 50

RF/RR (A)-(200)-9020

CCE RF & RR 13 81-E

31. Prove that “the lengths of tangents drawn from an external point to a

circle are equal”.

32. Construct two tangents to a circle of radius 3 cm from a point 8 cm

away from its centre.

33. The volume of a solid right circular cylinder is 2156 cm 3 . If the

height of the cylinder is 14 cm, then find its curved surface area.

22
[ Take π = ]
7

V. Answer the following questions : 4 × 4 = 16

34. Find the solution of the given pair of linear equations by graphical

method :

x + 2y = 6

x+y= 5

35. The angle of elevation of the top of a building from the foot of a tower

is 30° and the angle of elevation of the top of the tower from the foot

of the building is 60°. Both the tower and building are on the same

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81-E 14 CCE RF & RR

level ground. If the height of the tower is 50 m, then find the height

of the building.

OR

As observed from the top of a 75 m high light house from the sea-

level, the angles of depression of two ships are 30° and 45°. If one

ship is exactly behind the other on the same side of the light house,

then find the distance between the two ships.

RF/RR (A)-(200)-9020

CCE RF & RR 15 81-E

36. Construct a triangle with sides 4·5 cm, 6 cm and 8 cm. Then
3
construct another triangle whose sides are of the corresponding
4
sides of the first triangle.

37. In the figure AXB and CYD are the arcs of two concentric circles
with centre O. The length of the arc AXB is 11 cm. If OC = 7 cm and
∠ AOB = 30°, then find the area of the shaded region.
22
[ Take π = ]
7

VI. Answer the following question : 1×5=5

38. Prove that “the ratio of the areas of two similar triangles is equal to

the square of the ratio of their corresponding sides”.

RF/RR (A)-(200)-9020 [ Turn over

81-E 16 CCE RF & RR

RF/RR (A)-(200)-9020