Karnataka SSLC Preparatory Exam Question Paper 2022 Maths

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sSorlvo& - 560 oo3
KARI{ATAKA SECOITDARY EDUCATION EI(I{MINATION BOARD,
6.h CROSS, MALLESHWARAIII, BANGALORE - 560 OO3

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STATE LEVEL SSLC PREPARATORY EXAMINATION,
FEBRUARY 2022

iofed iosS" : 8l-Ee)
Code No. :81-E
Ddo$ : dt3d
Subject : MATHEMATICS
( e.o[d t uCoS / English Medium )

DOao* : 24. 02. ZOZZ I I nate :24. 02.2022
xd>o$ : e3*r1 10-30 Ood a$mrE 1-45 dddrl ] [tin,e : 1o-30 A.M. to 1-4s P.M
rlOd uodrl#: : 80 ] I tutur. Marks : 80

General Irrstructions to the Candidate :
1. This Question Paper consists of objective and subjective types of
38 questions.
2. Follow the instructions given against both the objective and subjective
types of questions.
3. Figures in the right hand margin indicate maximum marks for the
questions.
4. The maximum time to answer the paper is given at the top cif the question
paper. It includes l5 minutes for reading the question paper.

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81-E 2

I. ffour aXternatives are given for each of the following questions I
incomplete statements. Choose the correct alternative and write the
eomplete ai!.sil,er along with its letter of alphabet. 8x1=8
1. rr pair cf iinear equations atx + brA + c,= 0 and a2x + brA +
"2 =
O

have unique solution. Then the correct relation among the
foilowing is
a. b.
(A) != r-
a2 b2

(B) lt =o, = ",
b. b2 c2
'a.b"
(c) --1- + ;L
a2 D2

a".
b. c.
(D) -l- f
a2 D,2* c2
- ,r .

2. The formula to find the sum of first 'n' terms of positive odd
numbers is

W Sr, = n(n+l) .@ Sr, = n(n-l)
(C) S,, = n3 (?) sn=n2.
3. The quadratic equation in the following is

sr *2,)--3*+2 = o (B)
-2x+3
=O
(ci x- -5x+-b (D) 2x3 +7x+l= O.
4. If A = 30o, then the value of sin 2,4 is
.

1
t;
{'J
(A) (B)
J2 2

1
(c)
2

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3 81-E

The distance of the co-ordinates.( 3,4 )from the x-a-xis is

(A) . 3 units (B) 4 units
(C) 5 units (D) 7 units.
6. The x-coordinate of the point of intersection of "less than and mrre

than" types of ogive gives ti-re

(A). Standarddeviation ( B Mode

(C) Mean iv
(D Median.

7^ L ADE - L ABC, if AD = 1 cm and AB = 2 cm then ihe ai'ea of
L ABC : area of A ADE is
/\

C'

.94 :1 (B) I :4
(c) 1 :2 (D) 2 : 1.
8. The formula to Iirrd tlre iateral surface area of a frustum of a cone
whose circular ends havrng radii r I and r 2 and slant height

I units is
(A) n(rr-r, )l sq.units (B) n 12 sq.units
(C) n (r, +-r, )/ sq.units P/ ir- (r, + r, ) h sq.units

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81-E 4

il. Answer the following questions : 8x1=8

,4' Write the number of solutions that the pair of linear equations
alx + brA +.1 =0 and arx+brU * c2=O have ( c * c
, 2),

10. The 17th term of an Arithmetic progression exceeds its loth term
by 7. Write the common difference of this progression.

1. If sin A =
* write the value of cosec A.
1

W Write the coordinates of the mid-point of the line segment joining the
points A( x, Ut) and B( xz, U) .

,K State "Basic proportionality theorem,'.

14. If the diameter of a circle is 7 cm then write the length of its semi-
circular arc.

A
+-- 7 cm
--+ B

?

15 write the formula to find the surface area of a sphere whose radius

is 'r' units.

16. Find the length of the side of a cube whose volume is 64 3
.
"*

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s 81-E

UI. Answerthefollowingquestions: g xZ=L6
17. solve the foilowing pair of linear equations by Erimination method
:

2x+U = 14

x-a=4

OR

"The difference between two positive numbers
is 26 and one number
is 3 times the other." Represent this statement in
the form of the
pair of linear equations.

)"91 Find the rsth term of the Arithmetic ,:rog'i:ssiori r g, 13, .....
Find the sum of first 2o terms of the A'thmetic
-ls: se.es ,2 + 7 + 12 + ...
using the formula.

Find the value of the discriminant of the equation
-.w1 3x2 -.sx + 2 = a

and hence write the nature of the roots.

OR

Find, for what var,e of 'k'the equatron kx2 .r
cx + l. = 0 has equal
roots.

21. Find the roots of the quadratic equatron 2,xt +
.l_- 4 =_ 0 using
quadratic formula.

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81-E 5

22. In the figure find the valt'.e cf sin P and tan R.
R

a lts P

Find the distance between the points ( 2, 3 ) and ( 6, 6 ) using
the
2{
distance formula.

W Draw a line segment of length 8 cm and divide it in the ratio 2 : 3
geometricallY.

fV. Answerthefollowingquestions: 9x3=27
25. Firrd the sum of all the multiples of 4 between 1O and 250.
26. lf A+ B=90o, Provethat
cosA 1+cosB 2
1+cosB cosA cosA
OR
5 cos2 6o' + 4 sec2 30' - tan2 45" 67
Prove that =E

27. Findthevalue of ,k'if thepointsA(7, -21, B(5' 1)and
C(3, k) arecollinear'
OR

,tiirla the coorclinates of the point which d'ivides the line segment
joining the points (4, -3 ) and ( 8, 5 ) in the ratio 3 : 1 internally'

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7 81-E

28. Find. the mean of the following data using direct method :

Class-interual Frequbncg

0- 10 5

lo-20 8

20-30 20

30-40 15

40-50 7

OR

Find the mode of the following data :

Class-interual Frequencg

l-4 7

4-7 4

7-ro 8

10-13 6

13-16 4

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81-E 8

29. The following table gives production yield of wheat per hectare of

100 farms in a village. Draw a "less than type ogive" for the given

data:

Production yield Number of farms

(in kg / hectare ) ( cumulatiue frequencg )

Less than 5O 2

Less than 55 10

Less than 6O 22

Less than 65 46

Less than 70 74

Less than 75 100

t( Prove that "the lengths of tangents drawn from an'external point to a

circle are equal".

Draw a pair of tangents to a circle of radius 3 cm which are inclined
.*f
to each other at angle of 70' .

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81-E

32. In a circle of radius 2I cm an arc AC subtends an angle 60" at the

centre as shown in the figure then find

i) the length of the arc AC

ii) area of the sector OAC.

OR

ABCD is a squaie of side 14 cm P, Q, R and S are the mid-points of

AB, BC, CD and AD respectively. Also PS', PQ, QR and SR are the

arcs of the circles. Find the area of the shaded region.

A- t'i s .iD

t
., {

3 .; '. .i'A C ry
j
^€ rl t

lr
-
i I .,1'
P D R
.
.;..d
-{.f 'Ul
-i1

: Li .1'
_.N

'! t, -i st+

B o r:;i
\( t ,q#"rl
1,\
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81-E 10

33. A tent is il1 the shape of a cylinder surrounded by a conical top as

shown in the figure. The height and radius of the cylindrical part are

2.1 m attd. 2m respectively. Also slant height of the cone is 2'8 m.

Find the area of the canvas used for making the tent'

I
2'! m

1

v. Answer the following questions : 4x4=L6

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

x+U=S

2x* g= 4

35. An express train takes I hOur less than a passenger train to travel
132 km between two towns A and B. If the average speed of the

express train is 11 km/hr more than that of a passenger train, Iind

the average sPeed ofthese trains.

OR
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11 81-E

Find the roots of the following equation :

'1 1 11
x+4 x-7 = fr(x*-4andx*7)

36. A building on the ground is in the form of a conical tomb
surmounted by a cylinder of height i0 feet as strown in the figure.

From a point 'P'oflthe same ground the angle of elevation of the top

edge of the cylinder is found to be 30" and the angle of elevation to

the vertex of the cone is found to be 45'. If the diameter of the outer

edge of circular base of the cylinder is 9'4 feet, then frnd the height of

the conical shaped tomb.

( Take !6 = I'73 )

o

<- 9'1 ft --->

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