Karnataka SSLC Model Question Paper 2027 for Mathematics (Paper 3, English Medium)

FOR KARNATAKA CLASS 10 PREPARATION

Karnataka SSLC Model
Question Paper 2027 for
Mathematics (Paper 3,
English Medium)
EXAM YEAR TYPE SUBJECT
Karnataka Class 10 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

.
.co s e m

s em l a
a ag
PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë ªÀÄvÀÄÛ ªÀiË®å ¤tðAiÀÄ ªÀÄAqÀ°
À gÀÄ – 560003
ªÀįÉèñÀégÀA, ¨ÉAUÀ¼Æ
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
MALLESHWARAM, BENGALURU- 560003
m
om . co
.c
2026-27mJ¸ï.J¸ï.J¯ï.¹ em
e
ªÀiÁzÀj ¥Àæ±ÉߥÀwæPÉ - 3
l as
as
l S.S.L.C. MODEL QUESTION PAPER- 3 2026-27 ag
ag
«µÀAiÀÄ : UÀtÂvÀ
SUBJECT: MATHEMATICS

(ಇಂ ಧ ಮ/ ENGLISH MEDIUM)

m
m .co
ಷಯ ಸಂ ೕತ : 81-E
s e Subject Code : 81-E

l a
ag
ಸಮಯ: 3 ಗಂ 15 ಷಗ (Time: 3 Hours 15 Minutes)

ಗ ಷ ಅಂಕಗ : 80 (Max. Marks: 80)

General Instructions to the candidate:
1. This question paper consists of 38 questions.
m
m 2. Follow the instructions given against the questions. .co
m .co 3. Figures in the right-hand margin indicate maximum marks for the s e m
s e g la
g la Questions.
a
a 4. 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.

om
1
. c
. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 1 of 10

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. If the lines represented by the pair of linear equations a 1x + b1y + c1=0 and
a2x + b2y + c2 =0 intersect each other, then the correct relation among the following is

a1 b1 a1 b1 c1
(A)  (B)  
a2 b2 a2 b2 c2

a1 b1 a1 b1 c1
(C)  (D)  
a2 b2 a2 b2 c2

2. If α and β are the zeroes of the polynomial p(x) = ax 2 + 𝑏𝑥 + 𝑐, then the value of α + β is

–
(A) (B)

–
(C) (D)

3. The formula to find the sum of all terms of the arithmetic progression with first term
‘a’ and last term ‘l’ is

(A) sn= (𝑎 + 𝑙) (B) sn = (𝑎 − 𝑙)

(C) sn = (a × 𝑙) (D) sn = (a ÷ 𝑙)

4. The value of cosec 600 + sec 300 is

√ √
(A) (B)

(C) (D)
√ √

2

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 10

.
.co s e m

s em l a
a ag
5. The formula to find the total surface area of cube of edge ‘a’ unit is

(A) 4a2 Sq. units (B) 6a2 Sq. units

(C) 4a3 Sq. units (D) 6a3 Sq. units
m
om . co
. c e m
6. Which measure m
e of central tendency is calculated by finding Cumulative frequency?
l as
l as ag
(A)g
Mean (B) Median
a
(C) Mode (D) Deviation

7. If p and q are co-primes, then the H.C.F of 𝑝 and 𝑞 is

(A) pq (B) 1
m
(C) p + q (D) p2q2
m .co
s e
l a
ag
8. In the figure, if EF∥CA and FG ∥AB, then is equal to

m
m .co
m .co s e m
s e g la
g la (A) (B)
a
a
(C) (D)

om
3
. c
. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 3 of 10

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

9. Write the zeroes of the polynomial y=p(x) in the given graph.

10. Find the roots of the quadratic equation (𝑥 − 1)(𝑥 + 3) = 0

11. Write the coordinates of the point P which divides the line segment joining the points
𝐴(𝑥 , 𝑦 ) and B (𝑥 , 𝑦 ) internally in the ratio 1:1.

12. When a die is rolled once, find the probability of getting the number 6 on the top.

13. How many solutions does the pair of linear equations 2𝑥 + 3𝑦 − 9 = 0 and

4𝑥 + 6𝑦 − 18 = 0 have?

14. If the nth term of an arithmetic progression is a n= 2𝑛 − 1 then find its 4th term.

15. If the area of base of a cylinder is 22cm2 and height is 10cm, then find the volume the
cylinder.

16. In ΔLMN, ∠L = 50° and ∠N = 60°. If ΔLMN ~ ΔPQR, then find the measure of ∠Q .

4

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 10

.
.co s e m

s em l a
a ag
III. Answer the following questions: 8 x 2 = 16

17. Prove that 4 + √3 is an irrational number.

m
co
18. Solve the given pair of linear equations by elimination method.
2x − y = 8
. c om em .
x+y=7
e m l as
l as ag
g
a (2x+3) x = x +1 in the standard form of quadratic equation.
19. Express 2

OR
For what value of ‘k’ the roots of the equation 𝑘𝑥 + 6𝑥 + 1 = 0 are equal?

20. Find how many numbers between 201 and 401 are divisible by 6 using formula.
OR
Find the sum of first 20 terms of the arithmetic progression 2, 5, 8, 11,....... using formula.

m
m .co
21. If 𝑠𝑖𝑛 𝐴 =
e
then find the value of tan A
s
l a
22. Find the H.C.F and L.C.M of 68 andg72 by the method of prime factorization and verify
a
that L.C.M X H.C. F = The product of numbers.

23. AD and BC are tangents to the circles with centre M and N and they intersect at point P

as shown in the figure. If ∠𝐴𝑀𝑃 = 60° , AP = 4 cm and 𝐴𝑃: 𝑃𝐷 = 1: 2 , then find the

measure of ∠𝑁𝑃𝐷 and length of BC.
m
m .co
m .co s e m
s e g la
g la a
a

om
5
. c
. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 5 of 10

24. The centre of a circle is ‘P’ whose coordinates are P(6, 7). In this circle AB is a chord and
the coordinates of its end points are A (3, 4) and B (9, 4). Find the perpendicular
distance to the chord from the centre of the circle using formula.

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

25. Find the zeroes of the quadratic polynomial p(x) = x 2 + 6x + 8 and verify the relationship
between the zeroes and the coefficients.
OR
Write the quadratic polynomial whose sum of the zeroes is 3 and product of the zeroes
is −10. And also find the zeroes of this polynomial.

26. Prove that “the lengths of tangents drawn from an external point to a circle are equal”.

27. Find the coordinates of the point which divides the line segment joining the points
(4, −3) and (8, 5) internally in the ratio 3 ∶ 1.

28. In the figure, = and  PST =  PRQ. Prove that PQR is an isosceles triangle.

29 . Prove that cosec A (1 – cos A) (cosec A + cot A) = 1

OR

Prove that + = 𝑐𝑜𝑡𝜃 + 𝑠𝑒𝑐𝜃. 𝑐𝑜𝑠𝑒𝑐𝜃

6

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 10

.
.co s e m

s em l a
a ag
30. A bag contains 26 cards numbered from 5 to 30. A card is drawn at random from the bag.
Find the probability that the card drawn is
(i) a multiple of both 2 and 3
(ii) a square number
m
(iii) a multiple of 3
om . co
. c e m
m OR
e balls, 5 white balls and 8 blue balls in a bag. A ball is drawn at randomgl as
s
There are 3ared
l Find the probability that the ball drawn is a
ag
from the bag.
(i) a red ball
(ii) not a white ball
(iii) a green ball

31. A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has only 30m
m
.co
barbed wire, he fences the sides of the rectangular garden letting his house compound
m
s e
wall act as the fourth side fence. Find the dimensions of the garden.
l a
ag
32. In the given figure, area of the sector OAC is cm2. If OR = RA and ∠AOC = 600 then,

find the area of the segment ABC and length of the arc PQR.

m
m .co
m .co s e m
s e g la
g la a
a

om
7
. c
. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 7 of 10

33. Find the Median for the given data
Class interval frequency
50 − 60 6
60 − 70 9
70 − 80 20
80 − 90 10
90 − 100 5

OR

Find the Mode for the following frequency distribution table

Class 10 -20 20 -30 30 -40 40 -50 50 - 60
interval
frequency 6 4 12 3 5

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

34. In an arithmetic progression the first term is 22, n th term is −11 and the sum of the first
‘n’ terms is 66. Find the number of terms of the progression , common difference and the
7th term.
OR

An arithmetic progression contains 30 terms. 17th term of the progression is 4 more than
thrice of its 5th term. The 10th term of the progression is 31. Find the last three terms
of the progression and also find the progression.

35. Solve the given pair of linear equations by graphical method.
𝑥 + 2𝑦 = 10
𝑥 + 𝑦 = 8

8

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 8 of 10

.
.co s e m

s em l a
a ag
36. Prove that “If in two triangles, sides of one triangle are proportional to (i.e., in the same
ratio of) the sides of the other triangle, then their corresponding angles are equal and
hence the two triangles are similar.
OR
m
om
Prove that “If one angle of a triangle is equal to one angle of the other triangle and the . co
. c
sides including these angles are proportional, then the two triangles are similar.” e m
e m l as
a s a g
l‘AB’ is used to climb the terrace of a room (APQC) in the first floor of a building
ag
37. A ladder
𝟒√𝟑(√𝟑 𝟏)
(QRTU) as shown in the figure. The foot of the ladder ‘B’ is at a distance of m
𝟑

from the point ‘C’. From a point ‘S’ on the ground which is 4m away from the building the

angle of elevations to the point ‘P’ on the terrace and to the point ‘Q’ on the base of the

room are 600 and 450 respectively. Find the length of the ladder and the ∠ABC made by
m
the ladder with the wall.
m .co
s e
l a
ag

m
m .co
m .co s e m
s e g la
g la a
a

om
9
. c
. c e m
m as
se
For more Question Papers, Sample Papers, Notes & Syllabus visit
gl
Page 9 of 10

VI. Answer the following question: 1x5=5

38. A cylindrical hall has a hemispherical roof and the total height of the hall is equal to the

diameter of the hemisphere. Find the area of the floor if the capacity of the hall is

48510m3. If the inner surface of the hall is to be painted, then find the area to be painted.

OR
50 tents are to be built in a village for an upcoming fair. The lower part of each tent is

cylindrical with base radius 2.8m and height 3.5m and the upper part is conical with the

same base radius as that of the cylinder. If the height of the cone is 2.1m then find the area

of the canvas used to make 50 such tents.

****************************

10

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 10