Karnataka SSLC Model Question Paper 2027 for Mathematics (Paper 1, English Medium)

FOR KARNATAKA CLASS 10 PREPARATION

Karnataka SSLC Model
Question Paper 2027 for
Mathematics (Paper 1,
English Medium)
EXAM YEAR TYPE SUBJECT
Karnataka Class 10 2027 Sample Paper Maths

Notes · Sample Papers · Previous Year Papers · Mock Tests

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KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
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SUBJECT: MATHEMATICS

(ಇಂ ಧ ಮ/ ENGLISH MEDIUM)

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ಷಯ ಸಂ ೕತ : 81-E
s e Subject Code : 81-E

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ಸಮಯ: 3 ಗಂ 15 ಷಗ (Time: 3 Hours 15 Minutes)

ಗ ಷ ಅಂಕಗ : 80 (Max. Marks: 80)

General Instructions to the candidate:
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1. This question paper consists of 38 questions.

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2. Follow the instructions given against the questions.
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a Questions.
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.

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Page 1 of 9

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 pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 have unique solution,
then the correct relation among the following is

(A) = (B) = =

(C) ≠ (D) = ≠

2) If the graph of a linear polynomial intersects x-axis at the point (3, 0) then the
polynomial is
(A) P(x) = x − 3 (B) P(x) = x + 3

(C) P(x) = 3x (D) P(x) = 3

3) If the roots of the quadratic equation 𝑥 + 6𝑥 + 𝑘 = 0 are real and equal, then the
value of ‘k’ is
(A) 5 (B) 8

(C) −9 (D) 9

4) The common difference of the arithmetic progression −7, −9, −11, −13………. is
(A) 2 (B) −2

(C) −7 (D) −9

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5) In the figure, ∠𝐴𝐵𝐶=∠𝐴𝐸𝐷, AD=3 units, AE=4 units and EC= 2 units.
The value of x is,
(A) 5 units (B) 6 units

(C) 3 units (D) 1.5 units
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6) The value of sin30 0 0
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(C) (D)

7) A cone and a cylinder have the same base radius and equal volumes. If the height of
the cylinder is 12 cm, then the height of the cone is,

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(A) 6 cm (B) 12 cm

(C) 4 cm (D) 36 cm
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8) The lower limit of the modal classain the given frequency distribution table is,

Class Interval 10-20 20-30 30-40 40-50
Frequency 6 4 12 3

(A)10 (B)20

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(C)30 (D)50
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g la II. Answer the following questions: a 8 ×𝟏 =𝟖
a 9) What is a composite number?

10) Write the degree of the polynomial p(x) = x 3 + 2x2 − 5x4 – 6

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11) If the lines represented by the equations 𝑥 + 2𝑦 − 4 = 0 and 3𝑥 + 𝑏𝑦 − 12 = 0 are

coincident, then find the value of ‘b’.

12) If an , Sn and Sn – 1 represent the nth term, sum of the first n terms and sum of first ( n – 1)

terms then, express an in terms of Sn and Sn – 1 .

13) State AAA criterion for similarity of triangles.

14) Find the coordinates of the midpoint of the line segment joining
the points 𝑃(3, 4) and 𝑄(5, 6)
15) Write the formula to find the total surface area of a right circular cone of base
radius ‘r’, and slant height ‘l’.
16) Find the probability of getting a head when a fair coin is tossed once.

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

17) Find the L.C.M and H.C.F of 72 and 120 by prime factorization method.

18) Prove that 7 + √5 is an irrational number.

19) Solve the given pair of linear equations by elimination method.

3𝑥 – 𝑦 = 4
𝑥 + 𝑦 = 8
20) Find the discriminant of the quadratic equation 3x2 + 5x − 3 = 0 and write the nature
of roots.
OR
Find the roots of the quadratic equation 3𝑥 − 5𝑥 + 2 = 0

21) Find the sum of the first 20 terms of the arithmetic progression 6, 10, 14, ........
using formula.

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22) Two concentric circles with centre ‘O’ and radii 5cm and 3cm are drawn. Find the
length of the chord of the larger circle which touches the smaller circle at point P.

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23) Findagldistance between the points 𝑃(2, 4) and 𝑄(8, 12) using ‘distance formula’.a
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24) In the figure, find the value of sin P and tan R.

OR

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and cosθ = , then find the value of secθ and tanθ
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IV. Answer the following questions: g l a
a 9 x 3 = 27

25) Find the zeroes of the quadratic polynomial P(x) = x 2 −5x −14 and verify the
relationship between the zeroes and the coefficients.
OR
Write the quadratic polynomial whose sum of the zeroes is 2 and the product of the
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a numerator and denominator the new fraction obtained is more than the original

fraction. Find the original fraction.

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27) In the figure, altitudes AD and CE of  ABC intersect each other at the point P.
Prove that: (i)  AEP ~  CDP
(ii)  ABD ~  CBE

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

29) Find the ratio in which the line segment joining the points 𝐴(1, – 5) and 𝐵(– 4, 5) is
divided by the 𝑥 − 𝑎𝑥𝑖𝑠. Also find the coordinates of the point of division.
OR
Find the coordinates of the point of trisection of the line segment joining the
points (2, −2) and (−7, 4).

30) Prove that + = 𝑠𝑖𝑛𝐴 + 𝑐𝑜𝑠𝐴.

OR
√
Evaluate :
√

31) A horse is tied to a peg at one corner of a square shaped grass field of side 15m by
means of a 5m long rope.
Find (i) the area of that part of the field in which the horse can graze.
(ii) the increase in the grazing area if the rope were 10m long instead of 5m.

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32) Find the Mean for the following frequency distribution table.

Class interval frequency
10 – 14 2
15 -19 3
20 -24 5 m
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30 – 34 2
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Find a
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the Median for the following frequency distribution table.

Class 100-150 150-200 200-250 250-300 300-350
interval
frequency 6 3 5 20 10

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33) Two fair dice are rolled simultaneously. Find the probability of getting
i) two different digits on the top faces
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iii) the difference of digits on the a
top faces to be 1

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

34) In an arithmetic progression of 40 terms the sum of first 9 terms is 153 and the sum of

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last 6 terms is 687. Find the first term and the common difference of the progression
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The digits of a positive integer having 3 digits are in arithmetic
a of the digits is 9. The number obtained by reversing the digits is 396 more than the
original number. Find the number.

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35) Solve the given pair of linear equations by graphical method.
2𝑥 + 𝑦 = 8
𝑥 − 𝑦 = 1

36) State and prove Basic Proportionality theorem (Thales Theorem).
OR
Prove that ‘If one angle of a triangle is equal to one angle of the other triangle and the
sides including these angles are proportional, then the two triangles are similar. ‘

37) The angle of elevation of a bird at B from a point 100m above the surface of a lake is
300 and the angle of depression of its reflection (D) in the lake from the same point is
600. Find the height of the bird from the surface of the lake.

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VI. Answer the following question: 1x5=5

38) A solid is in the shape of a cone placed on the cylinder as shown in the figure. The radii
of both the cylinder and the cone are equal to 5cm. If the height of the cylinder is 11cm

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and the total height of the solid is 23cm, then find the curved surface area and volume
of the solid.
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A milk tank is in the shape of a cylinder
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ends of it as shown in figure. If the total height of the tank is 6m and the radius is 1m,
calculate the maximum quantity of milk in litres that can be filled in the tank.

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