Karnataka SSLC Model Question Paper 2027 for Mathematics (Paper 4, English Medium)

FOR KARNATAKA CLASS 10 PREPARATION

Karnataka SSLC Model
Question Paper 2027 for
Mathematics (Paper 4,
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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SUBJECT: MATHEMATICS

(ಇಂ ಧ ಮ/ ENGLISH MEDIUM)
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ಷಯ ಸಂ ೕತ : 81-E .co Subject Code : 81-E
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ಸಮಯ: 3 ಗಂ 15 ಷಗ
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ಗ ಷ ಅಂಕಗ : 80
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General Instructions to the candidate:

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1. This question paper consists of 38 questions.
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Figures in the right-hand margin indicate maximum marks

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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 11

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 maximum number of zeroes of a quadratic polynomial is,

(A) 4 (B) 1

(C) 2 (D) 3

2. If the pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 have infinite
solutions, then the correct relation among the following is,

a1 b1 a1 b1 c1
(A)  (B)  
a2 b2 a2 b2 c2
a b c
(C) ≠ = (D) 1  1  1
a2 b2 c2

3. If one of the roots of the quadratic equation 2x2 +ax +6 =0 is 2, then the value of ‘a’ is

(A) 7 (B)

(C) −7 (D)

4. The formula to find the sum of first ‘ n’ natural numbers is,

(A) Sn =n(n+1) (B) Sn = n2

( ) ( )
(C) Sn = (D) Sn =

2

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5. In the given figure, the value of ‘x’ is

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(A) 4 cm (B) 5 cm

(C) 6cm (D) 8 cm

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6. The formula to find mean of the grouped data by direct method is

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(A)𝑥̅ =
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(C) 𝑥̅ = (D) 𝑥̅ = Σ𝑓 𝑥

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7. The volume of a cube with edge is 5 cm is
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8. If sin 𝐴 = , then the value of 𝐴 is,
√

(A) 300 (B ) 450

(C) 900 (D) 600

II ANSWER THE FOLLOWING QUESTIONS : 8 X1 = 8

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

10. If the lines represented by the equations 12x + py + 8 = 0 and 4x + 2y + 2 = 0 are

parallel, then find the value of ‘p’.

11. In an arithmetic progression the sum of the first 4 terms is 20 and the sum of first 3

terms is 12, then find the 4th term of the progression.

12. In ∆ABC, DE || AB. If CD = 3 cm, EC = 4 cm, BE = 6 cm, then find the measure of DA.

13. If the probability of winning a game is 0.8 then find the probability of losing the same

game.

14. If a and b are prime numbers, then write their H.C.F.

15. Two diagonals of a parallelogram intersect at a point ‘O’. If the coordinates of the end

points of one of the diagonals are (1, 1) and (7, 4) then find the coordinates of the point ‘O’.

16. Write the formula to find the surface area of a sphere whose radius is ‘r’ units.

4

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

17. There are 10 terms in an arithmetic progression. If the last term is 34 and common
difference is 3, then find the first term of the progression.

OR
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Find the number of terms in the arithmetic progression 7, 13, 19..........205
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18. Determine the nature of the roots of the quadratic equation 𝑥 − 9 = 0
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19. Solve the

5x − y = 14

x − y = −2

20. Write the coordinates of the origin and also write the distance of the point D (3, −4)
from the 𝑥-axis.

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21. Prove that 2 − √5 is an irrational number. .
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22. A quadrilateral ABCD is drawn toacircumscribe a circle. Prove that AB + CD = AD + BC

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is supplementary to the angle subtended by the line segments joining the points of
contact at the centre.

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23. Evaluate: 2tan2450 + cos2300 – sin2600

24. The length and breadth of a rectangular field are 147m and 56m respectively. Calculate

the maximum length of a rod that can be used to measure both length and breadth

exactly. How many times this rod has to be used to measure the length of the field?

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

25. Write the quadratic polynomial whose sum of the zeroes is 2 and product of the zeroes

is −15. Also and find the zeroes of this polynomial.

26. An umbrella has 8 ribs which are equally spaced . Assuming umbrella to be a flat circle

of radius 45 cm, find the area between the two consecutive ribs of the umbrella.

OR

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm
sweeping through an angle of 115°. Find the total area cleaned at each sweep of the
blades.

6

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27. In the figure, ABCD is a parallelogram. If point P divides AB in the ratio 2:3 and the
point Q divides DC in the ratio 4 : 1, then prove that OA = 2 × OC.

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OR

In the trapezium ABCD, AB || DC. Diagonals AC and BD intersect each other at the point
O. Prove that AO . DO = CO . BO

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28. Prove that, "The tangent at any point of a circle is perpendicular to the radius through

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the point of contact."
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29. A game consists of tossing a coin three times and noting its outcome each time. Person

‘A’ wins if all the tosses give the same result and loses otherwise. Person ‘B’ wins if the

outcome is at least two heads and loses otherwise. Calculate which person has the

greater probability of losing the game.
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pens he bought and the price of each pen.

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Page 7 of 11

31. In the figure, find the coordinates of the point which divides the line segment ‘AB’

internally in the ratio 1:2 using section formula.

32. Find the Mode for the following frequency distribution table.

class interval 10 -20 20 -30 30 -40 40 -50 50 - 60
frequency 3 9 6 7 5
OR

Find the Median for the following frequency distribution table.

class interval frequency
0 – 10 4
10 – 20 9
20 – 30 15
30 – 40 14
40 – 50 8

33. Prove that: − = 2 𝑐𝑜𝑡 𝐴

OR

Prove that: (𝑐𝑜𝑠𝑒𝑐𝐴 – 𝑠𝑖𝑛𝐴)(𝑡𝑎𝑛𝐴 + 𝑐𝑜𝑡𝐴) = 𝑐𝑜𝑡𝐴. 𝑐𝑜𝑠𝑒𝑐𝐴

8

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

34. 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”.
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Prove that “If in two triangles, corresponding angles are equal, then their corresponding
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35. The sum of first 5 terms of an arithmetic progression is 70 and the sum of first 10

terms is 290. Find the progression. Find which term of this progression is 48 more than

its 10th term.
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36. Solve the given pair of linear equationsa
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x + 3y = 11

x+y=5

37. Two poles of height 1.5m are standing vertically on either side of a flag post on a level
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elevation from the foot of the pole AB to the top of the flag 0

elevation from the top of pole CD to the top of the flag post is 450. Find the distance

between the poles. ( 𝑡𝑎𝑘𝑒 √3=1.7)

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OR

A building(AB) and a lamp post (CD) are standing vertically on a level ground as

shown in the figure. The angles of depression of the top and bottom of the lamp post

from the top of the building are found to be 30 0 and 600 respectively. If the height of

the building is 60m, then find the

(i) distance between the building and lamp post

(ii) height of the lamp post.

10

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VI. Answer the following questions: 1X5=5

38. A solid is made by joining a cone and a hemisphere on either sides of a cylinder with the

same radius as that of the cylinder as shown in the figure. The height of the cylinder and
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the cone are 30cm and 24cm respectively. If the volume of the cylinder is 4620cm 3 , then . co
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find the total surface area of the solid.
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OR

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Sanvi made a solid as shown in the figure. The total height of the solid is 14cm and the

diameter of the hemisphere and cone is 12cm. Find the total surface area and volume of

the solid.

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