Karnataka SSLC Model Question Paper 2027 for Mathematics (Paper 2, English Medium)

FOR KARNATAKA CLASS 10 PREPARATION

Karnataka SSLC Model
Question Paper 2027 for
Mathematics (Paper 2,
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
MALLESHWARAM, BENGALURU- 560003
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«µÀAiÀÄ : UÀtÂvÀ
SUBJECT: MATHEMATICS

(ಇಂ ಧ ಮ/ ENGLISH MEDIUM)

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ಷಯ ಸಂ ೕತ : 81-E Subject Code : 81-E

ಸಮಯ: 3 ಗಂ 15 ಷಗ
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ಗ ಷ ಅಂಕಗ : 80 l as (Max. Marks: 80)
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General Instructions to the candidate:
1. This question paper consists of 38 questions.
2. Follow the instructions given against the questions.
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The maximum time to answer the paper is given at the ltop
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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. Rational number among the following is

(A) √3 (B) √4

(C) √5 (D) √7

2. The Empirical relationship between the three measures of central tendency is

(A) 3Mean= 2Median+ Mode (B) Mean = 3Median + Mode

(C) 3Median = 2Mean + Mode (D) Mode = 3Mean + 2Mode

3. The first term of an arithmetic progression is ′𝑎′ and the common difference is ′𝑑′.

The nth term of the progression is,

(A) 𝑎 = 𝑎 + (𝑛 − 1)𝑑 (B) 𝑎 = 𝑎 + (𝑛 + 1)𝑑

(C) 𝑎 = 𝑎 − (𝑛 − 1)𝑑 (D) 𝑎 = (𝑛 + 1)𝑑

4. In the following, 𝑠𝑖𝑛 30° + 𝑐𝑜𝑠 30° is equal to

(𝐴) sin 60° (𝐵)2 sin 30°

(𝐶) cos 90° (𝐷)2 cos 45°

5. If the curved surface area of a cylinder is 100𝑐𝑚 and its height is 10𝑐𝑚, then the
circumference of its base is,

(𝐴) 100 𝑐𝑚 (𝐵) 20 𝑐𝑚

(𝐶) 50 𝑐𝑚 (𝐷) 10 𝑐𝑚

6. The lines represented by the pair of linear equations 𝑥 + 2𝑦 − 4 = 0 and
2𝑥 + 4𝑦 − 12 = 0 are,

(𝐴) Intersecting lines (𝐵) Perpendicular lines

(𝐶) Coinciding lines (𝐷) Parallel lines

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7. A bird flies along OA from point O to point A as shown in the figure. The distance
covered by the bird is,

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a (𝐴) 4 units (𝐵) 3 units

(𝐶) 5 units (𝐷) 7 units

8. In ∆𝐴𝐵𝐶, 𝐴𝐵 = 4𝑐𝑚, 𝐵𝐶 = 3.5𝑐𝑚, 𝐴𝐶 = 2.5𝑐𝑚 and in ∆𝐷𝐸𝐹, 𝐷𝐹 = 7.5𝑐𝑚.

If ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹, then the perimeter of ∆𝐷𝐸𝐹 is,

om15𝑐𝑚
(A) 30𝑐𝑚 (B) 20𝑐𝑚
c. (D)
(C) 10𝑐𝑚
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Answer the following questions: 8×𝟏=𝟖

9. Write the formula to find the volume of a sphere with radius ′𝑟′.

10. Write the quadratic equation 2𝑚 = 2 − 𝑚 in the standard form.

11. Write the conditions for the two polygons of same number of sides to be similar.

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13. If the 4th term of an arithmetic progression is 11 and the 3rd term is 7, then find its
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14. Find the value of 𝑝(2) in the polynomial 𝑝(𝑥) = 𝑥 − 1.

15. Write the value of 𝑃(𝐸 ) + 𝑃(𝐸) with reference to the probability of an event.

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Page 3 of 9

16. If the pair of liner equations in two variables are inconsistent, then how many
solutions do they have?

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

17. Find which term of the arithmetic progression 2, 7, 12......is 47 using formula.

OR

In an arithmetic progression if the first term is 1 and 14th term is 53 then, find its
nth term.

18. In the figure, find the value of sin∝ + cosθ

19. Solve the given pair of linear equations by elimination method.
4𝑥 + 𝑦 = 13
𝑥−𝑦 =2

20. State the fundamental theorem of arithmetic. Write the prime factors of 30.

21. If the quadratic equation 𝑥 + 𝑏𝑥 + 9 = 0 has two equal real roots, then find the
value of ‘b’ and hence find the equation.

22. Find the distance between the points 𝑃 (−5, 7) and Q (−1, 3) using the distance
formula.

23. In the given figure, AP, AX and AY are the tangents drawn to the circles with centres
𝐶 𝑎𝑛𝑑 𝐷. Prove that AY=AX.

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24. In a school, there are 45 and 54 students in A and B sections of 10th standard
respectively. Find the minimum number of books to be purchased for the school
library so that when distributed to section-A or section-B separately such that each
student gets equal number of books.

OR

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The HCF of two numbers is 14 and their LCM is 28 more than 10 times the HCF. If
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one of the numbers
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IV. Answer 9 x 3 = 27

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

through the point of contact."

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26. Prove that, = 𝑐𝑜𝑠𝑒𝑐 𝐴 + cot 𝐴

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Prove that, secθ(1 – sinθ) (secθ

27. In a quadratic polynomial sum of the zeroes is 1 and the difference of the zeroes is 7.
Find the quadratic polynomial.

28. The ages of two students A and B are 19 years and 15 years respectively. Find
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how many years it will take so that the product of their ages becomes equal to 480.

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A dealer sells an article for Rs.24 and gains as much percent as
a the cost price of the article.

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Page 5 of 9

29. The triangle PQR is right angled at ∠𝑄 with sides 𝑃𝑄 = 6𝑐𝑚 and 𝑄𝑅 = 12𝑐𝑚.
square ABCQ is inscribed in the triangle as shown in the figure. Find the length of
the side of the square.

30. Find the Mean for the following data.
Class interval Frequency
2−6 4
6 − 10 8
10 − 14 2
14 − 18 1
18 − 22 5

OR

Find the Mode for the following data.
Class interval Frequency
0 − 10 6
10 − 20 9
20 − 30 15
30 − 40 9
40 − 50 1

31. A box contains 20 discs with numbers 1 to 20 written on them. A disc is drawn at
random from the box. Find the probability that the number obtained on the disc is
(i) divisible by 2 but not by 3.
(ii) both perfect square and perfect cube.

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32. In the figure, the area of the sector 𝑂𝐴𝑌𝐵 is 462𝑐𝑚 . If ∠𝐴𝑂𝐵 = 120°, then find the
length of the arc 𝐴𝑌𝐵.

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In the figure, if the radius of the circle is 21𝑐𝑚 and ∠𝐴𝑂𝐵 = 120°, then find the area
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33. Find the ratio in which the point (−4, 6) divides the line segment joining the points
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(−6,10) 𝑎𝑛𝑑 (3, −8) internally.
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V. Answer the following questions:a 4 x 4 = 16

34. Prove that, "If a line is drawn parallel to one side of a triangle to intersect the other
two sides in distinct points, then the other two sides are divided in the same ratio."

OR

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35. Solve the given pair of linear equations by graphical method.

2𝑥 + 𝑦 = 4
𝑥+𝑦 =3

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Page 7 of 9

36. Sum of the first five terms of an arithmetic progression is 75 less than the sum of the
next five terms. If the sum of 2nd term and 12th term of the same progression is 50,
then find the progression.

37. A television tower stands vertically on the bank of a canal. From a point on the
other bank directly opposite the tower, the angle of elevation of the top of the tower
is 60°. From another point 20𝑚 away from this point, on the line joining this point
to the foot of the tower, angle of elevation of the top of the tower is 30°. Find the
height of the tower and the width of the canal. (Use √3 = 1.732)

OR

A straight highway leads to the foot of a tower. A man standing at the top of the
tower observes a car at an angle of depression of 30°, which is approaching the foot
of the tower with a uniform speed. 6 seconds later, the angle of depression of the car
is found to be 60°. Find the time taken by the car to reach the foot of the tower from
this point.

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VI. Answer the following question: 1x5=5

38. A warehouse is in the shape of a cuboid surmounted by a half cylinder as shown in
the figure. A merchant plans to paint the outer surface of the warehouse excluding
the door of dimension 2𝑚 × 3𝑚 installed in the front wall. The length and breadth of
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the warehouse are 12𝑚 and 4𝑚 respectively and its total height is 6𝑚. If half a litre
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of paint covers cone
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OR
A girl purchases a hemispherical wooden pen stand of radius 7𝑐𝑚 as shown in the
figure. 5 conical holes are drilled on it. If the radius of the base of each hole is 0.7𝑐𝑚 and
depth is 2.4𝑐𝑚 then find the total surface area of the pen stand and also find the
quantity of wood in it.
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