Karnataka SSLC Preparatory Exam Model Question Paper 2023 Maths

PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003

KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru-560003

S.S.L.C. MODEL QUESTION PAPER 2022-23
Subject : MATHEMATICS
Medium : English
Time : 3 hours 15 minutes Subject Code : 81E
Max. Marks : 80
CCE-RF
Regular Fresh

General Instructions to the Candidate :

1. This question paper consists of objective and subjective types of 38 questions.

2. This question paper has been sealed by reverse jacket. You have to cut on
the right side to open the paper at the time of commencement of the
examination. Check whether all the pages of the question paper are intact.

3. Follow the instructions given against both the objective and subjective types of
questions.

4. Figures in the right hand margin indicate maximum marks for the questions.

5. 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.

81-E 2
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 x 1 = 8]

1. If the nth term of an arithmetic progression is an=3n+1, then the 4th term
of the progression is

(A) 10 (B) 13 (C) 11 (D) 12

2. The rational number having a non-terminating and repeating decimal
expansion in the following is
1 7 5 1
(A) 2 (B) (C) (D)
5 2 x5
2
2x 7 23

3. In a class, ''the number of boys (x) is 5 more than the number of girls
(y)." The linear equation form of this statement is

(A) x - y = 5 (B) x = 5y

(C) y - x = 5 (D) x + y = 5

4. The quadratic polynomial whose sum and product of zeroes are 4 and
5 respectively is

(A) p(x) = x²-4x-5 (B) p(x) = x+4x-5

(C) p(x) = x²-5x+4 (D) p(x) = x²-4x+5

5. The coordinates of the midpoint of the line segment joining the points
(4, 3) and (2, 1) is

(A) (2, 3) (B) (2, 2) (C) (3, 2) (D) (1, 1)

3 81-E
D
6.

A

4.5 cm

3 cm

B 4 cm C E ? F

In the figure ABC ∼ DEF. If AB=3cm, BC= 4cm and
DE = 4.5cm, then the measure of EF is

(A) 8 cm (B) 6 cm (C) 7 cm (D) 6.5 cm

7. In the figure, BP and BQ are the tangents to the circle with centre 'O'.
If OPQ = 20°, then the measure of PBQ is
P

200

O B

Q

(A) 40° (B) 160° (C) 140° (D) 20°

[ Turn over

81-E 4
8. The total surface area of the solid given in the figure is

'l'cm

'h'cm

'r'cm

(A) A = πrl cm2 (B) A = 2πrh cm2

(C) A = πr(r+l) cm2 (D) A = πr2l cm2

II. Answer the following questions [8 x 1 = 8]

9. Find the HCF of 7 and 11.

10. How many solutions do the pair of linear equations has, if the lines
represented by them are coincident?

11. Write the degree of the polynomial p(x) = x²+2x3-5x4+6 ?

12. Find the discriminant of the quadratic equation x²-2x-3=0.

13. Write the formula to find the volume of the frustum of a cone, if the
radii of its circular bases are 'r1' and 'r2' and its height is 'h'.

14. If the probability of raining on a particular day is 0.75, then find the
probability of not raining on the same day.

5 81-E
15. If the ratio of the areas of two similar triangles is 64 : 121, then find the
ratio of their corresponding sides.

16. Find the distance between the origin and the point (3, 4).

III. Answer the following questions. [8x2=16]

17. Solve the given pair of linear equations.

2x+y = 7

x-y = 2

18. Find the 30th term of the arithmetic progression 7, 11, 15 .................
using formula.

19. Find the roots of the quadratic equation x²+4x+5=0, using the 'quadratic
formula'.
OR
Find the roots of the quadratic equation 2x²+x-4=0 by the method of
completing the square.

20. Prove that 5+√3 is an irrational number.

OR

Find the LCM of 12, 15 and 21 by the method of prime factorization.

[ Turn over

81-E 6
21. In the figure, write the value of sinP and sin (90°-R).
P

I
√2

Q R
I

22. Construct a pair of tangents to the circle of radius 3.5cm, which are
inclined to each other at an angle of 80°.

23. There are 6 red, 5 blue and 4 green balls in a box. A ball is drawn at
random from the box. What is the probability that the ball drawn is

(i) not green

(ii) red

24. In the figure, ABC is a right angled triangle and BAC = 90°. If AD⊥BC
and BD=DC then prove that BC² = 4AD2.
A

B D C

IV. Answer the following questions [9x3=27]

25. Divide the polynomial p(x) = x3-3x²+5x-3 by the polynomial
g(x) = x²-2 and find the quotient q(x) and remainder r(x).

7 81-E
26. The area and perimeter of a rectangular field are 60m² and 32m
respectively. Find the length and breadth of the field.

OR

A bus travels 360 km distance with uniform speed. If the speed of the
bus had been 10km/h more, it would have taken 3 hours less for the
same journey. Find the speed of the bus.

27. Find the 'mean' for the following grouped data.

Class-Interval Frequency
0-20 12
20-40 14
40-60 8
60-80 6
80-100 10

OR

Find the 'median' for the following grouped data

Class-Interval Frequency
0-10 5
10-20 8
20-30 20
30-40 15
40-50 7
50-60 5

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81-E 8
28. A life insurance agent found the following data for distribution of
age of 100 policy holders. Draw 'less than type' ogive for the given
data.

Number of policy holders
Age (In years)
(cumulative frequency)
Less than 20 12
Less than 25 25
Less than 30 40
Less than 35 66
Less than 40 84
Less than 45 100

29. Prove that "the lengths of tangents drawn from an external point to a
circle are equal".
1
30. Prove that (cosecA - sinA) (secA - cosA) =
tanA+cotA
OR
sin30o + tan45o - cosec60o
Find the value of
sec30o + cos60o + cot45o

31. Construct a triangle of sides 6cm, 8cm and 10cm. Then construct
3
another triangle whose sides are times the corresponding sides of
4
the given triangle.

9 81-E
32. In the figure, the length of the arc AB of the circle with centre 'O' is.
11cm. If OP=4cm then find the area of the shaded region.
A

P

O B

33. Find the coordinates of the point which divides the line segment joining
the points (-1,7) and (4,-3) in the ratio 2:3.

OR

Find the area of the triangle whose vertices are (7, -2), (5, 1) and (1, 4)

V. Answer the following questions. [4x4=16]

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

x + y= 5

2x + y = 7

35. State and prove 'Basic Proportionality Theorem' (Thales Theorem).

[ Turn over

81-E 10
36. As observed from the top of a building standing vertically on the
ground, the angle of depression of a point 'C' on the ground is 60°.
From the foot (B) of the building when moved through point 'C' in a
straight line and observe the top of the building, from point 'P', if the
angle of elevation has to be 30O (as shown in the figure) then show that
the distance moved from 'C' to 'P' is twice the distance BC.

A
600

300
B P
C

37. The sum of first 'n' terms of an arithmetic progression is 222 and sum of
its first (n-1) terms is 187. If the first term of the progression is 2, then
find the arithmetic progression.

OR

The last term of an arithmetic progression consisting of 12 terms is
37. If the sum of the two middle terms of the progression is 41, then
find the arithmetic progression and also the sum of the terms of the
arithmetic progression.

11 81-E
VI. Answer the following question. [1x5=5]

38. A metal memento has to be prepared by placing a solid sphere on a solid
cylinder as shown in the figure. Find quantity of the metal required to
prepare this memento, such that the radius of the cylinder is 6cm and its
height is 14cm and the radius of the sphere is 2.1cm. And also calculate
the cost of painting the surface of the sphere with golden colour at the
rate of 10 paise per cm2.

2.1cm

14cm

6cm

[ Turn over

PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003

KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
Malleshwaram, Bengaluru-560003

J¸ï.J¸ï.J¯ï.¹. ªÀiÁzÀj ¥Àæ±ÉߥÀwæPÉ 2022-23
«µÀAiÀÄ : UÀtÂvÀ
ªÀiÁzsÀåªÀÄ : PÀ£ÀßqÀ
¸ÀªÀÄAiÀÄ: 3 UÀAmÉ 15 ¤«ÄµÀUÀ¼ÀÄ «µÀAiÀÄ ¸ÀAPÉÃvÀ: 81K
UÀjµÀ× CAPÀUÀ¼ÀÄ : 80
CCE-RF
±Á¯Á C¨sÀåyðUÀ½UÉ

¥ÀjÃPÁëyðUÀ½UÁV ¸ÁªÀiÁ£Àå ¸ÀÆZÀ£ÉUÀ¼ÀÄ :

1. F ¥Àæ±ÉߥÀwæPÉAiÀÄÄ ªÀ¸ÀÄÛ¤µÀ× ªÀÄvÀÄÛ «µÀÀAiÀĤµÀ× ªÀiÁzÀjAiÀÄ MlÄÖ 38 ¥Àæ±ÉßUÀ¼À£ÀÄß ºÉÆA¢zÉ.

2. F ¥Àæ±ÉߥÀwæPÉAiÀÄÄ »ªÀÄÄäR eÁPÉmï ªÀÄÆ®PÀ ªÉƺÀgÀÄ (¹Ã¯ï) ªÀiÁqÀ¯ÁVzÉ.
¥ÀjÃPÉë ¥ÁægÀA¨sÀªÁUÀĪÀ ¸ÀªÀÄAiÀÄPÉÌ ¤ªÀÄä ¥Àæ±ÉߥÀwæPÉAiÀÄ §®§¢ ¥Á±ÀéðªÀ£ÀÄß PÀvÀÛj¹,
¥Àæ±ÉߥÀwæPÉAiÀÄ°è J¯Áè ¥ÀÅlUÀ¼ÀÄ EªÉAiÉÄà JAzÀÄ ¥ÀjÃQë¹PÉƽî.

3. ªÀ¸ÀÄÛ¤µÀ× ªÀÄvÀÄÛ «µÀÀAiÀĤµÀ× ªÀiÁzÀjAiÀÄ ¥Àæ±ÉßUÀ½UÉ PÉÆnÖgÀĪÀ ¸ÀÆZÀ£ÉUÀ¼À£ÀÄß ¥Á°¹.

4. §® ¨sÁUÀzÀ°è PÉÆnÖgÀĪÀ CAQUÀ¼ÀÄ ¥Àæ±ÉßUÀ½VgÀĪÀ ¥ÀÇtð CAPÀUÀ¼À£ÀÄß vÉÆÃj¸ÀÄvÀÛªÉ.

5. ¥Àæ±ÉߥÀwæPÉAiÀÄ£ÀÄß N¢PÉƼÀî®Ä 15 ¤«ÄµÀUÀ¼À PÁ¯ÁªÀPÁ±ÀªÀÇ ¸ÉÃjzÀAvÉ, GvÀÛj¸À®Ä
¤UÀ¢¥Àr¸À¯ÁzÀ ¸ÀªÀÄAiÀĪÀ£ÀÄß ¥Àæ±ÉߥÀwæPÉAiÀÄ ªÉÄïÁãUÀzÀ°è ¤ÃqÀ¯ÁVzÉ.

81-K 2
I. F PɼV
À £À ¥À±
æ ßÉ UÀ½UÉ CxÀªÁ C¥ÀÇtð ºÉýPÉU½
À UÉ £Á®ÄÌ ¥ÀAiÀiÁðAiÀÄ GvÀg
Û U
À ¼
À £
À ÄÀ ß
¤ÃqÀ¯ÁVzÉ. CªÀÅUÀ¼À°è ¸ÀÆPÀÛªÁzÀ GvÀÛgÀªÀ£ÀÄß Dj¹, CzÀgÀ PÀæªÀiÁPÀëgÀzÉÆqÀ£É
¥ÀÇtð GvÀÛgÀªÀ£ÀÄß §gɬÄj.
[8 x 1 = 8]
1. MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ 'n' £Éà ¥ÀzÀ an=3n+1 DzÁUÀ D ±ÉæÃrüAiÀÄ
4£Éà ¥ÀzÀªÀÅ

(A) 10 (B) 13 (C) 11 (D) 12

2. EªÀÅUÀ¼À°è CAvÀåUÉƼÀîzÀ ªÀÄvÀÄÛ DªÀvÀðUÉƼÀÄîªÀ zÀ±ÀªÀiÁA±À «¸ÀÛgÀuÉAiÀÄ£ÀÄß
ºÉÆA¢gÀĪÀ ¨sÁUÀ®§Þ ¸ÀASÉåAiÀÄÄ
1 7 5 1
(A) (B) (C) (D)
52 2 x5
2
2x 7 23

3. MAzÀÄ vÀgÀUÀwAiÀÄ°è, ``UÀAqÀÄ ªÀÄPÀ̼À ¸ÀASÉåAiÀÄÄ (x) ºÉtÄÚ ªÀÄPÀ̼À ¸ÀASÉå
(y) VAvÀ 5 ºÉZÁÑVzÉ''. F ºÉýPÉAiÀÄ gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀt gÀÆ¥ÀªÀÅ

(A) x - y = 5 (B) x = 5y

(C) y - x = 5 (D) x + y = 5

4. ±ÀÆ£ÀåvÉUÀ¼À ªÉÆvÀÛ 4 ªÀÄvÀÄÛ UÀÄt®§Þ 5 DVgÀĪÀ MAzÀÄ ªÀUÀð§ºÀÄ¥ÀzÉÆÃQÛAiÀÄÄ
(A) p(x) = x²-4x-5 (B) p(x) = x2+4x-5

(C) p(x) = x²-5x+4 (D) p(x) = x²-4x+5

5. (4, 3) ªÀÄvÀÄÛ (2, 1) ©AzÀÄUÀ¼À£ÀÄß ¸ÉÃj¸ÀĪÀ gÉÃSÁRAqÀzÀ ªÀÄzsÀå©AzÀÄ«£À
¤zÉÃð±ÁAPÀUÀ¼ÀÄ
(A) (2, 3) (B) (2, 2) (C) (3, 2) (D) (1, 1)

3 81-K
D
6.

A

4.5 cm

3 cm

B 4 cm C E ? F

avÀæzÀ°è ABC ∼ DEF. AB=3cm, BC= 4cm ªÀÄvÀÄÛ DE = 4.5cm
DzÀgÉ EF £À C¼ÀvÉAiÀÄÄ
(A) 8 cm (B) 6 cm (C) 7 cm (D) 6.5 cm

7. avÀæzÀ°è 'O' PÉÃAzÀæªÁUÀļÀî ªÀÈvÀÛPÉÌ BP ªÀÄvÀÄÛ BQ UÀ¼ÀÄ ¸Àà±ÀðPÀUÀ¼ÁVªÉ.
OPQ = 20° DzÀgÉ PBQ C¼ÀvÉAiÀÄÄ
P

200

O B

Q

(A) 40° (B) 160° (C) 140° (D) 20°

[ Turn over

81-K 4
8. avÀæzÀ°è PÉÆnÖgÀĪÀ WÀ£ÁPÀÈwAiÀÄ ¥ÀÇtðªÉÄïÉäöÊ «¹ÛÃtðªÀÅ

'l'cm

'h'cm

'r'cm

(A) A = πrl cm2 (B) A = 2πrh cm2

(C) A = πr(r+l) cm2 (D) A = πr2l cm2

II. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. [8 x 1 = 8]

9. 7 ªÀÄvÀÄÛ 11 ªÀĸÁC ªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

10. JgÀqÀÄ eÉÆÃr gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀtUÀ¼À£ÀÄß ¥Àæw¤¢ü¸ÀĪÀ gÉÃSÉUÀ¼ÀÄ ¥ÀgÀ¸ÀàgÀ
LPÀåUÉÆAqÀgÉ, CªÀÅ JµÀÄÖ ¥ÀjºÁgÀUÀ¼À£ÀÄß ºÉÆA¢gÀÄvÀÛªÉ?

11. p(x) = x²+2x3-5x4+6 F §ºÀÄ¥ÀzÉÆÃQÛAiÀÄ ªÀĺÀvÀÛªÀÄ WÁvÀ(rVæ) §gɬÄj.

12. x²-2x-3=0 F ªÀUÀð ¸À«ÄÃPÀgÀtzÀ ±ÉÆÃzsÀPÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

13. ¥ÁzÀzÀ wædåUÀ¼ÀÄ 'r1' ªÀÄvÀÄÛ 'r2' ºÁUÀÆ JvÀÛgÀ 'h' DVgÀĪÀ ±ÀAPÀÄ«£À ©ü£ÀßPÀzÀ
WÀ£À¥sÀ®ªÀ£ÀÄß PÀAqÀÄ»rAiÀÄĪÀ ¸ÀÆvÀæªÀ£ÀÄß §gɬÄj.

14. MAzÀÄ ¤¢ðµÀÖ ¢£ÀzÀAzÀÄ ªÀÄ¼É §gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 0.75 DzÀgÉ,
CzÉà ¢£ÀzÀAzÀÄ ªÀÄ¼É §gÀ¢gÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

5 81-K

15. JgÀqÀÄ ¸ÀªÀÄgÀÆ¥À wæ¨sÀÄdUÀ¼À «¹ÛÃtðUÀ¼À C£ÀÄ¥ÁvÀ 64 : 121 DVzÀÝgÉ,
CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À C£ÀÄ¥ÁvÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

16. ªÀÄÆ®©AzÀÄ ªÀÄvÀÄÛ (3, 4) ©AzÀÄUÀ¼À £ÀqÀÄ«£À zÀÆgÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

III. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. [8x2=16]

17. PÉÆnÖgÀĪÀ gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀtUÀ¼À eÉÆÃrAiÀÄ£ÀÄß ©r¹.

2x+y = 7

x-y = 2

18. 7, 11, 15 ................. F ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ 30£Éà ¥ÀzÀªÀ£ÀÄß ¸ÀÆvÀæ
G¥ÀAiÉÆÃV¹ PÀAqÀÄ»r¬Äj.

19. x²+4x+5=0 F ªÀUÀð ¸À«ÄÃPÀgÀtzÀ ªÀÄÆ®UÀ¼À£ÀÄß ``ªÀUÀð ¸À«ÄÃPÀgÀtzÀ
¸ÀÆvÀæ'' G¥ÀAiÉÆÃV¹ PÀAqÀÄ»r¬Äj
CxÀªÁ
2x²+x-4=0 F ªÀUÀð¸À«ÄÃPÀgÀtzÀ ªÀÄÆ®UÀ¼À£ÀÄß ``ªÀUÀð¥ÀÇtðUÉƽ¸ÀĪÀ
«zsÁ£À¢AzÀ'' PÀAqÀÄ»r¬Äj.

20. 5+√3 MAzÀÄ C¨sÁUÀ®§Ý ¸ÀASÉå JAzÀÄ ¸Á¢ü¹.
CxÀªÁ
12, 15 ªÀÄvÀÄÛ 21 gÀ ®¸ÁC ªÀ£ÀÄß C«¨sÁdå C¥ÀªÀvÀð£À «zsÁ£À¢AzÀ
PÀAqÀÄ »r¬Äj.

[ Turn over

81-K 6
21. avÀæzÀ°è sin P ªÀÄvÀÄÛ sin (90°-R) UÀ¼À ¨É¯ÉAiÀÄ£ÀÄß §gɬÄj.
P

I
√2

Q R
I

22. 3.5cm wædåzÀ ªÀÈvÀÛªÀ£ÀÄß gÀa¹, ªÀÈvÀÛPÉÌ ¸Àà±ÀðPÀUÀ¼À £ÀqÀÄ«£À PÉÆãÀ 80°
EgÀĪÀAvÉ MAzÀÄ eÉÆvÉ ¸Àà±ÀðPÀUÀ¼À£ÀÄß gÀa¹.

23. MAzÀÄ ¥ÉnÖUÉAiÀÄ°è 6 PÉA¥ÀÅ, 5 ¤Ã° ªÀÄvÀÄÛ 4 ºÀ¹gÀÄ ZÉAqÀÄUÀ½ªÉ.
¥ÉnÖUɬÄAzÀ AiÀiÁzÀÈaÒPÀªÁV MAzÀÄ ZÉAqÀ£ÀÄß ºÉÆgÀvÉUÉzÁUÀ CzÀÄ
(i) ºÀ¹gÀÄ DUÀ¢gÀĪÀ
(ii) PÉA¥ÀÅ DUÀĪÀ
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

24. avÀæzÀ°è ABC MAzÀÄ ®A§PÉÆãÀ wæ¨sÀÄdªÁVzÀÄÝ BAC = 90° DVzÉ.
AD⊥BC ªÀÄvÀÄÛ BD=DC DzÀgÉ, BC² = 4AD2 JAzÀÄ ¸Á¢ü¹.
A

B D C

IV. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ [9x3=27]

25. p(x) = x3-3x²+5x-3 F §ºÀÄ¥ÀzÉÆÃQÛAiÀÄ£ÀÄß g(x) = x²-2
§ºÀÄ¥ÀzÉÆÃQÛ¬ÄAzÀ ¨sÁV¹ ¨sÁUÀ®§Ý q(x) ªÀÄvÀÄÛ ±ÉõÀ r(x) £ÀÄß
PÀAqÀÄ»r¬Äj.

7 81-K

26. MAzÀÄ DAiÀÄvÁPÁgÀzÀ ªÉÄÊzÁ£ÀzÀ «¹ÛÃtð ªÀÄvÀÄÛ ¸ÀÄvÀÛ¼ÀvÉUÀ¼ÀÄ PÀæªÀĪÁV
60m² ªÀÄvÀÄÛ 32m DVªÉ. ºÁUÁzÀgÉ ªÉÄÊzÁ£ÀzÀ GzÀÝ ªÀÄvÀÄÛ CUÀ®UÀ¼À£ÀÄß
PÀAqÀÄ»r¬Äj.
CxÀªÁ
MAzÀÄ §¸ÀÄì 360 km zÀÆgÀªÀ£ÀÄß KPÀgÀÆ¥À dªÀzÉÆA¢UÉ PÀæ«Ä¸ÀÄvÀÛzÉ.
CzÀgÀ dªÀªÀÅ 10km/h ºÉZÁÑzÀgÉ, CµÉÖà zÀÆgÀªÀ£ÀÄß PÀæ«Ä¸À®Ä CzÀÄ
3 UÀAmÉ PÀrªÉÄ PÁ®ªÀ£ÀÄß vÉUÉzÀÄPÉƼÀÄîwÛvÀÄÛ. ºÁUÁzÀgÉ §¹ì£À dªÀªÀ£ÀÄß
PÀAqÀÄ»r¬Äj.

27. F PɼÀV£À ªÀVÃðPÀÈvÀ zÀvÁÛA±ÀUÀ½UÉ `¸ÀgÁ¸Àj'AiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

ªÀUÁðAvÀgÀ DªÀÈwÛ
0-20 12
20-40 14
40-60 8
60-80 6
80-100 10

CxÀªÁ
F PɼÀV£À ªÀVÃðPÀÈvÀ zÀvÁÛA±ÀUÀ½UÉ ªÀÄzsÁåAPÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

ªÀUÁðAvÀgÀ DªÀÈwÛ
0-10 5
10-20 8
20-30 20
30-40 15
40-50 7
50-60 5

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28. M§â fêÀ «ªÀiÁ KeÉAlgÀÄ ¥ÀqÉzÀ 100 ¥Á°¹zÁgÀgÀ ªÀAiÀĸÀÄìUÀ¼À
«¸ÀÛgÀuÉAiÀÄ zÀvÁÛA±ÀUÀ¼ÀÄ PɼÀV£ÀAvÉ EªÉ. F zÀvÁÛA±ÀUÀ½UÉ `PÀrªÉÄ
«zsÁ£ÀzÀ Nfêï' gÀa¹.

ªÀAiÀĸÀÄì ¥Á°¹zÁgÀgÀ ¸ÀASÉå
(ªÀµÀðUÀ¼À°è) (¸ÀAavÀ DªÀÈwÛ)
20 QÌAvÀ PÀrªÉÄ 12
25 QÌAvÀ PÀrªÉÄ 25
30 QÌAvÀ PÀrªÉÄ 40
35 QÌAvÀ PÀrªÉÄ 66
40 QÌAvÀ PÀrªÉÄ 84
45 QÌAvÀ PÀrªÉÄ 100

29. "MAzÀÄ ªÀÈvÀÛPÉÌ ¨ÁºÀå ©AzÀÄ«¤AzÀ J¼ÉzÀ ¸Àà±ÀðPÀUÀ¼À GzÀݪÀÅ
¸ÀªÀĪÁVgÀÄvÀÛzÉ." JAzÀÄ ¸Á¢ü¹.
1
30. (cosecA-sinA) (secA - cosA) = JAzÀÄ ¸Á¢ü¹.
tanA+cotA
CxÀªÁ
sin30o + tan45o - cosec60o
EzÀgÀ ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ »r¬Äj.
sec30o + cos60o + cot45o

31. 6cm, 8cm ªÀÄvÀÄÛ 10cm ¨ÁºÀÄUÀ¼À£ÀÄß ºÉÆA¢gÀĪÀ wæ¨sÀÄdªÀ£ÀÄß gÀa¹
£ÀAvÀgÀ ªÀÄvÉÆÛAzÀÄ wæ¨sÀÄdªÀ£ÀÄß CzÀgÀ ¥ÀæwAiÉÆAzÀÄ ¨ÁºÀÄ ªÉÆzÀ®Ä
gÀa¹zÀ wæ¨sÀÄdzÀ C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À 3 gÀ¶ÖgÀĪÀAvÉ gÀa¹.
4

9 81-K

32. avÀæzÀ°è 'O' PÉÃAzÀæªÁUÀļÀî ªÀÈvÀÛzÀ PÀA¸À AB AiÀÄ GzÀÝ 11cm ªÀÄvÀÄÛ
OP=4cm DzÀgÉ, bÁAiÉÄUÉƽ¹zÀ ¨sÁUÀzÀ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
A

P

O B

33. (-1,7) ªÀÄvÀÄÛ (4,-3) ©AzÀÄUÀ¼À£ÀÄß ¸ÉÃj¸ÀĪÀ gÉÃSÁRAqÀªÀ£ÀÄß 2:3 gÀ
C£ÀÄ¥ÁvÀzÀ°è «¨sÁV¸ÀĪÀ ©AzÀÄ«£À ¤zÉÃð±ÁAPÀUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
CxÀªÁ
(7, -2), (5, 1) ªÀÄvÀÄÛ (1, 4) F ©AzÀÄUÀ¼À£ÀÄß ±ÀÈAUÀUÀ¼ÁV ºÉÆA¢gÀĪÀ
wæ¨sÀÄdzÀ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

V. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹ [4x4=16]

34. PÉÆnÖgÀĪÀ gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀtUÀ¼À eÉÆÃrAiÀÄ ¥ÀjºÁgÀªÀ£ÀÄß £ÀPÉëAiÀÄ
«zsÁ£À¢AzÀ PÀAqÀÄ »r¬Äj.
x + y= 5

2x + y = 7

35. `ªÀÄÆ® ¸ÀªÀiÁ£ÀÄ¥ÁvÀvÉAiÀÄ ¥ÀæªÉÄÃAiÀÄ' (xÉïïì ¥ÀæªÉÄÃAiÀÄ) ªÀ£ÀÄß
¤gÀƦ¹ ªÀÄvÀÄÛ ¸Á¢ü¹.

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36. £É®zÀ ªÉÄÃ¯É £ÉÃgÀªÁV ¤AwgÀĪÀ MAzÀÄ PÀlÖqÀzÀ vÀÄ¢¬ÄAzÀ £É®zÀ ªÉÄð£À
MAzÀÄ ©AzÀÄ 'C' ªÀ£ÀÄß «ÃQë¹zÁUÀ GAmÁUÀĪÀ CªÀ£ÀvÀ PÉÆãÀªÀÅ 60°
DVzÉ. avÀæzÀ°è vÉÆÃj¹gÀĪÀAvÉ, PÀlÖqÀzÀ ¥ÁzÀ (B) ¢AzÀ £É®zÀ ªÉÄð£À
'C' ©AzÀÄ«£À ªÀÄÆ®PÀ £ÉÃgÀªÁV ZÀ°¹, MAzÀÄ ©AzÀÄ (P) «¤AzÀ
PÀlÖqÀzÀ vÀÄ¢AiÀÄ£ÀÄß «ÃQë¹zÁUÀ G£ÀßvÀ PÉÆãÀªÀÅ 30° DUÀ¨ÉÃPÁzÀgÉ, 'C'
©AzÀÄ«¤AzÀ 'P' ©AzÀÄ«UÉ BC AiÀÄ JgÀqÀgÀµÀÄÖ zÀÆgÀ ZÀ°¸À¨ÉÃPÁUÀÄvÀÛzÉ.
JAzÀÄ vÉÆÃj¹.

A
600

300
B P
C

37. MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ªÉÆzÀ® 'n' ¥ÀzÀUÀ¼À ªÉÆvÀÛ 222 ªÀÄvÀÄÛ CzÀgÀ
ªÉÆzÀ® (n-1) ¥ÀzÀUÀ¼ÀªÀgÉV£À ªÉÆvÀÛ 187 DVzÉ. F ±ÉæÃrüAiÀÄ ªÉÆzÀ®£ÉÃ
¥ÀzÀªÀÅ 2 DzÁUÀ, ¸ÀªÀiÁAvÀgÀ ±ÉæÃrAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
CxÀªÁ
12 ¥ÀzÀUÀ½gÀĪÀ MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ°è PÉÆ£ÉAiÀÄ ¥ÀzÀªÀÅ 37 DVzÉ.
±ÉÃæ rüAiÀÄ ªÀÄzsåÀ zÀ JgÀqÄÀ ¥ÀzU
À ¼
À À ªÉÆvÀÛªÅÀ 41 DzÀg,É ¸ÀªiÀ ÁAvÀgÀ ±ÉÃæ rüAiÀÄ£ÀÄß
PÀAqÀÄ»rzÀÄ, F ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ¥ÀzÀUÀ¼À ªÉÆvÀÛªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

11 81-K

VI. PɼÀV£À ¥Àæ±ÉßUÉ GvÀÛj¹. [1x5=5]

38. MAzÀÄ WÀ£À ¹°AqÀj£À ªÉÄÃ¯É MAzÀÄ WÀ£ÀUÉÆüÀªÀ£ÀÄß PÀÆj¹ avÀæzÀ°ègÀĪÀAvÉ
MAzÀÄ ¯ÉÆúÀzÀ £É£À¦£À PÁtÂPÉAiÀÄ£ÀÄß vÀAiÀiÁj¸À¨ÉÃPÁVzÉ. ¹°AqÀgï£À
wædå 6cm ªÀÄvÀÄÛ JvÀÛgÀ 14cm ºÁUÀÆ UÉÆüÀzÀ wædå 2.1cm EgÀĪÀAvÉ F
£É£À¦£À PÁtÂPÉAiÀÄ£ÀÄß vÀAiÀiÁj¸À®Ä ¨ÉÃPÁUÀĪÀ ¯ÉÆúÀzÀ ¥ÀjªÀiÁtªÀ£ÀÄß
PÀAqÀÄ »r¬Äj ºÁUÀÆ UÉÆüÀzÀ ªÉÄïÉäöÊUÉ a£ÀßzÀ §tÚªÀ£ÀÄß ºÀZÀÑ®Ä ¥Àæw
ZÀzÀgÀ ¸ÉAn«ÄÃlgïUÉ 10 ¥ÉʸÉAiÀÄAvÉ, vÀUÀ®ÄªÀ ªÉZÀѪÀ£ÀÄß PÀAqÀÄ»r¬Äj.

2.1cm

14cm

6cm

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