AP Class 10 Model Paper 2027 Mathematics

FOR AP CLASS 10 EXAM PREPARATION

AP Class 10 2027
Model Paper ·
Mathematics
EXAM YEAR TYPE SUBJECT

AP Class 10 2027 Model Paper Mathematics

Notes · Sample Papers · Previous Year Papers · Mock Tests

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BLUE PRINT & MODEL PAPERS OF SSC PUBLIC EXAMINATIONS FOR THE ACADEMIC YEAR 2026-27
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se BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.

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a 15E & 16E

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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 32

15E & 16E

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15E & 16E

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m
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m .co BLUE PRINT & MODEL PAPERS OF SSC PUBLIC EXAMINATIONS FOR THE ACADEMIC YEAR 2026-27
s e m
se BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.

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SSC PUBLIC EXAMATIN
EXAMATINATIONS 2026 - 27
TINA

MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)

(ENGLISH VERSION)

Time : 3 Hours 15 Minutes Max. Marks : 100

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Instructions :

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1 . In the duration of 3hours 15 minutes, 15 minutes of time is allotted to read the question

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paper.

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2 . All answers shall be written in the answer booklet only.

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3 . Question paper consists of 4 Sections and 33 questions.

4 . Internal choice is available in section - IV only.

5 . Answers shall be written neatly and legibly.

SECTION - I 12 ´ 1 = 12 M

Note : i) Answer all the questions in one word or phrase.

ii) Each question carries 1 mark. 4
3
1. If a number Y is prime factorised then the y

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values of x and y in the given figure x ( )

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A) 10, 14 B) 21, 25 7

C) 21, 84

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D) 84, 21

2.
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Explore the pattern in the following polynomials and identify which one has zeroes 1

and 2. ( )

2 2 2 2
A) x – 3x + 2 B) x + 3x + 2 C) x – 2x + 3 D) x + 2x – 3

3. The pair of equations x – y = 1 and x + ky = 5 has a unique solution. If x = 2 and y = 1

then find the value of k ( )

1 −1
A) 3 B) –3 C) D)
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3 3
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4. Find the value of k if the equation x + kx + 6 = 0 has equal roots

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D) 2, 3, 5, 8

a 6. In Triangles PQR and TSM, ∠P = 55°, ∠Q = 25°, ∠M = 100° and ∠S = 25°. Which of the
following statement is correct. ( )

A) ∆PQR ∼ ∆TSM B) ∆QPR ∼ ∆SMT
C) ∆PRQ ∼ ∆TSM D) ∆QPR ∼ ∆TSM

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15E & 16E

7. Ravi is having a disgreement with his friend while comparing the values of sin 27° and

sin 72°. How would you help them resolve the conflict ? ( )

A) Ask them to stop discussing the problem to move to another question.

B) Explain the sine is an increasing function for angles between 0° and 90°, so sin 72° >

sin 27°.

C) Tell Ravi to accept his friends answer without any explanation.

D) Suggest that both answers are correct to avoid and argument.

8. A Group is finding the height of a tower using trignometric ratios arrange the following

steps in the correct sequence ( )

1) Calculate the height using the trigonometric ratio

2) Draw and label the right triangle

3) Identify the given measurements

4) Choose the appropriate trigonometric ratios

A) 3, 2, 4, 1 B) 2, 3, 1, 4 C) 4, 3, 2, 1 D) 3, 4, 2, 1

9. Draw a rough sketch to represent the following information.

The chord of larger circle is a tangent to a smaller concentric circle.

10. A farmer wants to sow seeds in a circular field of radius 14 m. Find the area of field to

be sown (in m ).
2
( )

A) 308 B) 616 C) 528 D) 704

11. The Total Surface Area of cylinder of radius r and height h is ( )

A) πr(r + h) B) 2πr(r + h) C) 2πr (r + h)
2
D) πr (r + h)
2

12. When a die is thrown once to find the Probability of getting an even number P(E).

Which of the following statements is true. ( )

A) Getting Even and Odd numbers are equally likely therefore P(E) = 0.5

n (E ) 3
B)
P (E ) = =
n (S ) 6
C) Both A and B. D) Neither A nor B.

SECTION - II 8 ´ 2 = 16 M

Note : i) Answer all the questions.

ii) Each question carries 2 marks.

13. Form a quadratic polynomial whose zeroes are a and b if a + b = 6 and ab = 4

14. Rahul believes that the qudartic equation x
2
+ 5x + 6 = 0 has both positive roots. Do you

agree with him justify your answer.

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15E & 16E

15. State AA criteria for similarity of two triangles.

16. The co-ordinates of the vertices of a triangle are A(5, 1), B(1, 5) and C(–3, –1). Find the

length of the median AD.

To solve the problem the class was divided into 3 groups.

Group 1: Draw triangle ABC and identified the median AD.

Group 2: Found the co-ordinates of the midpoint D of BC.

Group 3: Used the distance formula to find the length of AD.

Using the ideas contributed by all 3 groups, find length of AD.

1
17. If sin(A + B) = 1 and tan (A – B) = 0° < A + B ≤ 90° and A> B find the values of A
3
and B.

18. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at

Q so that OQ = 13 cm. Find the length of PQ.

a1 b1 c
19. On comparing the ratios
, and 1 findout whether the following equations one
a 2 b2 c2
consistent or inconsistent

5x – 3y = 11

–10x + 6y = 22

20. A person observes two banks of a river at angles of depression θ and θ (θ < θ ) from
1 2 1 2

the top of a tree of height h which is at a side of the river. The width of the river is 'd'.

Draw a rough diagram for the given situation.

Y

SECTION - III 8 ´ 4 = 32 M

Note : i) Answer all the questions.

ii) Each question carries 4 marks.

21. Observe the graph of a polynomial and answer
X' –1 3 X

the questions given below.

i) How many zeroes has the polynomial.

Y'

ii) What are the zeroes of given polynomial ?

−b
iii) If the polynomial is expressed as ax
2
+ bx + c what is the value of
a

iv) What is the product of its zeros.

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22. The speed of a boat in still wate is 11 km/hr. It can go 12 km upstream and return

downstream to the original point in 2 hours 45 min. Find the speed of the stream.

23. A Spiral is made up of successive semicircles with centres

alternatively at A and B starting with centre A of radii 0.5cm,

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1 cm, 1.5 cm, 2 cm as shown in figure what is the total length

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of such a spiral made up of 13 consecutive semicircles.

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24.

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State whether the following statements are true or false. Justify
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your answer.
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A) sin (A + B) = sin A + sin B B) sin θ = cos θ for all values of θ.
25. Joffer thinks that lengths of two tangents drawn to a circle from any external point are

not always equal. How would you resolve his conflict.

26. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest

diameter the hemisphere can have ? Find the surface area of the solid.

27. Write the formula for calculateing the median of grouped data. Explain the meaning of

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each symbol used in the formula.

28.

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Create any four different probability questions invloving two dice thrown simultaneously

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similar to the example question given below:

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Example: What is the probability of getting even numbers on the top faces of both dice

when two dice are thrown simultaneously.

SECTION - IV 5 ´ 8 = 40 M

Note : i) Answer all the questions.

ii) Each question carries 8 marks.

iii) There is an internal choice for each question.

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29. a) Given that 5 is an irrational number justify that 2 + 3 5 is also an irrational
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a b) Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18

respectively.

30. a) The following table shows the marks obtained by 40 students in a Maths test.

0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

3 5 9 10 8 5

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15E & 16E

i) Write class marks (x ) of each class.
i

ii) Find f x values for each class.
i i

iii) Find the mean of grouped data using the direct method.

OR

b) State and prove Basic proportionality (Thales) theorem.

31. a) The distance between points p(2, –3) and Q(10, y) is 10 units. By solving the problem

Jyothi says y has only one value. But Preethi disagrees with Jyothi. Resolve their

conflict by giving logical conclusion.

OR

b) A round table cover has six identical designs as shown in the

figure. The radius of the table cover is 28 cm. The cost of matching

2
the designs is `0.35 per cm . The students of class worked in

groups to solve the problem.

Group 1: Divided the design into six equal sectors and found the

angle of each sector.

Group 2 : Calculated the area of one design in a sector.

Group 3 : Calculated the total area of all 6 designs.

By using the ideas contributed by all the three groups. Find the total cost of making

the design.

32. a) One card is drawn from a well shuffled deck of 52 cards. Calculate the probability

of that card drawn will be

i) A numberd card ii) A letter card

iii) not a face card iv) A diamond but not face card.

OR

b) A solid cylinder has a height of 2.4 cm and a radius of 0.7 cm. A conical cavity of the

same height and radius is hollowed out. Find the total surface area of the remaining

2
solid to the nearest cm .

33. a) Draw the graph of the following pair of linear equations and find the solution from

the graph. x + 3y = 6 and 2x – 3y = 12

OR

b) The angles of depression of the top and the bottom of an 8 m tall building from the

top of a multi-storeyed building are 30° and 45°, respectively. Find the height of the

multi-storeyed building and the distance between the two buildings.

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BLUE PRINT & MODEL P
BLUE PAPERS ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN

BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

15E & 16E

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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 10 of 32

15E & 16E

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BLUE PRINT & MODEL P
BLUE PAPERS ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN

BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

15E & 16E

SSC PUBLIC EXAMATIN
EXAMATINATIONS 2026 - 27
TINA

MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 2)

(ENGLISH VERSION)

Time : 3 Hours 15 Minutes Max. Marks : 100

Instructions :

1 . In the duration of 3hours 15 minutes, 15 minutes of time is allotted to read the question

paper.

2 . All answers shall be written in the answer booklet only.

3 . Question paper consists of 4 Sections and 33 questions.

4 . Internal choice is available in section - IV only.

5 . Answers shall be written neatly and legibly.

SECTION - I 12 ´ 1 = 12 M

Note : i) Answer all the questions in one word or phrase.

ii) Each question carries 1 mark.

2
1. Prime factorisation of 156 = a ´ b ´ c then a + b + c =

2. Create a quadratic polynomial whose one zero is 2 + 3
3. Express y in terms of x from the equation 3x + 5y – 11 = 0.

4. Write any quadratic equation whose roots are reciprocals to each other.

5. Your friend writes the sequence 5, 8, 11, 15, 17 as an A.P. What would you tell to your

friend ?

6. In figure DE & BC, AD = 3 cm, BD = 4 cm and BC = 14 cm then DE = ___
A

3cm
A) 7 cm B) 6 cm
D E

4cm
C) 4 cm D) 3 cm
B C
14cm
adjacent side to θ
7. Your classmate writes cos θ=
opposite side to θ . Do you agree ? If not ?
State the correct trignometric ratio

8. Two students measure the height of a tree. One gets 20 m and the other get 22 m. What

should they do before deciding which answer is correct.

A) Accept the first answer only

B) Accept the second answer only

C) Recheck the measurements and calculations to system.

D) Ignore both answers.

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9. Draw a rough sketch of a circle and two lines parallel to a given line such that one is a

tangent and the other is a secant to the circle.

10. If the circumference of a circle and the perimeter of a square are equal, then the

A) Area of circle = Area of square

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B) Area of circle > Area of square

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C) Area of circle < Area of square

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D) We can't definitely say about the relation between Areas.
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11.
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The formula to find the volume of sphere of radius r cm is _________

4 2 4 3 3 3 3 2
A) πr B) πr C) πr D) πr
3 3 4 4

5
12. A friend says the probability of an event can be . How would you respond.
3
A) Agree, because probability can be any positive value

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B) Politely explain that probability of an event always lies between 0

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≤ P(Ε) ≤1. So, It
can't

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C) Ignore the friends opinion
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D) Say the answer is wrong without giving any reason.

SECTION - II 8 ´ 2 = 16 M

Note : i) Answer all the questions.

ii) Each question carries 2 marks.

13. Write two different linear polynomials in variable x, whose zero is –4 ?

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14. Student 1: The length of a recntangular park should be twice its breadth.

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Student 2 : The area of the park should 20 m . Use both student ideas to determine the

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length and breadth of the park.

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17. Draw a figure to represent the following sitatuion.

A student observes the top of a tower at angle of elevation 45°.

18. A tangent PQ at a point of a circle of radius 5 cm meets a line through the centre 'O' at

a point Q. So that OQ = 12 cm then what is the length of PQ.

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15E & 16E

19. For what condition will 3x + ky = 7 and 6x + 4y = 14 have exactly one solution ? Using

the condition find the value of k.

20. A point lies 4 units left of y - axis and 3 units below the x-axis many students ploted the

point is only in 1st quadrant. Write the correct co-ordinates. Name the quadrant.

SECTION - III 8 ´ 4 = 32 M

Note : i) Answer all the questions.

ii) Each question carries 4 marks.

21. A child has a die whose six faces shows the letters as given below.

A B C D E A
The die is thrown once using this data create 4 questions.

Eg: What is the probability of getting D when a die is thrown once ?

22. Write the formula to find mode of a grouped data and give the meanings of symbols

used in it.

23. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The

height of the cone is 2 cm and the diameter of the base is 4 cm Determine

the volume of the toy ?

24. Find two consecutive poisitive integers, sum of whose squares is 365.

25. In ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm Determine

i) sin A, cos A ii) sin C, cos C

26. How many two digit numbers are divisible by 3 ?

27. A circular rainwater harvesting pit has radius 4 m. Two support wires are drawn from

a common external point P and touches the pit boundary at points A and B.

a) Draw suitable figure.

b) What can you say about the lengths of two wires.

c) Name the theorem used.

d) Write the angle when a radius is drawn at the point of contact.

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15E & 16E

28. Observing the graph and answer the following Questions. y

1) Write the zeroes of the polynomial.

2) Find the sum of the zeroes of the polynomial.

3) Find the product of the zeroes of the polynomial.

4) Name the shape of the polynomial.

x' o 2 3 x

SECTION - IV 5 ´ 8 = 40 M

Note : i) Answer all the questions. y'

ii) Each question carries 8 marks.

iii) There is an internal choice for each question.

5+2 3
29. a) Given 3 is irrational. Prove that is also irrational. Using method of
7
contradiction.

OR

2
b) If the sum of the first n terms of an AP is 4n – n , what is the first term (that is S )?
1

What is the sum of first two terms? What is the second term similarly, find the third

th
the 10 and the nth terms.

30. a) In a classroom, 4 friends are seated at the points A, B, C and D. Champa and

Chameli walk into the class and after observing for a few minutes. They noticed the

co-ordinates of A, B, C and D are (3, 4), (6, 7), (9, 4) and (6, 1) respectively. Champa

asks Chameli, "Don't you think ABCD is a square", Chameli disagrees. Using distance

formula, find which of them is correct.

OR

b) A village has constructed a rain water harvesting pond in the shape of sector of a

circle with the radius 21 m and central angle 60° the curved boundary is fenced and

the area enclosed by the sector is used for storing rain water.

a) Find the length of curved boundary (arc)

b) Find the area of sector

c) Explain how rain water harvesting helps in conserving water resources.

31. a) The distribution below gives the weights of 30 students of a class. Find the median

weight of the students.

Weight (in kg) 40 - 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 70 - 75

No. of students 2 3 8 6 6 3 2

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 32

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OR

D C
b) i) Name the pair of similar triangles in the given
70°
figure. 125°
O
ii) Which similarity criterian is used in proving those

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triangles similar and state the similarity criterian.

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iii) Write the proportionality relation obtained from the similar triangles.

32.

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a) A game of chance consists of spinning an arrow which comes to rest pointing at one

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of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely out comes.
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7
8 1

2
i) 8 ii) an odd number

→
6 3
iii) a number greater than 3 iv) a number less than or equal to 8
5 4

OR

b) A solid design consisting of a right circular cone of height 120 cm and radius 60 cm

standing on hemisphere of radius 60 cm is placed upright in a right circular cylinder

full of water such that it touches the bottom. Find the volume of water left in the

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cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

33. a)
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graphicllay.

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i) 10 Students of Class X took part in a Mathematics quiz. If the number of girls is 4

more than the number of boys, find the number of boys and girls who took part

in the quiz.

OR

b) A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a

height of 88.2 m from the ground. The angle of elevation of the balloon from the

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to 30° (see figure). FInd the distance travelled by the balloon during the interval.
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 16 of 32

BLUE PRINT & MODEL P
BLUE PAPERS ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN

BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

15T & 16T

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15T & 16T

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m .co s e m
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a 15T & 16T

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a

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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 32

BLUE PRINT & MODEL P
BLUE PAPERS ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN

BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

15T & 16T

SSC PUBLIC EXAMATIN
EXAMATINATIONS 2026 - 27
TINA

MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)

(TELUGU VERSION)

Time : 3 Hours 15 Minutes Max. Marks : 100

dŸÖ#áq\T :
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‚ºÌq |Ÿ³+ýË x eT]jáTT y $\Te\T @$ ? y

A) 10, 14 B) 21, 25 x

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Š >± –q• k $\Te
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4. x
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5. ç¿ì+~ y{ìýË @~ n+¿£çXâ&ó (A.P)“ dŸÖºdŸTï+~ ?
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y{ìýË @ ç|Ÿ¿³
£ q dŸs q
Õ ~?

A) ∆PQR ∼ ∆TSM B) ∆QPR ∼ ∆SMT
C) ∆PRQ ∼ ∆TSM D) ∆QPR ∼ ∆TSM
7. sin 27° eT]jáTT sin 72° $\Te\qT bþýñÌ $wŸjTá +ýË sÁ$ eT]jáTT nÔᓠd•V¾²ÔáT& eT<ó«Š _óH•_óçbÍjáT+
@sÁÎ&+~. y] eT<ó«Š –q• ‡ $uó<
ñ ‘“• MTsÁT mý² |Ÿ]wŸØ]kÍïsTÁ ?
A) ‡ ç|ŸX•ø qT e~ýñd¾ eTsà ç|ŸX•ø Å£” yîÞßø eT“ #î|Ο &ƒ+.
B) 0° qT+& 90° esÁŔ £ sin $\Te\T ç¿£eT+>± ™|sÁT>·TԐjáT“ $e]+º sin 72° > sin 27°n“ nsÁe
Æ TjûT«ý²
#î|Ο &ƒ+.

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15T & 16T

C) mý²+{ì $esÁD ‚eÇÅ£”+&† sÁ$“ Ôáq d•V¾²ÔáT“ dŸeÖ<ó‘q+ ÿ|ŸÚοÃeT“ #î|Ο &ƒ+.
D) >=&ƒe sÅ£”+&† ‚<Š]
Ý dŸeÖ<ó‘H\T dŸs q
Õ yû n“ #î|Ο &ƒ+.
8. ÿ¿£ ‹+<Š+ çÜ¿ÃD$TÜ “wŸÎÔáT\
ï qT –|ŸjÖ
î Ð+º ÿ¿£ >Ã|ŸÚsÁ+ mÔáTq
ï T ¿£qT>=+³TH•sÁT. ¿ì+~ <ŠX\
ø qT dŸs q
Õ
ç¿£eT+ýË neTsÁÌ+&.
1) çÜ¿ÃD$TÜ “wŸÎÜï“ –|ŸjÖ î Ð+º mÔáTqï T ýÉ¿Øì +#á&+ƒ .
2) \+‹¿ÃD çÜuóT„ C²“• ^d¾ ¿=\ÔáqT >·T]ï+#á&+ƒ .
3) ‚ºÌq ¿=\Ôá\qT >·T]ï+#á&+ ƒ .
4) dŸs
 q
Õ çÜ¿ÃD$TÜ “wŸÎÜï“ m+#áT¿Ãe&ƒ+.
A) 3, 2, 4, 1 B) 2, 3, 1, 4 C) 4, 3, 2, 1 D) 3, 4, 2, 1

9. ¿ì+~ dŸeÖ#s“• dŸÖº+#á&†“¿ì ÿ¿£ qeTÖH ºçԐ“• ^jáT+&. ™|<ŠÝ eÔá+ï jîTT¿£Ø C²«, ºq• @¿£¿¹ +ç<Š
eÔï“¿ì dŸÎsÁôs¹ K>± –+~.
10. ÿ¿£ s Ô
Õ Tá 14 MT³sÁ¢ y«kÍsÁ+œ ¿£*Ðq eÔï¿±sÁ bõ\+ýË $ÔáH
ï \T #áý²¢\qTÅ£”+³TH•&ƒT. € bõ\+ jîTT¿£Ø
yîX
Õ æý²«“• #á.MT.\ýË ¿£qT>=q+&.
A) 308 B) 616 C) 528 D) 704

11. »rµ y«kÍsÁ+œ eT]jáTT »hµ mÔáTï ¿£*Ð dŸÖ|
œ +Ÿ jîTT¿£Ø dŸ+|ŸPsÁÔ
’ \
á yîX
Õ æ\«+ (Total Surface Area) dŸÖçÔá+
@~?
A) πr(r + h) B) 2πr(r + h) C) 2πr (r + h)
2
D) πr (r + h)
2

12. ÿ¿£ bͺ¿£qT ÿ¿£kÍ] <=]¢+ºq|ŸÚÎ&ƒT, dŸ] dŸ+K« e#ûÌ dŸ+uó²e«Ôá P(E)“ ¿£qT>=q&†“¿ì @ ç|Ÿ¿³
£ q dŸs q
Õ ~?
A) dŸ] dŸ+K« eT]jáTT uñd¾ dŸ+K«\T dŸeÖq ne¿±Xø+ ¿£*Ð –+{²sTT. ¿±‹{ì¼ P(E) R 0.5

n (E ) 3
B)
P (E ) = =
n (S ) 6

C) A eT]jáTT B Âs+&ƒÖ.
D) A eT]jáTT B @M ¿±eÚ.

$uó²>·+ ` II 8 ´ 2 = 16 M

dŸÖ#áq\T : i) n“• ç|ŸX•ø \Å£” dŸeÖ<ó‘q+ sjáT+&.
ii) ç|ŸÜ ç|ŸXø•Å£” 2 eÖsÁTØ\T.
13. ÿ¿£ esÁ‹
Z VŸQ|Ÿ~ jîTT¿£Ø XøSH«\T a eT]jáTT b nqTÅ£”+fñ, a + b = 6 eT]jáTT ab = 4 nsTTq|ŸÚÎ&ƒT €
‹VŸQ|Ÿ~“ sÁÖbõ+~+#á+&.
14. x
2
+ 5x + 6 = 0 nHû esÁZ dŸMT¿£sD
Á ²“¿ì s +&ƒT eTÖý²\T <óH
Š Ôሿ£+>± –+{²jáT“ sVŸQýÙ qeTTˆÔáTH•&ƒT.
MTsÁT nÔá“Ôà @¿¡u$
„ó kÍïs ? MT dŸeÖ<ó‘H“• dŸeT]œ+#á+&.
15. çÜuóT„ C²\ dŸsÖ
Á |Ÿ¿Ô
£ Åá ”£ dŸ+‹+~ó+º ¿Ã.¿Ã. dŸsÖ
Á |Ÿ¿Ô
£ á “jáTeTeTT sjáT+&.

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m
m .co

m .co s e m
se g l a
a 15T & 16T

16. ÿ¿£ çÜuóT„ È+ jîTT¿£Ø osü\T A(5, 1), B(1, 5) eT]jáTT C(–3, –1) ‚eNj&†¦sTT. AD eT<ó«Š >·Ôá s¹ K bõ&ƒeÚqT
¿£qT>=q+&. ‡ dŸeTdŸ«qT kÍ~ó+#á&†“¿ì Ôás>
Á Ü
· “ 3 ç>·Ö|ŸÚ\T>± $uó›
„ +#sÁT.
ç>·Ö|t 1: ∆ABC“ ^d¾ AD eT<óŠ«>·Ôá ¹sKqT >·T]ï+#sÁT.
ç>·Ö|t 2: BCjîTT¿£Ø eT<óŠ«_+<ŠTeÚ D jîTT¿£Ø “sÁÖ|Ÿ¿±\qT ¿£qT>=H•sÁT.
m
.co
ç>·Ö|t 3: AD bõ&ƒeÚqT ¿£qT>=q&†“¿ì s +&ƒT _+<ŠTeÚ\ eT<ó«Š <ŠÖsÁ+ ¿£qT>=qT dŸÖçԐ“• –|ŸjÖî Ð+#sÁT.
m
.co
‡ eTÖ&ƒT ç>·Ö|ŸÚ\T n+~+ºq €ýË#áq\qT –|ŸjÖ
î Ð+º AD bõ&ƒeÚqT ¿£qT>=q+&.
s e m
s em l a
nsTTÔû eT]jáaTg
la
1
eT]jáTT 0° < A + B ≤ 90° eT]jáTT A> B T
g
17. sin(A + B) = 1 tan (A – B) = A B

a
3
$\Te\“ ¿£qT>=q+&.

18. 5 ™d+.MT y«kÍsÁ+œ >± >·\ eÔï“• PQ dŸÎsÁôs¹ K P e<ŠÝ Ԑ¿ì+~. eÔΌï +ç<Š+ O qT+& dŸÎsÁôs¹ K™|Õ >·\ _+<ŠTeÚ
Q qÅ£” <ŠÖsÁeTT OQ R 13 ™d+.MT. nsTTq PQ bõ&ƒeÚqT ¿£qT>=q+&.

19. |˜TŸ q nsÁ>
œ ÃÞø+ jîTT¿£Ø dŸ+|ŸPsÁÔ
’ \
á yîX
Õ æ\«+ 462 #á.™d+.MT. <‘“ y«kÍsœ“• ¿£qT>=q+&.

om
20. ÿ¿£ q~ jîTT¿£Ø ÿ¿£y|
Õî ڟ –q• »hµ mÔáT>
ï \
· #î³T¼ ™|ÕqT+& q~ jîTT¿£Ø s +&ƒT rs\qT θ eT]jáTT θ (θ < θ )
1 2 1 2

“eT• ¿ÃD²\Ôà ÿ¿£ e«¿ìï |Ÿ]o*+#&ƒT. q~ yî&\ . c
ƒ TÎ »dµ nsTTq ‡ dŸ+<ŠsÒۓ¿ì |Ÿ{²“• ^jáT+&.
e m
s
la²>·+ ` III
$uó
dŸÖ#áq\T : i) g
a çyjáTTeTT.
ç¿ì+~ n“• ç|ŸXø•\Å£” dŸeÖ<ó‘qeTT\T
8 ´ 4 = 32 M

ii) ç|ŸÜ ç|ŸXø•Å£” 4 eÖsÁTØ\T.
21. ÿ¿£ ‹VŸQ|Ÿ~ jîTT¿£Ø ç>±|˜q
t T |Ÿ]o*+º, ¿ì+<Š ‚eNj&q ç|ŸX•ø \Å£” dŸeÖ<ó‘H\T ‚eÇ+&. Y

i) € ‹VŸQ|Ÿ~¿ì m“• XøSH«\T –H•sTT ?

ii) ‚ºÌq ‹VŸQ|Ÿ~ jîTT¿£Ø XøSH«\T @$T{ì ?
m
om
€ ‹VŸQ|Ÿ~“ ax + bx + c sÁÖ|Ÿ+ýË e«¿£|
ï ]
Ÿ dï, <‘“
.co
2
iii) X' –1 3 X

. c e m
e m −b
l as
las a
$\Te m+Ôá ?
ag
g
Y'

a iv) ‹VŸQ|Ÿ~ XøSH«\ \‹Æ+ m+Ôá ?

22. “XøÌ\ ú{ìýË ÿ¿£ |Ÿ&e
ƒ yû>+· >·+³Å£” 11 ¿ì.MT. € |Ÿ&e
ƒ ç|ŸyVŸä“¿ì m<ŠTsÁT>± 12 ¿ì.MT. yî[ß Ü]Ð ç|ŸyVŸ²~XøýË
çbÍsÁ+uó„ _+<ŠTeÚÅ£” #ûsTÁ ¿Ãe&†“¿ì 2 >·+³\ 45 “$TcÍ\ dŸeTjáT+ |Ÿ&Tƒ ÔáT+~. nsTTÔû ç|ŸyVŸ²+ jîTT¿£Ø yû>±“•
¿£qT>=q+&.

m .
.co s e m
s em l a
g la ag
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15T & 16T

23. nsÁe
Æ Ôï\#û ÿ¿£ dŸ]Îý²¿±sÁeTT ÔájÖ
á sÁT #ûjTá ‹&+~. |Ÿ³+ýË #áÖ|¾q $<ó+Š >±
nsÁe
Æ Ôáï ¿¹ +ç<‘\T »Aµ e<ŠÝ çbÍsÁ+_ó+#á‹& »Aµ, »Bµ \ eT<ó«Š eÖsÁTÔáÖ –H•sTT.
nq>± yîTT<Š{ì nsÁe Æ Ôáï ¿¹ +ç<ŠeTTT A, s +&ƒe nsÁe
Æ Ôáï ¿¹ +ç<ŠeTT B, eTÖ&ƒe nsÁe
Æ Ôáï
¿¹ +ç<ŠeTT A ... eT]jáTT nsÁe Æ Ôï\ y«kÍsœ\T esÁTdŸ>± 0.1 ™d+.MT., 1.5 ™d+.MT.,
2.0 ™d+.MT. ....... ‡ $<ó+Š >± yîTTÔá+ï 13 nsÁe Æ Ôï\T –q• dŸ]Î\+ yîTTÔá+ï
bõ&ƒeÚ m+Ôá ?
24. ¿ì+~ y¿±«\T dŸÔ«á eÖ ýñ<‘ ndŸÔ«á eÖ n“ Ôî\|Ÿ+&. MT dŸeÖ<ó‘H“• dŸeT]œ+#á+&.
A) sin (A + B) = sin A + sin B B) θ jîTT¿£Ø n“• $\Te\Å£L sin θ = cos θ neÚÔáT+~.
25. ÿ¿£ u²VŸ²« _+<ŠTeÚ qT+& eÔï“¿ì ^ºq s +&ƒT dŸÎsÁôs¹ K\ bõ&ƒeÚ\T m\¢|ڟ Î&ƒÖ dŸeÖq+>± –+&ƒe“ C²|˜sŸ Y
uó²$dŸTH
ï •&ƒT. nÔᓠdŸ+<ûVäŸ “• MTsÁT mý² “eÜï #ûkÍïsTÁ ?
26. 7 ™d+.MT uóT„ È+ >·\ ÿ¿£ dŸeT|˜TŸ q+™|Õ ÿ¿£ nsÁ>
Æ ÃÞø+ neTsÁ̋& –+~. € nsÁ>
Æ ÃÞ²“¿ì –+&ƒ>\
· >·]wŸ¼ y«dŸ+
m+Ôá ? € |˜TŸ H¿£Ü jîTT¿£Ø –|Ÿ]Ôá\ yîX
Õ æý²«“• ¿£qT>=q+&.
27. e¯Z¿£ Ôá <ŠÔï+X擿ì eT<ó«Š >·Ô“• ýÉ¿Øì +#á&†“¿ì dŸÖçԐ“• sjáT+&. dŸÖçÔá+ýË –|ŸjÖ
î Ð+ºq ç|ŸÜ dŸ+¿¹ Ôá+
jîTT¿£Ø nsœ“• $e]+#á+&.
28. s +&ƒT bͺ¿£\qT @¿£¿±\+ýË <=]¢+ºq|ŸÚÎ&ƒT dŸ+uó$
„ +#û @yîH
Õ  H\T>·T $_óq• dŸ+uó²e«Ôá ç|ŸX•ø \qT ÔájÖ
á sÁT#ûjTá +&.
n$ ¿ì+<Š ‚ºÌq –<‘VŸ²sÁD eýÉ –+&†*.
–<‘VŸ²sÁD : s +&ƒT bͺ¿£\qT @¿£¿±\+ýË <=]¢+ºq|ŸÚÎ&ƒT, s +&ƒT bͺ¿£\ ™|Õu²ó >±ýË¢ dŸ]dŸ+K«\T se&†“¿ì
>·\ dŸ+uó²e«Ôá m+Ôá ?
$uó²>·+ ` IV 5 ´ 8 = 40 M

dŸÖ#áq\T : i) n“• ç|ŸXø•\Å£” dŸeÖ<ó‘qeTT\T sjáT+&.
ii) ç|ŸÜ ç|ŸXø•Å£” 8 eÖsÁTØ\T.

iii) ç|ŸÜ ç|ŸXø•Å£” n+ÔásÁZÔá m+|¾¿£ ¿£\<ŠT.
29. a) 5 (ýñ<‘ ‚ºÌq dŸ+K«) ÿ¿£ ¿£sD
Á j
¡ Tá dŸ+K« n“ uó²$+º, 2 + 3 5 Å£L&† ÿ¿£ ¿£sD
Á j
¡ Tá dŸ+K« n“
“sÁÖ|¾+#á+&.
(ýñ<‘)
b) ÿ¿£ n+¿£çXâ&ó jîTT¿£Ø s +&ƒe eT]jáTT eTÖ&ƒe |Ÿ<‘\T esÁTdŸ>± 14 eT]jáTT 18 nsTTÔû, € n+¿£çXâDý
ì ˓
yîTT<Š{ì 51 |Ÿ<‘\ yîTTԐ ¿£qT>=q+&.
30. a) ¿ì+<Š ‚eNj&q |Ÿ{¿¼ì £ 40 eT+~ $<‘«sÁT\
œ T >·DÔ
ì X
á æg |Ÿ¯¿£ý
Œ Ë kÍ~ó+ºq eÖsÁTØ\qT #áÖ|ŸÚÔáT+~:
0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60

3 5 9 10 8 5

i) ç|ŸÜ Ôás>
Á Ü
· ¿ì Ôás>
Á Ü
· eÖsÁTØ\T (x ) sjáT+&.
i

ii) ç|ŸÜ Ôás>
Á Ü
· ¿ì f x $\Te\qT ¿£qT>=q+&.
i i

iii) ç|ŸÔ«á ¿£Œ |Ÿ<Ü
Ɗ “ –|ŸjÖ
î Ð+º e¯Z¿£ Ôá <ŠÔï+Xø+ jîTT¿£Ø dŸ>³
· TqT ¿£qT>=q+&.

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15T & 16T

(ýñ<‘)

b) çbÍ<¸$
Š T¿£ nqTbÍÔá d¾<‘Æ+Ԑ“• <¸ý
û Ùà d¾<‘Æ+Ôá+ Ôî*|¾ “sÁÖ|¾+#á+&.
31. a) p(2, –3) eT]jáTT Q(10, y) _+<ŠTeÚ\ eT<ó«Š <ŠÖsÁ+ 10 jáT֓³T¢. ‡ dŸeTdŸ«qT kÍ~ó+º, y¿ì ÿ¹¿ ÿ¿£
$\Te –+³T+<Š“ CË«Ü #î‹TÔÃ+~. ¿±ú ç|ÓÜ CË«ÜÔà $uó~
ñ kþï+~. Ԑ]Ø¿£ eTTÐ+|ŸÚqT ‚ºÌ y] dŸ+<ûVäŸ “•
“eÜï #ûjTá +&.
(ýñ<‘)
b) ÿ¿£ >·T+ç&ƒ“ fñ‹TýÙ ¿£esÁT |Ÿ³+ýË #áÖ|¾q $<ó+Š >± €sÁT dŸeÖq &Cq ÕÉ q
¢ T ¿£*Ð jáTTq•~. fñ‹TýÙ ¿£esY
y«kÍsÁ œ + 28 ™d+.MT. nsTTq, #á . ™d+.MT.Å£ ” 0.35 e+Ôá T q € & C É Õ q T¢
ÔájÖ á sÁT#ûjTá T³Å£” m+Ôá KsÁTÌ n>·TqT. π = 3.14 >± rdŸT¿Ã+&.
32. a) u²>·T>± ¿£\T|Ÿ‹&q 52 |¿£ eTT¿£Ø\ ¿£³¼ qT+& ÿ¿£ ¿±sÁT¦ rjáT‹&+~. nsTTÔû

€ rd¾q ¿±sÁT¦ ¿ì+~ $<ó+Š >± –+&ƒ{²“¿ì >·\ dŸ+uó²e«ÔáqT ýÉ¿Øì +#á+&.
i) n+¿¿±sÁT¦ ii) n¿£ŒsÁ+¿±sÁT¦

iii) eTTKºçÔá+ýñ“ ¿±sÁT¦ iv) &îe
Õ T+&Ž nsTT –+&, eTTKºçÔá+ ¿±“ ¿±sÁT¦
(ýñ<‘)
b) 2.4™d+.MT mÔáTï eT]jáTT 0.7 ™d+.MT y«kÍsÁ+œ ¿£*Ðq ÿ¿£ |˜TŸ qdŸÖ|
œ +Ÿ –+~. <‘“ qT+& n<û mÔáT,ï
y«kÍsÁ+œ ¿£*Ðq ÿ¿£ Xø+U²¿±sÁ|ڟ >·T+ÔáqT Ô=\º rdXæsÁT. $TÐ*q |˜TŸ q|Ÿ<‘sÁ+œ jîTT¿£Ø dŸ+|ŸPsÁÔ
’ \
á
yîX
Õ æý²«“• dŸMT|Ÿ #á.™d+.MTÅ£” ¿£qT>=q+&.
33. a) ç¿ì+~ s¹ FjáT dŸMT¿£sD
Á ²\ ÈÔáŔ£ ç>±|˜t ^d¾, € ç>±|˜t qT+& kÍ<óq
Š qT ¿£qT>=q+&. x + 3y = 6 eT]jáTT
2x – 3y = 12

(ýñ<‘)
b) ÿ¿£ ‹VŸQÞø n+ÔádTŸ ï uóe
„ q+™|Õ ™|Õ qT+& m<ŠTsÁT>± >·\ 8 MT³sÁ¢ mÔáTï >·\ ÿ¿£ uóe
„ q+ jîTT¿£Ø ™|Õu²ó >±“•
30° \ “eT•¿ÃD+ÔÃqT, uóe
„ q+ ¿ì+~ uó²>±“• 45° \ “eT•¿ÃD+ÔÃqT #á֝dï, ‹VŸQÞø n+ÔádTŸ ï uóe
„ q+ mÔáTï
m+Ôá ? s +&ƒT uóe
„ H\ eT<ó«Š <ŠÖsÁ+ m+Ôá ?

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m
m .co

m .co BLUE PRINT & MODEL P
BLUE PAPERS
s e
ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN
m
se BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

g l a
a 15T & 16T

m
m .co
m .co s e m
s e l a
g l a ag
a

m
m .co
s e
g la
a

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

m .
.co s e m
s em l a
g la ag
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15T & 16T

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15T & 16T

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m
m .co

m .co BLUE PRINT & MODEL P
BLUE PAPERS ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN
s e m
se BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

g l a
a 15T & 16T

SSC PUBLIC EXAMATIN
EXAMATINATIONS 2026 - 27
TINA

MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 2)

(TELUGU VERSION)

Time : 3 Hours 15 Minutes Max. Marks : 100

dŸÖ#áq\T : m
m
1. 3 >·+öö15 “öö\ýË 15 “$TcÍ\T ç|ŸX•ø |ŸçÔáeTTqT #á<TŠ eÚ³Â¿Õ ¿¹ {²sTT+#á‹&q~. .co
2. .co
n“• ç|ŸX•ø \Å£” dŸeÖ<ó‘qeTT\T MT¿ìeNj&q dŸeÖ<ó‘q |ŸçÔáeTTýËHû sjáTeýÉqT.
m s e m
3.
s e
‡ ç|ŸX•ø |ŸçÔá+ýË yîTTÔá+ï 4 $uó²>±\T eT]jáTT 33 ç|ŸX•ø \T –H•sTT. l a
4.
g l a
H\T>·e $uó²>·+ý˓ ç|ŸX•ø \Å£” eÖçÔáyTû n+ÔásÔ ZÁ á m+|¾¿Å£ ”£ ne¿±Xø+ ¿£\<ŠT. ag
5. a
n“• dŸeÖ<ó‘qeTT\T dŸÎwŸ+¼ >±qT, >·T+ç&ƒeTT>± sjáT+&.

$uó²>·+ ` I 12 ´ 1 = 12 M

dŸÖ#áq\T : i) n“• ç|ŸXø•\Å£” ÿ¿£ |Ÿ<Š+ ýñ<‘ ÿ¿£ eÖ³ýË dŸeÖ<ó‘q+ sjáT+&.
ii) ç|ŸÜ ç|ŸXø•Å£” 1 eÖsÁTØ.

1. 156 jîTT¿£Ø ç|Ÿ<‘ó q ¿±sÁD²+¿±\ \‹ÆeTT a ´ b ´ c nsTTq a + b + c =
2

ÿ¿£ XøSq«eTT 2 + 3 >± >·\ ÿ¿£ esÁ‹
Z VŸQ|Ÿ~“ sjáTTeTT.
m
2.

3. 3x + 5y – 11 = 0 dŸMT¿£sD
Á + qT+& y“ x |Ÿ<‘\ýË e«¿£|
.co
ï sŸ #
Á +á &.
4. ÿ¿£ esÁZ dŸMT¿£sD
s em
Á + jîTT¿£Ø eTÖý²\T ÿ¿£<‘“¿=¿£{ì eځÔáØeÖ\T njûT«ý² @<îH
Õ  ÿ¿£ esÁZ dŸMT¿£sD
Á ²“• sjáT+&.
MT d•V¾²ÔáT&ƒT 5, 8, 11, 15, 17 nHû ldŸa
5.

ag +K«\qT ÿ¿£ n+¿£çXâ&>ó ± sXæ&ƒT. MTsÁT MT d•V¾²ÔáT&¿ì @$T
#î‹TԐsÁT?

6. |Ÿ³eTTýË DE & BC, AD = 3 ™d+.MT, BD = 4 ™d+.MT eT]jáTT BC = 14 ™d+.MT
A

nsTTq DE = ___ 3™ d + . M T

D E

A) 7 ™d+.MT B) 6 ™d+.MT 4™ d + . M T

B C

14™d+.MT
™d+.MT ™d+.MT
m
C) 4 D) 3

.co
覄u
OE€Rv
VÔe5©F55
ú dŸV²Ÿ $<‘«]œ cos θ = 覄u
N
k5\Í
VÔe5©F55 n“ sXæ&ƒT. úeÚ, ú dŸV²Ÿ $<‘«]œÔà @¿¡u$
„ó kÍïy ýñ<‘ ýñ“#à dŸ]jîT® q
m çÜ¿ÃD$TrjáT “wŸÎÜï sjáT+&.
7.

m .co s em
e ï T ¿=*#sÁT. ÿ¿£sTÁ 20MT, eTs=¿£sTÁ 22MT>± #îbÍÎsÁlTa
las 8. ‚<ŠsÝ TÁ $<‘«sÁT\
œ T #î³T¼ mÔáTq
a g
. y]<Š]
Ý dŸeÖ<ó‘H\ýË @

ag dŸeÖ<ó‘qeTT dŸ] nsTTq<à “sÁs’ TT+#áT³Å£” eTT+<ŠT>± @$T #ûjÖ á *?
A) yîTT<Š{ì dŸeÖ<ó‘H“• eÖçÔáyTû n+^¿£]+#*.
B) s +&ƒe dŸeÖ<ó‘H“• eÖçÔáyTû n+^¿£]+#*.
C) ¿=\Ôá\qT eTs=¿£kÍ] ¿=*º dŸ]#áÖdŸT¿Ãy*.

D) ‚<Š]
Ý dŸeÖ<ó‘H\qT HûqT n+^¿£]kÍïqT.

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 28 of 32

15T & 16T

9. ÿ¿£ eÔï“• ^º, € eÔï“¿ì u²VŸ²«+>± >·\ ÿ¿£ s¹ KÅ£” dŸeÖ+Ôás+Á >± ÿ¿£ dŸÎsÁôs¹ KqT eT]jáTT ÿ¿£ #ó<
û q
Š s¹ KqT
^jáT+&.

10. ÿ¿£ eÔá|
ï ]
Ÿ ~ó eT]jáTT #áÔTá sÁçdŸ #áT³T¼¿=\Ôá\T dŸeÖqeTT nsTTq.

A) eÔáï yîX
Õ æ\«+ R #áÔTá sÁçdŸ yîX
Õ æ\«+

B) eÔáï yîX
Õ æ\«+ > #áÔTá sÁçdŸ yîX
Õ æ\«+
C) eÔáï yîX
Õ æ\«+ < #áÔTá sÁçdŸ yîX
Õ æ\«+
D) KºÌÛÔ+á >± y{ì eT<ó«Š dŸ+‹+<óe
Š TT #î|Ο ýñeTT.
11. y«kÍsÁe
œ TT r ™d+.MT>± >·\ >ÃÞø+ |˜TŸ q|Ÿ]eÖD+

4 2 4 3 3 3 3 2
A) πr B) πr C) πr D) πr
3 3 4 4

5
12. ú d•V¾²ÔáT&ƒT ÿ¿£ dŸ+|˜TŸ ³q dŸ+uó²e«Ôá n“ #î|ξ q, úeÚ mý² ç|ŸÜdŸÎ+~kÍïeÚ.
3
A) n+^¿£]kÍïqT, dŸ+uó²e«Ôá @<îH
Õ  ÿ¿£ <óq
Š dŸ+K«.
B) ÿ¿£ |˜TŸ ³q dŸ+uó²e«Ôá m\¢|ڟ Î&ƒÖ 0 ≤ P(Ε) ≤1 eT<ó«Š –+³T+<Š“ eTs«<Š>± $e]+#á+&. ¿±‹{ì,¼ n~ ný²
–+&ƒýñ<ŠT.
C) d•V¾²ÔáT“ n_óçbÍjá֓• |Ÿ]>·Dqý˓¿ì rdŸT¿ÃsÁT.
D) dŸeÖ<ó‘qeTT Ôá|ðŸ n“ ¿±sÁD+ #î|Ο Å£”+&† #îbÍïeÚ.

$uó²>·+ ` II 8 ´ 2 = 16 M

dŸÖ#áq\T : i) n“• ç|ŸX•ø \Å£” dŸeÖ<ó‘q+ sjáT+&.
ii) ç|ŸÜ ç|ŸXø•Å£” 2 eÖsÁTØ\T.

13. XøSq«eTT `4 eT]jáTT #ássÁ ¥ x>± >·\ s +&ƒT $_óq• ‹VŸQ|Ÿ<TŠ \qT sjáTTeTT.
14. $<‘«]œ 1: ÿ¿£ BsÁ#
é Ô
á Tá sÁçkÍ¿±sÁ bÍsÁTØ jîTT¿£Ø bõ&ƒeÚ <‘“ yî&\
ƒ TÎÅ£” s {ì+¼ |ŸÚ –+&†*.
$<‘«]œ 2: € bÍsÁTØ yîXÕ æ\«+ 20 #á.MT –+&†*.
‚<ŠsÝ TÁ $<‘«sÁT\
œ €ýË#áq\qT –|ŸjÖ
î Ð+º bÍsÁTØ jîTT¿£Ø bõ&ƒeÚ, yî&\
ƒ TÎ\qT ¿£qT>=q+&.
15. çbÍ<¸$
Š T¿£ nqTHÔá d¾<‘Æ+Ôá $|Ÿs«Á jáT+qT $e]+|ŸÚeTT.
16. sec θ + tam θ = P nsTTq P |Ÿs+
Á >± sec θ $\Te m+Ôá ?
17. ¿ì+~ |Ÿ]d¾Ü
œ “ dŸÖº+#á&†“¿ì ÿ¿£ ºçԐ“• ^jáT+&.
ÿ¿£ $<‘«]œ ÿ¿£ >Ã|ŸÚsÁ+ jîTT¿£Ø ™|Õu²ó >±“• 45° –sÁǜ ¿ÃD+ýË |Ÿ]o*dŸTH
ï •&ƒT.

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15T & 16T

18. 5 ™d+.MT y«kÍsÁe
œ TT>± >·\ eÔï“• PQ dŸÎsÁôs¹ K P e<ŠÝ Ԑ¿ì+~. eÔΌï +ç<ŠeTT »Oµ qT+& dŸÎsÁôs¹ K™|Õ >·\
_+<ŠTeÚ Q qÅ£” <ŠÖsÁeTT OQ R 12 ™d+.MT nsTTq PQ bõ&ƒeÚ.
19. 3x + ky = 7 eT]jáTT 6x + 4y = 14 dŸMT¿£sD
Á ²\ ÈÔáŔ£ @¿¿Õ £ kÍ<óq
Š –+&ƒT³Å£” wŸsÔ
Á Tá @$T{ì ? Ôá<‘Çs
k $\TeqT ¿£qT>=q+&.

20. ÿ¿£ _+<ŠTeÚ y ` n¿Œ±“¿ì m&ƒeTyî|
Õ ÚŸ 4 jáT֓{Ù\ <ŠÖsÁ+ýËqT eT]jáTT x ` n¿Œ±“¿ì ~>·Teq 3 jáT֓{Ù\
<ŠÖsÁ+ýËqT –q•~. mÅ£”ØeeT+~ $<‘«sÁT\ œ T <‘““ yîTT<Š{ì bÍ<Š+ýË >·T]ï+#sÁT. dŸ]jîT® q “sÁÖ|Ÿ¿±\qT eT]jáTT
dŸ]jîT® q bÍ<ŠeTTqT sjáTTeTT.

$uó²>·+ ` III 8 ´ 4 = 32 M

dŸÖ#áq\T : i) ç¿ì+~ n“• ç|ŸXø•\Å£” dŸeÖ<ó‘qeTT\T çyjáTTeTT.
ii) ç|ŸÜ ç|ŸXø•Å£” 4 eÖsÁTØ\T.

21. ÿ¿£ |¾\y
¢ & e<ŠÝ ÿ¿£ bͺ¿£ –+~, <‘“ €sÁT eTTU²\T ‡ ç¿ì+~ $<ó+Š >± n¿£sŒ \T #áÖ|ŸÚԐsTT.

A B C D E A

bͺ¿£qT ÿ¿£kÍ] <=]¢+ºq|ŸÚ&ƒT bõ+<û dŸ+uó²e«Ôá\T ¿£qT>=qT³Å£” 4 ç|ŸX•ø \qT sÁÖbõ+~+#á+&.

–<‘ : bͺ¿£qT ÿ¿£kÍ] <=]¢+ºq|ŸÚ&ƒT bͺ¿£ ™|ÕeTTK+™|Õ D bõ+<û dŸ+uó²e«Ôá m+Ôá ?

22. eT<ó«Š >·Ôe
á TT ¿£qT>=qT³Å£” dŸÖçÔáeTT sd¾ n+<Š* |Ÿ<‘\qT $e]+#á+&.

23. ÿ¿£ u¤eTˆ nsÁ>
Æ ÃÞø+™|Õ ç¿£eTeÔï¿±sÁ Xø+Å£”eÚqT neTsÁ̋& –q• |˜TŸ H¿£Ü €¿±sÁ+ýË –+~.
Xø+Å£”eÚ mÔáT,ï uóÖ
„ y«kÍ\T esÁTdŸ>± 2 ™d+.MT. eT]jáTT 4 ™d+.MT. € u¤eTˆ |˜TŸ q|Ÿ]eÖD²“•
¿£qT>=q+&. ÿ¿£ ç¿£eT eÔï¿±sÁ dŸÖ| œ +Ÿ ýË |ŸP]ï>± –+&û³³T¢ € u¤eTˆqT –+ºÔû € dŸÖ| œ +Ÿ
eT]jáTT u¤eTˆ\ |˜TŸ q|Ÿ]eÖD²\ eT<ó«Š uó<
ñ +Š qT ¿£qT>=q+&. (π = 3.14 >± rdŸT¿Ã+&)
24. s +&ƒT esÁTdŸ <óq
Š |ŸPsÁd
’ +Ÿ K«\ esZ\ yîTTÔá+ï 365 nsTTq € dŸ+K«\qT ¿£qT>=qTeTT.
25. ∆ABCýË \+‹¿ÃD+ B e<ŠÝ –+~ eT]jáTT AB = 24 ™d+.MT, BC = 7 ™d+.MT, nsTTq:
i) sin A, cos A ii) sin C, cos C \ $\Te\T ¿£qT¿ÃØ+&.
26. 3 #û uó²Ð+#á‹&û s +&ƒT n+¿\ dŸ+K«\T m“• ?
27. ÿ¿£ eÔï¿±sÁ ‚+Å£”&ƒT >·T+Ôá y«kÍsÁe
œ TT 4MT. eÔáe
ï TT ‹jáT³ –q• P nHû ÿ¿£ _+<ŠTeÚ qT+& ‚+Å£”&ƒT >·T+Ôá
n+#áT\qT A eT]jáTT B nqT _+<ŠTeÚ\ e<ŠÝ Ԑţ”q³T¢ s +&ƒTyîsÕ TÁ ¢ neTsÁ̋&q$.
a) B“¿ì dŸ]|Ÿ&Tƒ qeTÖH ºçÔáeTT ^jáTTeTT.
b) s +&ƒTyîsÕ TÁ ¢ bõ&ƒeÚ\T mý² –+{²sTT.
c) @ d¾<‘Æ+ÔáeTT –|ŸjÖ
î Ð+#á‹&+~.
d) yîsÕ TÁ ‚+Å£”&ƒT >·T+ÔáqT Ԑ¿ìq _+<ŠTeÚ qT+& ^jáT‹&q y«kÍsœ“¿ì, yîsÕ TÁ Å£” eT<ó«Š >·\ ¿ÃDeTT m+Ôá ?

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m
m .co

m .co s e m
se g l a
a 15T & 16T

28. ç¿ì+~ ç>±|˜q
t T |Ÿ]o*+º ‚ºÌq ç|ŸX•ø \Å£” dŸeÖ<ó‘H\T sjáT+&. y

1) ‹VŸQ|Ÿ~ XøSH«\qT çyjáT+&.
2) ‹VŸQ|Ÿ~ XøSH«\ yîTTÔá+ï ¿£qT>=q+&.
3) ‹VŸQ|Ÿ~ XøSH«\ \‹Ý+ ¿£qT>=qTeTT.
m
.co
‹VŸQ|Ÿ~¿ì €¿±sÁ+ |¹s$T{ì ?
m
4)

.co
x' o 2 3 x

e m
em l as
s
y'

g la $uó²>·+ ` IV 5 ´ 8 = 40 M ag
a
dŸÖ#áq\T : n“• ç|ŸXø•\Å£” dŸeÖ<ó‘qeTT\T sjáT+&.
i)

ii) ç|ŸÜ ç|ŸXø•Å£” 8 eÖsÁTØ\T.
iii) ç|ŸÜ ç|ŸXø•Å£” n+ÔásÁZÔá m+|¾¿£ ¿£\<ŠT.

5+2 3
29. a) 3 ¿£sD
Á j
¡ Tá dŸ+K« n“ ‚eNj&q~. nsTTq#Ã
7
Å£L&† ¿£sD
Á j
¡ Tá dŸ+K«jûT n“ $sÁT<ŠÔ
Æ á <‘Çs
“sÁÖ|¾+#á+&.
m
ýñ<‘
.co
b) ÿ¿£ n+çXâ&ý ó ˓ yîTT<Š{ì n |Ÿ<‘\ yîTTÔáe
em
ï TT 4n – n nsTTq yîTT<Š{ì |Ÿ<+Š m+Ôá ? (nq>± S )? yîTT<Š{ì
s
2

la
1

s +&ƒT |Ÿ<‘\ yîTTÔá+ï m+Ôá ? 2e |Ÿ<e Š TT m+Ôá ? n<û$<ó+Š >± 3e |Ÿ<e
Š TTqT, 10e |Ÿ<e
Š TTqT eT]jáTT ne
|Ÿ<e
Š TTqT ¿£qT>=qTeTT. ag
30. a) ÿ¿£ Ôás> Á Ü
· >·~ýË q\T>·TsÁT d•V¾²ÔáT\T A, B, C eT]jáTT D k͜HýË¢ Å£LsÁTÌH•sÁT. Ôás>
Á Ü
· ýË ¿=“• “$TcÍ\T
|Ÿ]o*+ºq ÔásÇÔá A, B, C eT]jáTT D k͜H\ “sÁÖ|Ÿ¿±\T esÁTdŸ>± (3, 4), (6, 7), (9, 4) eT]jáTT (6,
1) >± >·T]ï+#sÁT. #á+|Ÿ, #áyT û ©“ ‚ý² n&Ð+~ ABCD ÿ¿£ #áÔTá sÁçdŸ+ neÚÔáT+<Š“ úeÚ uó²$+#á&+ƒ ýñ<‘ ?
n+<ŠTÅ£” #áyTû © ÿ|ŸÚοÃýñ<TŠ . _+<ŠTeÚ\ eT<ó«Š <ŠÖsÁ+ Å£qT>=q&†Hû dŸÖçԐ“• –|ŸjÖî Ð+º, me] dŸeÖ<ó‘qeTT
dŸ]jîT® q<à Ôî\|Ÿ+&.
(ýñ<‘)
m
m y«kÍsÁ+Æ 21 MT eT]jáTT ¿¹ +ç<Š¿ÃD+ 60° –+&ƒTq³T¢ ÿ¿£ ç>±eTdŸT\ .co
ï T esÁü|ڟ ú{ì“ “\Te #ûdTŸ ¿=qT³Å£”
.co
b)

e m
e m
™d¿±¼sTÁ (çÜC²«+Ôás)Á €¿±sÁ+ýË ÿ¿£ ‚+Å£”&ƒT >·T+ÔáqT ÔájÖ
l as
á sÁT #ûd¾ <‘“ #áT³Ö¼ ¿£+#î yûXæsÁT.

las a) #|ŸeTT bõ&ƒeÚ m+Ôá ?
ag
ag b) #|ŸeTT#û @sÁÎ&û ™d¿±¼sTÁ yîX
Õ æ\«+ (çÜC²«+Ôás)Á
c) esÁü|ڟ ú{ì“ “\Te#ûjTá T³ e\q, ú{ì “\Ç \uó«„ ÔáŔ£ @$<ó+Š >± –|ŸjÖ
î >·|&
Ÿ Tƒ qT.
31. a) ç¿ì+~ $uóÈ „ q |Ÿ{¿¼ì ý
£ Ë ÿ¿£ Ôás>
Á Ü
· jîTT¿£Ø 30 eT+~ $<‘«sÁT\
œ ‹sÁTeÚ\T ‚eNj&†¦sTT. $<‘«sÁT\
œ ‹sÁTeÚ\
eT<ó«Š >·Ôe
á TT ¿£qT>=q+&.
‹sÁTeÚ (¿ì.ç>±\ýË) 40 - 45 45 – 50 50 – 55 55 – 60 60 – 65 65 – 70 70 - 75

$<‘«sÁT\
œ dŸ+K« 2 3 8 6 6 3 2

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 32

15T & 16T

(ýñ<‘) D C
b) i) |Ÿ³eTTýË –q• dŸsÖ
Á |Ÿ çÜuóT„ C²\T @$ ? 70°
O 125°
ii) € |Ÿ{²\T dŸsÖ
Á bÍ\T n“ “sÁÖ|¾+#áT³Å£” –|ŸjÖ
î Ð+#û çÜuóT„ È
dŸsÖ
Á |Ÿ¿Ô
£ á @~ ? € dŸsÖ
Á |Ÿ¿Ô
£ á “jáTeTeTT sjáTTeTT. A B
iii) € dŸsÖ
Á |Ÿ çÜuóT„ C²\ nqTbÍÔá dŸ+‹+<óe
Š TT sjáTTeTT.
32. a) ÿ¿£ €³q+<ŠT yû>+· >± Ü|ŸÎ‹&q u²D|ŸÚ >·TsÁTï 1, 2, 3, 4, 5, 6, 7, 8 dŸ+K«\ýË ÿ¿£ <‘“• #áÖ|¾dÖ Ÿ ï
€>·TÔáT+~. n“• |Ÿs«Á ekÍqeTT\T dŸeTdŸ+uóy „ ýÉÔÕ û u²D²“• ÿ¿£kÍ] Ü|ŸÎ&ƒ+ e\q n~ ç¿ì+~y““ dŸÖº+#û
dŸ+uó²e«Ôá\T m+Ôî+Ôá ? 8 1

2
ii) uñd¾ dŸ+K«
7

→
i) 8
6 3
iii) 3 ¿£+fñ ™|<ŠÝ dŸ+K« iv) 8 ¿£+fñ ÔáŔ £ Øe ýñ<‘ dŸeÖqeTjûT« dŸ+K« 5 4

(ýñ<‘)
b) 60™d+.MT y«kÍsÁ+ œ >·\ ÿ¿£ nsÁ> Æ ÃÞø+™|Õ 120™d.MT mÔáT,ï 60 ™d+.MT y«kÍsÁ+œ >·\ ÿ¿£ ç¿£eT eÔï¿±sÁ
dŸÖ|œ +Ÿ neTsÁ̋&+~. B““ |ŸP]ï>± ú{ìÔà “+|Ÿ‹& –q• 60™d+.MT uóÖ „ y«kÍsÁ+Æ 180 ™d+.MT mÔáT>
ï \
·
ç¿£eT eÔï¿±sÁ dŸÖ| œ +Ÿ ýË n&ƒT>·Tuó²>±“• Ԑţ”q³T¢>± “³¼“\TeÚ>± –+ºÔû, €dŸÖ| œ +Ÿ ýË ‚+¿± $TÐ*eÚq•
ú{ì |˜TŸ q|Ÿ]eÖD+ ¿£qT>=q+&.
33. a) 10 eT+~ |Ÿ<e
Š Ôás>
Á Ü
· $<‘«sÁT\
œ T ÿ¿£ >·DÔ
ì á ¿ìÇCÙýË bÍý¤ZH•sÁT. <‘“ýË bÍý¤Zq• u²*¿£\ dŸ+K« u²\TsÁ
dŸ+K« ¿£H• 4 mÅ£”Øe. nsTTq ¿ìÇCÙýË bÍý¤Zq u²\TsÁT eT]jáTT u²*¿£\ dŸ+K«qT ¿£qT>=q+&.
‡ dŸeTdŸ«Å£” s¹ FjáT dŸMT¿£sD
Á ²\ ÈÔáqT ÔájÖ
á sÁT#ûd¾ ç>±|˜t |Ÿ<Ü
݊ ýË kÍ<óq
Š ¿£qT>=q+&.
(ýñ<‘)
b) 1.2MT mÔáT>
ï \
· u²*¿£ €¿±Xø+ýË ¿ìÜ
Œ ÈdŸeÖ+Ôás+Á >±, >±*Ôà bͳT ç|ŸjÖ
á DìdTŸ q
ï • 88.2 MT. mÔáTý
ï Ë >·\
uÉ\ÖHŽ k͜H“• 60° }sÁœ Ç ¿ÃD+ýË >·eT“+º+~. ¿=+Ôá dŸeTjáT+ ÔásTÁ yÔá € }sÁǜ ¿ÃD+ 30°>± eÖ]+~.
(|Ÿ³+ #áÖ&ƒ+&). ‡ ¿=+Ôá dŸeTjáT+ýË uÉ\ÖHŽ ç|ŸjÖ
á Dì+ºq <ŠÖs“• ¿£qT>=q+&.

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