AP SSC Model Paper 2027 Mathematics - Model Paper 1 (English Medium)

FOR AP CLASS 10 PREPARATION

AP SSC Model Paper
2027 Mathematics -
Model Paper 1 (English
Medium)
EXAM YEAR TYPE SUBJECT

AP Class 10 2027 Sample Paper Maths

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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15E & 16E

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BLUE PRINT & MODEL PAPERS OF SSC PUBLIC EXAMINATIONS FOR THE ACADEMIC YEAR 2026-27

BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.

SSC PUBLIC EXAMATIN
EXAMATINATIONS 2026 - 27
TINA

MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)

(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. 4
3
1. If a number Y is prime factorised then the y

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

A) 10, 14 B) 21, 25 7

C) 21, 84 D) 84, 21

2. 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)
3 3
2
4. Find the value of k if the equation x + kx + 6 = 0 has equal roots

5. Which of the following could represent A.P. ( )

A) 2, 4, 8, 6 B) 5, 5, 5, 5 C) 1, 4, 9, 16 D) 2, 3, 5, 8

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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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°.

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

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

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8.

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A Group is finding the height of a tower using trignometric ratios arrange the following
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steps in the correct sequence

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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.

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

10.
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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

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A) 308 B) 616
ag 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

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P (E ) = =
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n (S ) 6

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C) Both A and B. D) Neither A nor B.

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a 8 ´ 2 = 16 M

a 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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28.

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Create any four different probability questions invloving two dice thrown simultaneously

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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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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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