AP SSC Model Paper 2027 Mathematics - Model Paper 2 (English Medium)

FOR AP CLASS 10 PREPARATION

AP SSC Model Paper
2027 Mathematics -
Model Paper 2 (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 PAPERS
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ATIONS FOR THE ACADEMIC YEAR 2026-27
EXAMINA
APERS OF SSC PUBLIC EXAMIN
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se BY THE DIRECTOR OF GO
DIRECTOR VERNMENT EXAMIN
GOVERNMENT ATIONS (SSC BO
EXAMINA ARD), A.P.
BOARD),

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15E & 16E

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 2 of 8

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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.

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 4 of 8

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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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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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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.

For more Question Papers, Sample Papers, Notes & Syllabus visit Page 6 of 8

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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.

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SECTION - IV 5 ´ 8 = 40 M

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Note : i) Answer all the questions. y'

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ii) Each question carries 8 marks.
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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

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

c
1

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

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th
and the nth terms.

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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

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

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

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15E & 16E

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

A B
triangles similar and state the similarity criterian.

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

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

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

Caliculate the probabilities that it will point at 8 1

7 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

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

33. a) Form the pair of linear equations in the following problems, and find their solutions

graphicllay.

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

eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces

to 30° (see figure). FInd the distance travelled by the balloon during the interval.

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