AP Class 10 Model Paper 2025 Maths

CLASS 10
SAMPLE PAPER
2025

@aglasem

BLUE PRINT & MODEL P
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2024-25
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..

S.S.C. PUBLIC EXAMINATIONS - MA
EXAMINATIONS THEMA
MATHEMATICS
THEMATICS

WEIGHTAGE TO QUESTION TYPE

S.No. Type of Question No. of Marks

Questions Allotted Percentage

1. 1 Mark Questions 12 12 12%

2. 2 Marks Questions 8 16 16%

3. 4 Marks Questions 8 32 32%

4. 8 Marks Questions 5 40 40%

Total 33 100 100%

BLUE PRINT
S.No. Academic Stand 1 M. Q 2 M.Q 4 M.Q 8 M.Q Total Total
No. of Marks Percentage
Quetions

1. Problem Solving 6 3 3 2 14 40 40%

2. Reasoning & Proof 2 1 2 1 6 20 20%

3. Communication 2 2 1 – 5 10 10%

4. Connections 1 1 1 1 4 15 15%

5. Visualisation &

Representation 1 1 1 1 4 15 15%

Total 12 8 8 5 33 100 100%

CHAPTERWISE WEIGHTAGE
S.No. Academic Stand 1 M. Q 2 M.Q 4 M.Q 8 M.Q Total
Marks
1. Real Numbers 1 – – 1 9
2. Polynomials 2 1 1 – 8
3. Pair of linear equations 1 – – 2 9(8)
4. Quadratic Equations 1 1 1 – 7
5. Arithmetic Progressions 1 – 1 1 5(8)
6. Triangles 1 1 – 1 11
7. Coordinate Geometry – 1 – 1 2(8)
8. Introduction to Trigonometry 1 1 1 – 7
9. Some Applications of Trignometry 1 1 – 1 3(8)
10. Circles 1 1 1 – 7
11. Area related to Circles – – – 1 8
12. Surface areas and Volumes 1 1 1 – 7
13. Statistics – – 1 1 4(8)
14. Probability 1 – 1 1 13
Total 12×1=12 8×2=16 8×4=32 5×8=40(40) 100(40)

Within the bracket numbers indicates Internal Choice

BLUE PRINT & MODEL P
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2024-25
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..

SSC PUBLIC EXAMATIN
EXAMATINATIONS 2024 - 25
TINA
MATHEMA
MATHEMATICS
THEMATICS
(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.
1. Find the prime factorization of 30.
2. Assertion : Sum of the zeroes of a Quadratic polynomial
−3
2x2 + 3x – 4 is .
2
Reason : Sum of the zeroes of a Quadratic polynomial
c
ax2 + bx + c is .
a
Now, choose the correct answer from the following.
A) Both Assertion and Reason are true, Reason is supporting the assertion.
B) Both Assertion and Reason are true but Reason is not supporting the assertion.
C) Assertion is true, but the Reason is false.
D) Assertion is false, but the reason is true.
3. The general form of linear equation in two variables is ...........
4. If nth terms of an A.P is an = 2n – 6 then
Match the following.
i) a 2 p) 0
ii) a 3 q) 2

iii) a4 –2

Choose the correct answer.

A) i – p, ii – r, iii – q

B) i – r, ii – q, iii – p

C) i – r, ii – p, iii – q

D) i – q, ii – r, iii – p

5. Statement-I : All similar triangles are congruent.

Statement-II : All right angled isosceles triangles are similar.

Now, choose the correct answer.

A) Both statements are true.

B) Statement I is true and Statement II is false.

C) Statement I is false and statement II is true.

D) Both statements are false.

6. A person standing 20 meters away from the base of a building observes that the angle
of elevation to the top of the building is 45° then the height of the building is .........

7. How many tangents can a circle have ?

8. Draw a rough figure of cylinder with height h cm and base radius r cm.

9. If p(E) = 0.05, what is the probability of 'not E' ?

10. Zero of the polynomial of ax + b is ( )

b a −a −b
A) B) C) D)
a b b a
11. If 4 cot A = 3 then tan A = ( )

3 4 4 3
A) B) C) D)
5 5 3 4

1
12. If x = then the roots are ( )
x

A) 1 B) –1 C) A, B D) None

SECTION - II 8 ´ 2 = 16 M
Note : i) Answer all the questions.
ii) Each question carries 2 marks.

13. Find the volume of a cylinder with radius of base 6 cm and height 7 cm.

14. Find a Quadratic polynomial whose sum and product of the zeroes are 3 and 2
respectively.

15. Check whether the following are Quadratic Equations or not.

i) (x – 2)2 + 1 = 2x – 3 ii) x(x + 1) + 8 = (x + 2) (x – 2)

16. Give an example for

i) Similar figures ii) non similar figures

17. Find the coordinates of mid point of the line segment joining (cos 0, 0) and (0, sin 90°)

18. Express the ratios cos A and tan A in terms of sin A.

19. Draw a diagram for the following situation.

A boy observed the top of an eletric pole at an angle of elevation of 60° when the
observation point is 8 meters away from the foot of the pole.

20. Calculate the length of tangent from a point 15 cm. away from the centre of a circle of
radius 9 cm.
SECTION - III 8 ´ 4 = 32 M
Note : i) Answer all the questions.
ii) Each question carries 4 marks.

21. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

i) a king of black colour

ii) a red face card.

22. Write the formula to find the mode of a grouped data and explain the terms involved in

it.

23. A solid is in the shape of a cone standing on a hemisphere with both their radii being
equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the

solid in terms of π.
24. Find two numbers whose sum is 27 and product is 182.

DPU " − DPT " DPTFD" − 
25. Prove that =
DPU " + DPT " DPTFD" 

26. Find the sum of odd numbers between 0 and 50.
27. Prove that the perpendicular at the point of contact to the tangent to a circle passes
through the centre.
28. Due to heavy storm an electric wire got bent as shown in the figure. It followed a
mathematical shape. Answer the following questions below.

Y

X' X
O

Y'

a) Name the shape in which the wire is bent.
b) How many zeroes are there for the polynomial (Shape of the wire)
c) The zeroes of the polynomial are
d) Sum of the zeroes of the polynomial

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.

29. a) Prove that 2 + 5 3 is irrational.

OR

b) 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.

30. a) Find the area of a rhombus if its vertices are (–4, –7), (–1, 2), (8, 5) and (5, –4) taken
in order.

OR
b) A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by
means of a 5 m long rope. Find
i) the area of that part of the field in which the horse can graze.
ii) the increse in the gazing area if the rope was 10 m log instead of 5 m.
31. a) A box contains 100 discs which are numbered from 1 to 100. If one disc is drawn at
random from the box, find the probability that it bears (i) a two-digit number (ii) a
perfect square (iii) a number divisible by 5. (iv) a number divisible by 10.
OR
b) The angles of depression of the top and 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.
32. 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

OR
b) If the sum of first 7 terms of an A.P is 49 and that of 17 terms is 289, find the sum of
first n terms.
33. a) Solve the following pair of linear equations graphically.
2x + y – 5 = 0
3x – 2y – 4 = 0
OR
b) Form the pair of linear equations in the following situation and find their solution
graphically.
3 pens and 4 pencils together coast ` 44 whereas 4 pens and 3 pencils together cost
` 47.

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