AP Class 10 Model Paper 2022 Maths (English Medium)

BLUE PRINT FOR MODEL PAPER
Subject : MATHEMATICS (Paper - I&II) Max. Marks: 100 Time : 3 hrs.15min

TABLE 1

WEIGHTAGE FOR ACADEMIC STANDARDS

SL.NO. ACADEMIC STANDARD WEIGHTAGE MARKS

1 AS1 40% 40

2 AS2 20% 20

3 AS3 10% 10

4 AS4 15% 15

5 AS5 15% 15

100% 100

TABLE 2

TYPE OF QUESTIONS

SL.NO. TYPE OF QUESTION MARKS QUESTION NO.s TOTAL MARKS

1 VERY VERY SHORT 1 1 - 12 12

2 VERY SHORT 2 13 - 20 16

3 SHORT 4 21 - 28 32

4 ESSAY 8 29 - 33 40

TOTAL 33 Q 100 M

1

MODEL PAPER FOR 15E & 16E

SSC PUBLIC EXAMINATIONS - 2022
MATHEMATICS : PAPER - I & II (English Version)

Class : X Max.Marks : 100 Time : 3hrs.15min.
Instructions :
1. In the duration of 3hrs, 15 min, 15 min 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
1. Answer all the questions in one word or phrase
2. Each question carries 1 mark

1. The exponent of 2 in the prime factorisation of 144, is .....................
A) 4 B) 5 C) 6 D) 3
2. Statement (A) : Degree of constant polynomial is “0”.
Statement (B) : Degree of zero polynomial is “0”.
Choose the correct answer
i) Both (A) and (B) are TRUE ii) (A) is TRUE, (B) is FALSE
iii) (A) is FALSE, (B) is TRUE iv) Both (A) and (B) are FALSE
3. 'ABC is an isosceles triangle right angled at ‘C’ and AB2 = n.AC2 then, n = ............
4. When A B then A - B = ......................

5. If AP and AQ are the two tangents to a circle with centre “O” so that
‘POQ = 110º then ‘PAQ = ...........

6. Match the following
A) Tan ( 90 - T) i) cosT
B) 1- cos 2θ ii) sinT
1
C) iii) cotT
secθ
a) A - iii, B - ii, C - i b) A - ii, B - iii, C - i
c) A - iii, B - i, C - ii d) A - ii, B - i, C - iii

2

7. In an A.P. a = 10, d = 10 then the fourth term of A.P is .........................
8. A ladder of length x meter is leaning against a wall making an angle Twith the ground. Which trigono-
metric ratio would you like to consider to find the height of the point on the wall at which the ladder is
touching ?
9. Assertion : x + 2y - 30 = 0, 2x + 4y - 66 = 0 equations are inconsistent equations.

a1 b1 c1
Reason : a1x + b1y + c1 = 0, a2x + b2y + c2 = 0 represent parallel lines if a z
2 b2 c2

A) Both Assertion and Reason are true. Reason is supporting the Assertion.
B) Both Assertion and Reason are true. Reason does not support the Assertion.
C) Assertion is true. Reason is False
D) Assertion is False. Reason is True
10. The line of sight is above the horizontal line and angle between the line of sight and the horizontal line
is called ..........................
11. If P(E) = 0.05, then P(not E) = ..................
12. The distance of the point (4, 7) form X - axis is ....................

SECTION - II 8 × 2 = 16 M

1. Answer all the questions.
2. Each question carries 2 marks.

13. The points (2, 3), (-5, -1), (3, -2) are vertices of a triangle. Find the centroid of the triangle.
14. Two concentric circles of radii 5 cm and 3 cm are drawn. Find the length of the chord of larger circle
which touches the smaller circle.
15. If x = log23, y = log25 then express log215 in terms of x and y.
16. Check whether the equations 2x + 3y = 1, 3x - y = 7 have a unique solution, infinitely many solutions
or no solution.
17. Find the arithmetic mean of the data 5, 6, 9, 10, 6, 6, 7
18. Two dice, one red and one yellow are thrown at the same time. Write down the possible out comes that
the sum of the two numbers appearing on the top of the dice is 8.
19. Draw the venn diagram of A - B where A and B are non empty sets.
20. The wickets taken by a bowler in 10 cricket matches are as follows : 2, 6, 4, 5, 0, 2, 1, 3, 2,3. Find the
mode of the data.

3

SECTION - III 8 × 4 = 32 M

1. Answer all the questions.
2. Each question carries 4 marks.

1
21. Find a quadratic polynomial with zeroes -2 and .
3
22. For what positive value of ‘p’, the following pair of linear equations have infinitely many solutions.
px + 3 y - (p - 3) = 0
12x + py - p =0
23. Find a point on the Y-axis which is equidistant from both the points A (6, 5) and B (-4, 3).
24. Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its
diagonals.
25. Write the following sets in set builder form
(a) {-2, -1, 0, 1, 2}

­ 1 1 1 1½
(b) ®1, , , , ¾
¯ 2 3 4 5¿

26. Show that cotT+ tanT= secT.cosecT.
27. Subba Rao started work in 1995 at an monthly salary of `5000 and received an increment of `200
each year. In which year did his income reach `7000 ?
28. Draw a diagram for the following situation
“A person observes two banks of a river at angles of depression T1 and T2 (T1 < T2) from the top of
a tree of height h which is at a side of the river. The width of the river is “d”.

SECTION - IV 5 × 8 = 40 M

1. Answer all the questions.
2. Each question carries 8 marks.

3. Each question has an internal choice.

29. (a) If A = {x : x is a natural number}
B = {x : x is an even natural number}
C = {x : x is an odd natural number}
D = {x : x is a prime number}
Find A-B, BˆC, A‰B, B-D
(OR)

4

(b) The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
Here CI stands for class interval and Fr for frequency.

CI 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000

Fr 2 5 x 12 17 20 y 9 7 4

30. (a) Find the value of K if the points (7, -2), (5, 1) and (3, K) are collinear.
(OR)
(b) The hypotenuse of a right triangle is 6m more than twice of the shortest side. If the third side is
2 m. less than the hypotenuse, find the sides of the triangle.
31. (a) Prove that 2  3 is irrational.
(OR)

k2 1
(b) If cosecT + cotT = k then prove that cos T .
k2 1
32. (a) 200 logs are stacked in the following manner : 20 logs in the bottom row, 19 in the next row, 18 in
the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in
the top row?
(OR)
(b) A box contains 90 discs which are numbered from 1 to 90. 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.
33. (a) Draw the graph of p(x) x2 – 6x+9 and find the zeroes.
(OR)
(b) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle
of 60º.

5