AP Class 10 Model Paper 2023 Maths

This Model Question Paper contains 8 pages. 15E & 16E

MATHEMATICS, Paper-I & II
(English Version)

Time : 3 Hours, 15 Minutes Maximum Marks : 100
Instructions :
1. In the duration of 3 hours, 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

Notes : 1. Answer all the questions in One Word or Phrase.
2. Each question carries 1 mark.

1. ''The cost of 2 pens and 5 pencils is Rs. 20''. Express this data as a linear
equation.

2. Choose the correct answer satisfying the following statements.
Statement (A) : Number of maximum zeroes of a cubic polynomial is 3.

Statement (B) : Zero of a linear polynomial x − 2 is –2.

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.

1 Turn Over

3. Find the value of Log6 36 .

4. Find the discriminant of quadratic equation x 2 − 5x + 6 = 0 .

5. Find the volume of a cylinder whose base radius is 3 cm and height is
7 cm.

6. If n ( A ) = 10, n ( B ) = 6 and n ( A U B ) = 12 , then n ( A I B ) = ................

7. Give two different examples of pair of similar figures.

8. Match the following :

Cosθ
A) Tanθ i)
Sin θ

B) Cotθ ii) 1 + Cot2 θ

C) Cosecθ iii) Sec2 θ − 1

a) A → (i), B → (ii), C → (iii) b) A → (ii), B → (iii), C → (i)

c) A → (iii), B → (i), C → (ii) d) A → (ii), B → (i), C → (iii)

2

15. Express the following sets in set-builder form :

i) A = {1, 8, 27, 64}

ii) B = {−3, − 2, −1, 0 , 1 , 2}

16. Find the HCF of 220 and 40 by using Euclid Division Lemma.

17. Draw 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.

7
18. If Tanθ = , then find the value of Secθ .
24

19. Write the formula to find mean of grouped data in direct method and

explain the terms in it.

20. Show that the centroid of a triangle formed by the vertices ( 0 , 0 ) , (2 , 0)

and (1, 3) is (1,1) .

4

26. Express the following in terms of trigonometric ratios of angles between

00 and 450.

i) Sin 810 + Tan 750 ii) Cos 650 + Cot 750

27. When a die is thrown once, find the probability of getting on its face :

i) 8

ii) a number less than 6

iii) a prime number

iv) a composite number

28. ABCD is a trapezium in which AB P DC and its diagonals intersect each

AO CO
other at the point 'O'. Show that = .
BO DO

SECTION IV 5 × 8 = 40

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

3. Each question has internal choice.

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

OR

b) Check whether - 150 a term of the AP : 11,8, 5, 2, ............

6

30. a) Find the roots of the quadratic equation x 2 + 3x − 18 = 0 by the
method of completing the square.

OR
b) Two cubes each of volume 64 cm3 are joined end to end together.
Find the lateral surface area and total surface area of resulting
Cuboid.

31. a) Find the area of the quadrilateral whose vertices taken in order are
A (1,1 ) , B (7, − 3 ) , C (12,2) , D ( 7,21 ) .

OR
b) If the median of 60 observations given below is 28.5 , then find the
values of x and y .

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

Frequency 5 x 20 15 y 5

32. a) A straight highway leads to the foot of a tower. Ramaiah standing at
the top of the tower observes a car at an angle of depression 300. The
car is approaching the foot of the tower with a uniform speed. Six
seconds later, the angle of depression of the car is found to be 600.
Find the time taken by the car to reach the foot of the tower from
this point.

OR

b) One card is drawn from a well shuffled deck of 52 cards. Find the
probability of getting :
i) A queen of black colour ii) a face card
iii) a jack of diamond iv) a club card

7 Turn Over

33. a) Draw the graph of the polynomial P ( x ) = x 2 − 2x − 8 and find its
zeroes.

OR

b) Construct an isosceles triangle whose base is 6 cm and altitude is
1
3 cm. Then draw another triangle whose sides are 1 times the
3
corresponding sides of the isosceles triangle.

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