# HALF YEARLY EXAM : 10 TH MATHEMATICS Model Question Paper

The possible syllabus for the half yearly examination 2022-23 10 TH MATHEMATICS is as follows

mathematics -

Chapter 1 Real Numbers (1.2 Euclid's Division Lemma and 1.5 Rationale of Rational Numbers and their Decimal Expansions have been omitted for this session)

- Chapter 2 Polynomials (2.4 removed)

- Chapter 3 Linear Equations in Two Variables (3.4.3 removed)

- Chapter 4 Quadratic Equations

- Chapter 5 Arithmetic Series

- Chapter 6 Triangles

- Chapter 7 Coordinate Geometry (7.4 has been removed)

- Chapter 8 Trigonometry An Introduction

- Chapter 9 Some Applications of Trigonometry

- Chapter 10 Circle

Chapter 11 Compositions

Chapter 12 Areas Related to Circles

Chapter 13 Surface Area

project work

Note - Questions are not likely to come from the deleted course

Objective type questions of 30 marks in 10th maths

Will be asked Objective questions will be asked mainly in 5 types

1. Choose the correct option 06 marks

2. Write answer in one word/sentence 06 marks

3. Fill in the blanks 06 marks

Match 4 Correct Pairs 06 Marks

5. Write True/False 06 Marks

Apart from this, 12 questions of 2 marks, 3 questions of 3 marks and 3 questions of 4 marks will also be asked.

M P board half yearly exam 2022-23

model question paper

MATHEMATICS

Class: 10

Time-3.00 hours Integer-75

Instructions:-1. It is compulsory to attempt all the questions.

2. Question no. Internal options are given from 06 to 23.

3. Question no. Marks 01 to 05 are objective type questions. Separate marks are prescribed for each question.

4. Marks for each question are indicated against it.

5. Question no. Answer questions from 06 to 15 in 30-40 words each.

6.Question no. Answer questions 16 to 19 in about 75-80 words each.

7. Question no. Answer questions from 20 to 23 in about 120-130 words each.

**Question 1. Write the correct option- 1×6=6**

i. HCF of 96 and 404 will be

(A) 120 (B) 4 (C) 10 (D) 3

II. What is the highest degree of variable in any quadratic equation?

(a) 1 (b) 2 (c) 3 (d) 4

III. The 30th term of A,P ,10 , 7 ,4 ---- is -

A.97 B.77 C. -77 D. -87

iv. Pythagoras theorem was done in India by the following mathematician-

(A) Aryabhatta (B) Sridharacharya (C) Brahma Gupta (D) Buddhist ion

v. If the coordinates of a point P are (x , y ), then X is called -

(a) abscissa of P (b) ordinate of P

(c) y coordinate (d) none of these

vi. If the length of the shadow of a straight pole is √3 times the height of the pole, then the angle of elevation of the sun will be

(A) 45° (B) 30°

(C) 75° (D) 60°

**Question 2. Fill in the blanks - 1×6 = 6**

The mode of cosec 45° will be --------------.

II. The zeroe of the linear polynomial ax+b is ------------

iii. The difference of any two consecutive terms of parallel series is called

iv The arithmetic mean of 9 and 7 is--------

v. All circles are ------------- (congruent / similar)

vi. The ordinate of the point ( -2,3 ) is ------------

**Question 3. Match the correct pair 1×6 = 6**

A B

All squares - π r² h

Medians of triangles - (πr2ϴ) / 360

tan 60° - 1/2

sin 30 - √3

area of sector - contiguous

volume of cylinder - homogeneous

**Question.4. Write answer in one sentence. 1×6 = 6**

i. What is the longest side of a right triangle called?

II. is √5 an irrational number

iii. Write the statement of Thales theorem?

iv. What is the line connecting our eye to the object we are looking at called?

v. What is a line that intersects a circle at two points called?

vi The shape of Delhi in the game of gilli danda is the combination of which solids?

**Q.5 Write True/False 1×6 =6**

i. sin θ = cos θ for all values of θ

II. degree of zero polynomial is zero

iii. A linear equation in two variables has many solutions

iv. If abscissa of a point is zero and ordinate is 3 then it will lie on X axis

v. Tangents drawn from an external point to a circle are equal

vi. A pencil tapered at one end is a combination of a cone and a cylinder.

Question.6. Express the number 140 as a product of prime factors? (2)

Or

Find the HCF and LCM of the integers 12, 15 and 21 by the prime factorization method.

Question.7. Prove that √2 is a rational number. (2)

Or

Prove that √3 is a rational number.

Question 8. If the sum of the zero angles of the polynomial is 0 and the product is √5, then find the polynomial (2)

Or

Find a quadratic polynomial whose sum and product of zeroes are 1/4, -1 respectively?

Question 9. Find a quadratic polynomial whose sum and product of zeroes are -3 and 2 respectively (2)

Or

Find the zeroes of 4u^2+8u?

Question 10 The cost of three bats and 6 balls is ₹ 3900 and the cost of one bat and 3 balls is ₹ 1300, form the algebraic equations? (2)

Or

pair of linear equations

7x-15y=2

x+2y=3

solve by elimination method?

Question 11. Find the roots of the quadratic equation 2 x^2-7x+3= 0? (2)

Or

The altitude of a right triangle is 7 cm less than its base if the hypotenuse is 13 cm then find the other two sides

Question 12. If 8, A, 6 are in A.P. then find the value of A? (2)

Or

How many 3 digit numbers are divisible by 7?

Question.13. The length of the shadow of a vertical pillar of length 6 m is 4 m on the ground, at the same time the length of the shadow of a tower is 28 m, find the height of the tower? (2)

Or

Two poles whose heights are 6 m and 11 m and are standing on level ground, if the distance between their foot points is 12 m, then find the distance between their upper ends.

Question.14. Find the distance between the points (0 ,0 ) and (36 , 5 ) (2 )

Or

Find the centroid of the triangle whose vertices are (1,4 ) (-1,-1 ) (3 ,-2 )

Question 15. If sin θ = cos θ then what will be the value of θ? , (2 )

Or

Calculate the value of (Tan 65°)/(Cot 25°)

Question 16. If the third and ninth terms of an A.P. are 4 and -8 respectively, then which of these terms will be zero. 2

Or

find the sum of first 100 positive integer numbers

Question 17. Find two numbers whose sum is 17 and product is 72. (2)

Or

A train covers a distance of 360 km at a uniform speed if the speed is increased by 5 km per hour it takes 1 hour less for the same journey find the speed of the train

Question 18. From a point on a bridge across a river, the angles of depression of the opposite banks of the river are 30° and 45° respectively. If the bridge is at a height of 3 meters from the banks, find the width of the river. (3)

Or

The angles of elevation of the top of the tower from two points 4 m and 9 m apart from the base of the tower and in a straight line are complementary angles, prove that the height of the tower is 6 m.

Question 19. The minute hand of a clock whose length is 21 cm, find the area covered by this hand in 5 minutes (3 )

Or

The radii of two circles are 8 cm and 6 cm respectively, find the radius of the circle whose area is equal to the sum of the areas of these two circles.

Question 20. Prove that the tangents drawn at the origin of a diameter of a circle are parallel. ( 3)

Or

Prove that a parallelogram circumscribing a circle is a rhombus

Question 21 Ritu can row 20 km in 2 hours downstream and can swim 4 km upstream in 2 hours, find her swimming speed in still water and the speed of the current ( 4)

Or

Aftab tells his daughter that 7 years ago I was 7 times as old as you, 3 years from now I will be only 3 times as old as you. Express this situation algebraically and graphically.

Q22 The difference of two numbers is 26. One number is three times the other number. Find these numbers. (4)

Or

Romila went to a stationery shop and bought 2 pencils and 3 erasers for Rs.9. Her friend Sonali saw Romila have a new type of pencil and eraser. She also bought 4 pencils and 6 erasers of the same type for Rs.18. express graphically

Question 23: A medicine capsule is in the shape of a cylinder with a hemisphere attached to each end. The length of the entire capsule is 14 mm and its diameter is 5 mm. Find its surface area. (4)

Or

A hemisphere is placed on top of a cubical block of side 7 cm. What can be the maximum diameter of the hemisphere? Find the surface area of the solid so formed.

**Note-**

**1. Some grammatical errors are possible in the question paper and text material, please ignore them and take the efforts made in a positive way.**

**2 . Click and remember the site https://www.vimarshportal.in for model question paper, blue print, question bank, and practice paper for upcoming annual examination etc. of all other subjects of class 9th to 12th**

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