Half Yearly Exam 2025- Class 10th Mathematics Model / practice Question Paper

          Half Yearly Exam 2025- Class 10th  

Mathematics Model / practice Question Paper

The Madhya Pradesh School Education Department's Class 10th half-yearly examinations will begin on November 3rd. The timetable has been released. The syllabus and blueprint for the half-yearly examination have also been released. 

Class 10th  Mathematics Model / practice Question Paper

MATHEMATICS will consist of 30 objective questions.

Objective questions will be asked for 30 marks. Objective questions will be asked in five main types:

1. Choose the correct option - 06 marks

2. Write the answer in one word/sentence - 06 marks

3. Fill in the blank - 06 marks

4. Match the correct pair - 06 marks

5. Write true/false - 06 marks

In addition, 12 questions of 2 marks, 3 of 3 marks, and 3 of 4 marks will also be asked.

Half Yearly Exam 2025: Class 10 Mathematics Question Paper

Mathematics

Class: 10

Time: 3.00 hours, Marks: 75

Instructions: 1. All questions are compulsory.

2. Questions 6 to 23 have internal choices.

3. Questions 1 to 5 are objective questions. Each question carries a different number of marks.

4. The marks for each question are indicated opposite them.

5. Questions 6 to 17 carry 2 marks each.

6. Questions 18 to 20 carry 3 marks each.

7. Questions No. Questions 21 to 23 carry 4 marks each

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

i. HCF of 96 and 404 will be i

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

II. What is the maximum degree of the 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 by the following mathematician in India-

(a) Aryabhata (b) Sridharacharya (c) Brahma Gupta (d) Buddhist ion

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

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

(c) the coordinate of y (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 is ______

(A) 45° (B) 30°

(C) 75° (D) 60°

Question 2. Fill in the blank - 1 × 6 = 6

i. The cosecant of 45° is _______.

ii. The zero of the linear polynomial ax + b is _______.

iii. The difference between two consecutive terms of an arithmetic progression is called _______.

iv. The arithmetic mean of 9 and 7 is _______.

v. Sridharacharya formulated a formula now known as _______.

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

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

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

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

ii. Is √5 an irrational number?

iii. Write the statement of Thales' theorem.

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

v. Write the definition of a 'secant' of a circle.

vi. Write the definition of an angle of elevation.

Question 5. Write True or False. 1 × 6 = 6

i. For all values ​​of θ, sin θ = cos θ.

ii. The degree of the zero polynomial is zero.

iii. A linear equation in two variables has multiple solutions.

iv. If the abscissa of a point is zero and the ordinate is 3, then it lies on the x-axis.

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

vi. The probability of a certain event is 1.

Q.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 using the prime factorization method.

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

                           OR

Prove that √3 is a rational number.

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

                              OR

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

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

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

Question 10. Three bats and six balls cost ₹3900, and one bat and three balls cost ₹1300. Construct algebraic equations.(2)

                               OR

Solve the pair of linear equations

7x-15y=2

x+2y=3

by elimination method. Question 11. Find the roots of the quadratic equation 2 x^2 - 7x + 3 = 0? 2

                                    Or

The height of a right triangle is 7 centimeters less than its base. The hypotenuse is 13 centimeters. Find the other two sides.

Question 12. If 8, ±, and ± are in arithmetic progression, find the value of ±? (2)

                                    Or

How many 3-digit numbers are divisible by 7?

Question 13. A vertical pillar of length 6 meters casts a shadow of length 4 meters on the ground. At the same time, the shadow of a tower is 28 meters long. Find the height of the tower. (2)

                                 Or

Two poles 6 meters and 11 meters high are standing on level ground. If the distance between their foot points is 12 meters, find the distance between their top vertices.

Q. 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).

Q. 15. If sin θ = cos θ, what is the value of θ? (2)

                              Or

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

Q. 16. Define impossible event 2

                              Or

Find the sum of the first 100 positive integers.

Question 17. Find two numbers whose sum is 17 and their product is 72.

                          Or

A train travels a distance of 360 kilometers at a uniform speed. If this speed were 5 kilometers per hour more, it would take 1 hour less to complete the same journey. Find the speed of the train.

Question 18. From a point on a bridge over a river, the angles of depression of the banks facing the river are 30 degrees and 45 degrees, respectively. If the bridge is 3 meters above the banks, find the width of the river. (3)

                                     Or

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

Question 19. The minute hand of a clock has a length of 21 centimeters. Find the area traced by this hand in 5 minutes. (3)

                                                     Or

The radii of two circles are 8 centimeters and 6 centimeters 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 beginning of a diameter of a circle are parallel. 3

                                             OR

Prove that the parallelogram circumscribing a circle is a rhombus.

Question 21    Ritu can swim 20 kilometers downstream in 2 hours and 4 kilometers upstream in 2 hours. Find her swimming speed in still water and the speed of the current. 4

                                             Or

Aftab tells his daughter, "Seven years ago, I was seven times your age. Three years from now, I will be only three times your age." Express this situation algebraically and graphically.

Question 22  The difference between two numbers is 26. One number is three times the other. Find these numbers. 4

                                         Or

Romila went to a stationery store and bought two pencils and three erasers for 9 rupees. Her friend Sonali saw a new kind of pencil and eraser with Romila. She also bought them. Bought 4 identical pencils and 6 erasers for ₹18. Express this situation algebraically and graphically.

Question 23: Construct a triangle similar to the given triangle ABC whose sides are 3/4 of the corresponding sides of the given triangle. 4 points

                                    Or

Construct a triangle with sides 4 cm, 5 cm, and 6 cm, and then construct another triangle similar to it whose sides are 3/4.

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