Class 9th Math Half Yearly Paper 2025 – Hello students, if you’re preparing for the Class 9th Math Half Yearly Paper 2025, then you’ve come to the right place. Today, we’re going to tell you how your Class 9th Math Half Yearly Paper 2025 will be and what questions you’ll see in the Class 9th Math Half Yearly Question Paper. Let’s find out:
Class 9th Math Half Yearly Paper 2025 PDF Download
According to the half-yearly exam timetable released by the Madhya Pradesh Directorate of Public Instruction, the Class 9th Math Half Yearly Paper is scheduled to be held on 10 November , with exam timings from 10:00 am to 1:00 pm. You can check the timetable for more information.
Time Table
Class 9th Mathematics Half-Yearly Paper 2025
Half-Yearly Exam 2025–26
Class – 9th
Subject – Mathematics
Time – 03:00 hours, Marks – 75
Instructions:
All questions are compulsory.
Answer the questions as per the instructions.
Questions 1 to 5 are objective type questions carrying 1 × 30 marks.
Questions 6 to 17 are worth 2 marks each, with a word limit of 30 words.
Questions 18 to 20 are worth 3 marks each, with a word limit of 75 words.
Questions 21 to 23 are worth 4 marks each, with a word limit of 120 words.
Question 1. Choose the correct option and write:
The product of any two rational numbers is:
a. Always an irrational number
b. Always a rational number
c. Always an integer
d. Sometimes rational, sometimes irrational
The degree of the polynomial 𝑥2 + 3𝑥4 + 𝑥 – 4𝑥3 + 7 is
a. 2 b. 4 c. 3 d. 0
In which quadrant will the point (-3, 2) lie?
a. First quadrant
b. Second quadrant
c. Third quadrant
d. Fourth quadrant
The measure of an acute angle is:
a. Between 0° and 90°
b. Between 90° and 180°
c. Between 180° and 360°
d. Between 180° and 270°
A diagonal of a parallelogram divides it into two congruent parts:
a. Square
b. Trapezoid
c. Triangle
If the base of a triangle is 4 centimeters and the height is 6 centimeters, the area of the triangle is:
a. 12 square centimeters
b. 10 square centimeters
c. 6 square centimeters
d. 8 square centimeters
Answer: 1. b. is always a rational number, 2. b. 4, 3. b. second quadrant, 4. a. between 0° and 90°, 5. c. triangle, 6. a. 12 square centimeters
Question 2: Fill in the blanks
A number r is called a rational number if it can be written in the form p/q. P and q are _______ and q ≠ 0.
The value of the ordinate in the coordinates (-3, -2) is _______.
The sum of the three interior angles of a triangle is _______.
An angle that measures more than 180° but less than 360° is called a _______.
The longest side in a right-angled triangle is _______.
Each angle of a rectangle is a _______.
Answer: 1. Integer, 2. -2, 3. 180°, 4. Reflex angle, 5. Hypotenuse, 6. Right angle.
Question 3: Make the correct pair.
(𝑥 + 4). (𝑥 + 10) a. A straight line parallel to the y-axis
(𝑥 + 8). (𝑥 − 10) b. 180°
Graph of x = a. c. 𝑥2 + 14𝑥 + 40
Angle of a semicircle d. 𝑥2 − 2𝑥 − 80
Sum of opposite angles of a cyclic quadrilateral e. 5
Average mean of data f. 90
Answer: 1. c, 2. d, 3. a, 4. b, 5. f, 6. e
Question 4: Write true or false:
The degree of the sum of two multiple terms of degree 3 is always 3.
The point (-1, 2) will lie in the first quadrant.
The point (4, 2) is located 2 units from the x-axis.
Linear equations in two variables have infinitely many solutions.
The point (2,3) is the case of the equation 𝑥 + 𝑦 = 4.
Two circles with equal radii are similar.
Answer: 1. True, 2. False, 3. True, 4. True, 5. False, 6. True
Question 5: Answer this in words or a sentence:
Write one solution of 4𝑥 + 3𝑦 = 𝑦.
What are the outer boundaries of a solid called?
How many right angles can a triangle have at most?
What is an equilateral triangle?
What is the volume of a sphere with a radius of 3 centimeters?
Find the arithmetic mean of the numbers 3, 4, and 5.
Answer: 1. (0,4) or (3,0), 2. Surface area, 3. One, 4. A triangle whose three sides measure the same, 5. 36 π cubic centimeters, 6. 4
Question 6: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
Question 7: Find three rational numbers between ⅗ and ⅘.
or
Simplify (5 + √7)(3 + 2√2).
Question 8: Find 𝑃(0) and P(1) for the polynomial 𝑃(𝑦) = 𝑦2 − 𝑦 + 1.
Or
Factorize 4𝑦2 − 4𝑦 + 1 using the appropriate best identity.
Question 9 The point (1, 2) and (3, 2) lie in the quadrant.
Or
Write the abscissa and ordinate values at the point (16, -12).
Question 10 Plot the following number pairs as points on the Cartesian plane.
Take a 1 centimeter radii on the axes = 1 unit.
Or
Locate the points (0, 5) (0, 9) (5, 7) (–6, 0) in the Cartesian plane.
Question 11 Express 2𝑥 + 3𝑦 = 4.37 as 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0.
Or
Solve the equation 2x + 1 = x – 3.
Question 12: If point 34 lies on the graph of the equation 3y = ax + 7, what is the value of a?
Or
Write the equation of the line passing through the point (2,14).
Question 13: Define ‘line segment’
Or
Define ‘radius of a circle’
Question 14: In the given figure, POQ is a line and ray OP is perpendicular to line PQ.
Question 14: In the given figure, line POQ is a ray. ray OR is perpendicular to line PQ. OS is another ray between rays OP and OR. Prove that ∠ROS = 1/2 (∠QOS – ∠POS).
Or
In the given figure, if AB|CD, ∠APQ = 50 and ∠PRD = 127, find 𝑥 and y.
Question 15: Write the SAS congruence rule.
Or
In 𝐴𝐵𝐶, the bisector AD of ∠𝐴 is perpendicular to side BC. Show that 𝐴𝐵 = 𝐴𝐶.
Question 16: The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the quadrilateral.
Or
If the diagonals of a parallelogram are equal, show that it is a rectangle.
Question 17: Find the radius of a sphere whose surface area is 154 square centimeters.
Or
The height of a cone is 15 centimeters. If its volume is 1570 cubic centimeters, find the radius of the base.
Question 18 ABC is a triangle right-angled at C. A line parallel to BC, passing through the midpoint M of the hypotenuse AB, intersects AC at D. Show that:
(i) D is the midpoint of AC.
(ii) MD ⊥ AC
(iii) CM = MA = 1/2 AB
Or
Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Question 19: The volume of a right circular cone is 9856 cubic centimeters. If the diameter of its base is 28 centimeters, find the following:
Height of the cone
Slant height of the cone
Surface area of the cone
Or
Find the total surface area of a hemisphere of radius 10 centimeters and a thin sphere (take π = 3.14).
Question 20: From the following table, find the mean salary of 60 employees working in a factory.
Or
The following observations are arranged in ascending order. If the median of the data is 63, find the value of x.
29,32,48,50,𝑥, 𝑥 + 2,72,78,84,95
Question 21 Apply the factor theorem and tell whether 9 (x) is a factor of p(x) or not, if P (x) = 2x 3 + x 2 – 2x – 1 and g (x) = x + 1
Or
If 𝑥 + 𝑦 +𝑧 = 0 then show that 𝑥3 + 𝑦3 + 𝑧3 = 3𝑥𝑦𝑧.
Question 22: As shown in the figure, ABCD is a cyclic quadrilateral, in which AC and BD are diagonals. If ∠DBC = 55° and ∠BAC = 45° then find ∠BCD.
Or
If a line parallel to the base of an isosceles triangle is drawn to intersect its equal sides, prove that the quadrilateral formed is cyclic.
Question 23: The base and corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. Find the area of the parallelogram.
Or
A traffic signboard reads “School Ahead” and is in the shape of an equilateral triangle with side a. Find the area of this signboard using Heron’s formula. If the perimeter of the signboard is 180 cm, what is its area?
