10th Maths One Mark Questions with Answers PDF

Mathematics plays a crucial role in academic exams, especially in the 10th grade. Understanding one mark questions ensures clarity of concepts and improves problem-solving skills. Below are well-structured questions and answers that encompass various topics in 10th-grade mathematics, aiming to help students excel in their exams.

Algebra

Question: What is the quadratic equation in standard form?

Answer: ax² + bx + c = 0, where a, b, and c are constants.

Question: If the roots of the quadratic equation are 2 and 3, find the equation.

Answer: x² – 5x + 6 = 0

Question: What is the value of x if 5x – 10 = 0?

Answer: x = 2

Question: Solve for x: 3x + 7 = 16.

Answer: x = 3

Question: What is the formula for the sum of roots of a quadratic equation?

Answer: Sum of roots = -b/a

Question: Define a linear equation.

Answer: An equation of the form ax + b = 0 is a linear equation.

Question: If 2x – 4 = 10, what is x?

Answer: x = 7

Question: What is the discriminant of a quadratic equation?

Answer: The discriminant is b² – 4ac.

Question: Factorize x² – 9.

Answer: (x + 3)(x – 3)

Question: What is the slope of a line passing through (0, 0) and (3, 3)?

Answer: Slope = 1

Question: Simplify 2(x + 3) + 4.

Answer: 2x + 10

Question: Solve for y: 4y = 20.

Answer: y = 5

Question: Write the equation of a line parallel to y = 2x + 3.

Answer: y = 2x + c, where c is a constant.

Question: What is the standard form of a linear equation?

Answer: Ax + By + C = 0

Question: Solve for x: 6x – 12 = 0.

Answer: x = 2

Question: Simplify (x + 1)².

Answer: x² + 2x + 1

Question: Write the quadratic formula.

Answer: x = (-b ± √(b² – 4ac)) / 2a

Question: If the roots of x² – 6x + 9 = 0 are equal, find the value.

Answer: x = 3

Question: What is the product of the roots of a quadratic equation?

Answer: Product of roots = c/a

Trigonometry

Question: What is sin 90°?

Answer: sin 90° = 1

Question: What is the value of cos 0°?

Answer: cos 0° = 1

Question: Write the formula for tan θ.

Answer: tan θ = sin θ / cos θ

Question: Simplify sin² θ + cos² θ.

Answer: 1

Question: What is the reciprocal of tan θ?

Answer: cot θ

Question: Find the value of tan 45°.

Answer: tan 45° = 1

Question: If sin θ = 1/2, find θ.

Answer: θ = 30°

Question: What is the value of sec 60°?

Answer: sec 60° = 2

Question: Simplify 1 + tan² θ.

Answer: sec² θ

Question: Write the value of cot 0°.

Answer: cot 0° = undefined

Question: What is cosec 90°?

Answer: cosec 90° = 1

Question: Write the value of cos 90°.

Answer: cos 90° = 0

Question: Simplify tan² θ – sin² θ.

Answer: tan² θ – sin² θ = sin² θ / cos² θ

Question: What is the value of tan 30°?

Answer: tan 30° = 1/√3

Question: If sec θ = 2, find cos θ.

Answer: cos θ = 1/2

Question: Write the Pythagoras theorem in trigonometric form.

Answer: sin² θ + cos² θ = 1

Question: Simplify cot² θ + 1.

Answer: cosec² θ

Question: Find the value of cosec 30°.

Answer: cosec 30° = 2

Question: What is sec 0°?

Answer: sec 0° = 1

Question: Write the formula for cot θ.

Answer: cot θ = cos θ / sin θ

Geometry

Question: Define a circle.

Answer: A circle is a set of points equidistant from a fixed point.

Question: What is the formula for the area of a circle?

Answer: Area = πr²

Question: What is the circumference of a circle with radius r?

Answer: Circumference = 2πr

Question: Define a tangent.

Answer: A tangent is a line that touches a circle at one point.

Question: How many tangents can a circle have?

Answer: Infinite tangents

Question: What is the sum of the angles in a triangle?

Answer: 180°

Question: Define a parallelogram.

Answer: A parallelogram is a quadrilateral with opposite sides parallel.

Question: Write the formula for the area of a triangle.

Answer: Area = 1/2 × base × height

Question: Define a rhombus.

Answer: A rhombus is a quadrilateral with all sides equal in length.

Question: What is the area of a square with side length a?

Answer: Area = a²

Question: Write the Pythagoras theorem.

Answer: In a right triangle, a² + b² = c²

Question: Define a chord.

Answer: A chord is a line segment joining two points on a circle.

Question: What is the area of a rectangle with length l and breadth b?

Answer: Area = l × b

Question: Define a regular polygon.

Answer: A regular polygon has all sides and angles equal.

Question: What is the formula for the volume of a cube?

Answer: Volume = a³

Question: Write the formula for the volume of a cylinder.

Answer: Volume = πr²h

Question: Define an acute angle.

Answer: An acute angle is less than 90°.

Question: What is the formula for the area of a parallelogram?

Answer: Area = base × height

Question: Define a secant.

Answer: A secant is a line that intersects a circle in two points.

Question: What is the total surface area of a sphere with radius r?

Answer: Total surface area = 4πr²

Practicing these one-mark questions helps students revise key mathematical concepts effectively. Covering algebra, trigonometry, and geometry ensures thorough preparation. Use this resource for quick and comprehensive revision to boost confidence in exams.