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 = 2Ï€r
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.
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