Chapter Wise Important Topics and Key Concepts in CBSE Class 10 Maths
FAQs on CBSE Class 10 Maths Important Topics for Board Exam Preparation
1. What are the most important topics in CBSE Class 10 Maths?
The most important topics in CBSE Class 10 Maths are Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Trigonometry, Circles, Constructions, Surface Areas and Volumes, and Statistics & Probability. These chapters carry high weightage in board exams and form the foundation for Class 11 Mathematics. Students should especially focus on:
- Quadratic Equations (factorization and quadratic formula)
- Trigonometric Identities and heights & distances
- Arithmetic Progressions (AP) formulas
- Surface Areas and Volumes mensuration problems
- Statistics (mean, cumulative frequency, ogive)
2. What is the quadratic formula in Class 10 Maths?
The quadratic formula is x = (-b ± √(b² − 4ac)) / 2a for a quadratic equation of the form ax² + bx + c = 0. It is used to find the roots of any quadratic equation where a ≠ 0.
- Step 1: Identify values of a, b, and c.
- Step 2: Calculate the discriminant (D = b² − 4ac).
- Step 3: Substitute in the formula.
3. How do you find the HCF of two numbers using Euclid’s Division Lemma?
The HCF of two numbers using Euclid’s Division Lemma is found by repeatedly applying the formula a = bq + r until the remainder becomes 0. The last non-zero remainder is the HCF.
- Step 1: Divide the larger number by the smaller number.
- Step 2: Replace divisor with remainder.
- Step 3: Repeat until remainder = 0.
4. What is an Arithmetic Progression (AP) and its formula?
An Arithmetic Progression (AP) is a sequence where the difference between consecutive terms is constant, called the common difference (d). The nth term is given by an = a + (n − 1)d.
- a = first term
- d = common difference
- n = term number
5. What are the trigonometric identities in Class 10?
The three basic trigonometric identities in Class 10 are:
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
6. How do you solve a pair of linear equations in two variables?
A pair of linear equations in two variables can be solved using the substitution, elimination, or graphical method. The elimination method is most commonly used in exams.
- Step 1: Make coefficients of one variable equal.
- Step 2: Subtract or add equations to eliminate one variable.
- Step 3: Substitute the value to find the other variable.
7. What is the distance formula in Coordinate Geometry?
The distance formula between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ − x₁)² + (y₂ − y₁)²]. It is derived from the Pythagoras theorem.
- Subtract x-coordinates.
- Subtract y-coordinates.
- Square, add, and take square root.
8. What is the formula for the volume of a sphere?
The volume of a sphere is given by V = (4/3)πr³, where r is the radius. This formula is part of Surface Areas and Volumes in CBSE Class 10 Maths.
- π ≈ 22/7 or 3.14
- r = radius of the sphere
9. How do you find the mean using the step deviation method in Statistics?
The mean by step deviation method is calculated using Mean = a + (Σfui / Σf) × h. It simplifies large data calculations.
- a = assumed mean
- h = class width
- ui = (xi − a)/h
- f = frequency
10. What is the formula for probability in Class 10 Maths?
The probability formula is P(E) = Number of favourable outcomes / Total number of possible outcomes. It is based on classical probability.
- 0 ≤ P(E) ≤ 1
- P(impossible event) = 0
- P(sure event) = 1
