Class 10 Maths All Formulas Chapter-wise | CBSE 2025

If you're a CBSE Class 10 student looking for a quick revision of Class 10 Maths formulas chapter-wise, this post is for you. We've curated all the important formulas from the NCERT Class 10 Maths book to help you boost your board exam preparation. Each chapter's formulas are arranged neatly for your easy reference.

Table of Contents

• 1. Real Numbers
• 2. Polynomials
• 3. Pair of Linear Equations in Two Variables
• 4. Quadratic Equations
• 5. Arithmetic Progressions
• 6. Triangles
• 7. Coordinate Geometry
• 8. Introduction to Trigonometry
• 9. Applications of Trigonometry
• 10. Circles
• 11. Constructions
• 12. Areas Related to Circles
• 13. Surface Areas and Volumes
• 14. Statistics
• 15. Probability

1. Real Numbers

• Euclid’s Division Lemma: a = bq + r, 0 ≤ r < b
• HCF × LCM = Product of two numbers
• Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes.

2. Polynomials

• For ax² + bx + c:
  Sum of zeroes = -b/a
  Product of zeroes = c/a
• Relationship between zeroes and coefficients

3. Pair of Linear Equations in Two Variables

• General form: ax + by = c
• Solution methods: Substitution, Elimination, Cross-Multiplication
• Condition for consistency:
  - a₁/a₂ ≠ b₁/b₂ → unique solution
  - a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → no solution
  - a₁/a₂ = b₁/b₂ = c₁/c₂ → infinite solutions

4. Quadratic Equations

• Standard form: ax² + bx + c = 0
• Discriminant: D = b² - 4ac
• Roots: x = (-b ± √D) / 2a
• Nature of Roots based on D

5. Arithmetic Progressions

• nth term: aₙ = a + (n - 1)d
• Sum of n terms: Sₙ = n/2 × [2a + (n - 1)d]

6. Triangles

• Pythagoras Theorem: (Hypotenuse)² = (Base)² + (Height)²
• Basic Proportionality Theorem
• Area of similar triangles = (ratio of sides)²

7. Coordinate Geometry

• Distance: √[(x₂ - x₁)² + (y₂ - y₁)²]
• Mid-point: ((x₁ + x₂)/2, (y₁ + y₂)/2)
• Section: (mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)

8. Introduction to Trigonometry

• sinθ = Perpendicular/Hypotenuse
• cosθ = Base/Hypotenuse
• tanθ = Perpendicular/Base
• Identities:
  sin²θ + cos²θ = 1
  1 + tan²θ = sec²θ
  1 + cot²θ = cosec²θ

9. Applications of Trigonometry

• Use of height & distance
• Angle of elevation and depression

10. Circles

• Tangent: Perpendicular to the radius at point of contact
• Only two tangents from external point

11. Constructions

• Division of line segment
• Tangents to a circle from an external point

12. Areas Related to Circles

• Area = πr²
• Circumference = 2πr
• Sector area = (θ/360) × πr²
• Arc length = (θ/360) × 2πr

13. Surface Areas and Volumes

• Cylinder:
  TSA = 2πr(h + r), Volume = πr²h
• Cone:
  TSA = πr(l + r), Volume = (1/3)πr²h
• Sphere:
  TSA = 4πr², Volume = (4/3)πr³
• Hemisphere:
  TSA = 3πr², Volume = (2/3)πr³

14. Statistics

• Mean = Σfx / Σf
• Median = l + [(n/2 – cf)/f] × h
• Mode = l + [(f₁ – f₀)/(2f₁ – f₀ – f₂)] × h

15. Probability

• P(E) = Number of favorable outcomes / Total outcomes
• 0 ≤ P(E) ≤ 1

Conclusion

Understanding and practicing these Class 10 Maths formulas chapter-wise will help you solve questions faster in your board exams. Revise them regularly and apply them in NCERT and sample papers to improve your accuracy and speed.

Frequently Asked Questions (FAQs)

Q1. How can I remember all Class 10 Maths formulas?
A: Practice is key. Write them down daily, use flashcards, and solve questions to apply them.

Q2. Are these formulas enough for CBSE Class 10 Maths board exam?
A: Yes, these formulas are based on the NCERT syllabus and cover all exam-relevant topics.

Q3. Which chapters have the most formulas?
A: Trigonometry, Surface Areas & Volumes, Statistics, and Quadratic Equations have the most formulas.

Q4. Where can I download the PDF of these formulas?
A: A downloadable PDF version will be added soon. You can bookmark this blog for quick access.

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