Math Formulas for Class 10 – Complete Guide for Students

 Mathematics is one of the most scoring subjects in Class 10, and having a firm grip on math formulas for Class 10 can make problem-solving faster and more accurate. Whether you are preparing for the board exams or class tests, learning all the important formulas chapter-wise is essential.

In this blog post, we are going to provide a complete and easy-to-understand list of important math formulas for Class 10, which will help you revise and retain them more effectively.

🔗 Also Read: Math Formulas for Class 10 – Complete Chapter-wise List

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📘 Why Are Math Formulas Important in Class 10?

Formulas are the foundation of mathematics. If you remember the correct formula, half of the problem is already solved. Here's why they are important:

• Saves Time: Helps solve problems quickly during exams.

• Improves Accuracy: Reduces the chances of calculation errors.

• Boosts Confidence: Makes you feel more prepared and less stressed.

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✅ Chapter-wise Math Formulas for Class 10

Here’s a quick chapter-wise breakdown of the most important formulas you must remember:

1. Real Numbers

• Euclid’s Division Lemma:
  If a And if there b are two positive integers, then there exist unique integers q and r such that:
  a = bq + r where 0 ≤ r < b

• Fundamental Theorem of Arithmetic:
  Every composite number can be expressed as a product of primes.

2. Polynomials

• If α andAree the zeroes of the quadratic polynomial ax² + bx + c, then:

  • Sum of zeroes = α + β = -b/a

  • Product of zeroes = αβ = c/a

3. Pair of Linear Equations in Two Variables

• General form: ax + by + c = 0

• Methods of solving:

  • Substitution

  • Elimination

  • Cross Multiplication

4. Quadratic Equations

• General form: ax² + bx + c = 0

• Roots:
  x = (-b ± √(b² - 4ac)) / 2a

• Nature of roots:

  • D > 0 → Two real and distinct roots

  • D = 0 → Real and equal roots

  • D < 0 → No real roots

5. Arithmetic Progression (AP)

• nth term: an = a + (n – 1)d

• Sum ofthe  first n terms:
  Sn = n/2 [2a + (n – 1)d]

6. Triangles

• Pythagoras Theorem: a² + b² = c² (Right-angled triangle)

• Area using Heron’s Formula:
  s = (a + b + c)/2
Area = √[s(s – a)(s – b)(s – c)]

7. Coordinate Geometry

• Distance Formula:
  d = √[(x2 – x1)² + (y2 – y1)²]

• Midpoint Formula:
  M = ((x1 + x2)/2 , (y1 + y2)/2)

8. Introduction to Trigonometry

• Basic Ratios:

  • sinθ = Opp/Hyp

  • cosθ = Adj/Hyp

  • tanθ = Opp/Adj

• Trigonometric Identities:

  • sin²θ + cos²θ = 1

  • 1 + tan²θ = sec²θ

  • 1 + cot²θ = cosec²θ

9. Some Applications of Trigonometry

• Height and Distance problems using trigonometric ratios and angles of elevation and depression.

10. Circles

• Tangent to a circle is perpendicular to the radius at the point of contact.

• Lengths of tangents from an external point are equal.

11. Areas Related to Circles

• Area of circle: πr²

• Circumference: 2πr

• Area of sector: (θ/360) × πr²

12. Surface Areas and Volumes

• Cube:

  • Surface Area = 6a²

  • Volume = a³

• Cuboid:

  • Surface Area = 2(lb + bh + hl)

  • Volume = l × b × h

• Cylinder:

  • Surface Area = 2πr(h + r)

  • Volume = πr²h

• Cone:

  • Surface Area = πr(l + r)

  • Volume = (1/3)πr²h

• Sphere:

  • Surface Area = 4πr²

  • Volume = (4/3)πr³

13. Statistics

• Mean:
  Mean = Σfx / Σf

• Mode (Using formula):
  Mode = l + [(f1 – f0) / (2f1 – f0 – f2)] × h

• Median:
  Median = l + [(n/2 – cf) / f] × h

14. Probability

• Probability of an event:
  P(E) = Number of favorable outcomes / Total number of outcomes

📌 Tips to Memorize Math Formulas

• Create a formula chart and paste it near your study desk.

• Revise regularly.

• Practice formulas through problems.

• Make flashcards for quick revision.

📥 Download Full PDF of Class 10 Math Formulas

Want a ready-to-print version? Click below to download all the Math Formulas for Class 10 chapter-wise in one PDF.

👉 Download PDF of Class 10 Math Formulas