Ultimate Guide to Maths Formulas for Class 10 (Free Formula Sheet PDF)

Are you looking for a complete list of maths formulas for Class 10 to help you excel in your exams? Whether you’re preparing for school exams, board exams, or just want to revise, you’ve come to the right place! In this comprehensive guide, we’ll walk you through all the essential maths formulas, neatly organized by chapters. Plus, we’ve got a Formula Sheet for Maths available for free download!

Let’s dive into the key maths formulas  that will help you solve problems faster and improve your understanding of the subject.

📌 Why Knowing Maths Formulas for Class 10 is Essential

Class 10 maths covers a wide range of topics, including algebra, geometry, trigonometry, and statistics. Mastering the formulas for Class 10 is crucial because:

• ✅ They help solve complex problems quickly and accurately
  
• ✅ They lay the foundation for higher-level maths in Class 11 and beyond
  
• ✅ They ensure you understand the underlying concepts, not just the equations
  
• ✅ They increase your speed and accuracy during exams
  

With the right set of formulas, you’ll not only be able to solve problems faster but also gain confidence in tackling even the most difficult questions.

Chapter-wise Maths Formulas for Class 10

Here’s a chapter-wise list of essential maths formulas for Class 10. Having these formulas at your fingertips will make it easier to solve even the toughest problems.

📏 1. Algebra

• Quadratic Formula:
  x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac​​
  Use this formula to find the roots of quadratic equations in the form ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0.
• Identity for Squares:
  • (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2
  • (a−b)2=a2−2ab+b2(a – b)^2 = a^2 – 2ab + b^2(a−b)2=a2−2ab+b2

These identities are essential for expanding expressions and simplifying algebraic equations.

📐 2. Geometry

• Area of Triangle:
  Area=12×Base×Height\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}Area=21​×Base×Height
  This formula helps you calculate the area of any triangle when you know the base and height.
• Pythagoras Theorem (Right-Angled Triangle):
  a2+b2=c2a^2 + b^2 = c^2a2+b2=c2
  Where ccc is the hypotenuse. This theorem is fundamental in solving problems involving right-angled triangles.
• Surface Area and Volume of 3D Figures:
  • Volume of a Cube: V=a3V = a^3V=a3
  • Volume of a Cuboid: V=l×b×hV = l \times b \times hV=l×b×h
  • Surface Area of a Sphere: A=4πr2A = 4\pi r^2A=4πr2

These formulas are key for calculating the surface area and volume of common 3D objects.

🧮 3. Trigonometry

• Basic Trigonometric Ratios:
  • sin⁡θ=OppositeHypotenuse\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}}sinθ=HypotenuseOpposite​
  • cos⁡θ=AdjacentHypotenuse\cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}}cosθ=HypotenuseAdjacent​
  • tan⁡θ=OppositeAdjacent\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}tanθ=AdjacentOpposite​

These ratios are crucial for solving problems involving right-angled triangles. You’ll often use them to find unknown sides or angles.

• Trigonometric Identities:
  • sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1sin2θ+cos2θ=1
  • 1+tan⁡2θ=sec⁡2θ1 + \tan^2\theta = \sec^2\theta1+tan2θ=sec2θ

These identities form the backbone of most trigonometry problems, so it’s important to remember them and understand how they’re used.

📊 4. Statistics

• Mean:
  Mean=Sum of observationsNumber of observations\text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}}Mean=Number of observationsSum of observations​
  This formula is used to calculate the average of a set of numbers.
• Probability:
  • P(Event)=Number of favorable outcomesTotal number of outcomesP(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}P(Event)=Total number of outcomesNumber of favorable outcomes​
    Understanding probability and how to apply this formula is essential for Class 10 statistics.

📐 5. Coordinate Geometry

• Distance Formula:
  d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
  Use this formula to find the distance between two points on the coordinate plane.
• Midpoint Formula:
  M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)M=(2×1​+x2​​,2y1​+y2​​)
  The midpoint formula helps to find the center point between two points.

📥 Download the Free Class 10 Maths Formula Sheet PDF

Want to keep these formulas handy for revision or exam preparation? We’ve created a FREE Maths Formulas for Class 10 PDF that includes all the essential formulas you need. Download it and keep it as a quick reference while practicing problems.

👉 Click here to download the Maths Formulas for Class 10 PDF
(Replace with actual download link)

This Formula Sheet for Class 10 Maths is designed to be concise and easy to use, giving you everything you need to excel in your exams.

🧩 Tips to Master Maths Formulas for Class 10

While knowing the formulas is important, understanding how and when to apply them is just as crucial. Here are a few tips to help you memorize and use these formulas effectively:

1. 🔄 Practice Regularly: The more you practice using these formulas, the easier they’ll be to recall when you need them.
2. 📚 Understand the Concepts: Don’t just memorize formulas—understand the logic behind them and when they should be used.
3. 📝 Solve Practice Problems: Apply these formulas in different types of problems to strengthen your skills.
4. 📅 Revise Frequently: Schedule regular revision sessions to keep the formulas fresh in your memory.
5. 🎯 Use Flashcards: Write down the formulas on flashcards and test yourself regularly.

✅ Conclusion

Mastering maths formulas for Class 10 is key to achieving success in your exams. By understanding and practicing these formulas regularly, you’ll be able to solve complex problems quickly and accurately. Whether you’re revising for your school exams or preparing for board exams, these formulas are essential tools for excelling in Class 10 maths.

Don’t forget to download your Formula Sheet for Class 10 Maths PDF from Learnosphere for quick reference during your studies. With consistent practice, you’ll be well on your way to acing your exams!