This formula sheet is designed as a complete exam-ready and concept-based resource for Class 10 CBSE students. It is not just a list of formulas, but a smart revision guide that helps you understand, remember, and apply formulas effectively in your board exams.
Instead of searching multiple books, notes, and PDFs, this guide brings everything together in a structured, easy-to-revise format. Each chapter below not only lists formulas but also explains when and how to use them, what examiners expect, and the mistakes students commonly make.
This guide will help you:
- Revise all formulas in one place
- Understand where and how formulas are used
- Identify high-weightage topics
- Improve speed and accuracy
- Avoid common exam mistakes
Real Numbers
Key Formulas
- HCF × LCM = Product of two numbers
- Euclid’s Division Lemma: a = bq + r (0 ≤ r < b)
Concept Explanation
The Real Numbers chapter builds your fundamental understanding of number properties. Euclid’s Division Lemma is not just a formula—it is a method used to systematically break down numbers and find their HCF. In board exams, this concept is often tested through step-based questions where presentation matters as much as the answer.
Exam Insight
CBSE frequently asks questions based on irrationality proofs, especially involving √2, √3, and √5. These questions test your logical reasoning and ability to write structured proofs.
Common Mistake
Students often jump directly to the conclusion without showing intermediate steps in contradiction-based proofs, which leads to loss of marks.
Polynomials
Key Formulas
- Sum of zeros = −b/a
- Product of zeros = c/a
Important Identities
- (a + b)² = a² + b² + 2ab
- (a − b)² = a² + b² − 2ab
- a² − b² = (a + b)(a − b)
Concept Explanation
Polynomials focus on understanding the relationship between coefficients and roots. These relationships allow you to solve equations faster without lengthy calculations. Algebraic identities act as shortcuts that help simplify expressions and reduce complex calculations into manageable steps.
Exam Insight
Direct formula-based questions are common, especially asking to find sum or product of roots without solving the equation completely.
Common Mistake
Students frequently make sign errors while expanding identities or factorizing expressions, which leads to incorrect answers even if the method is correct.
Pair of Linear Equations
General Form
- a1x + b1y + c1 = 0
- a2x + b2y + c2 = 0
Nature of Solutions
- Unique solution → Intersecting lines
- Infinite solutions → Coincident lines
- No solution → Parallel lines
Concept Explanation
This chapter connects algebra with graphs. Instead of solving equations every time, you can understand the nature of solutions by comparing coefficients. This saves time and helps you quickly identify the correct answer in MCQs or short questions.
Exam Insight
Questions based on identifying the type of solution are very common and can be solved within seconds using ratio comparison.
Quadratic Equations
Key Formulas
- Discriminant: D = b² − 4ac
- Roots: x = [−b ± √D] / 2a
Concept Explanation
Quadratic equations are one of the most important topics in Class 10 Maths. The discriminant plays a crucial role because it tells you the nature of roots even before solving the equation. This helps you decide the correct approach quickly.
Exam Insight
Almost every board exam includes at least one question from this chapter, making it a high-priority topic.
Common Mistake
Students often fail to simplify square roots properly or make calculation mistakes while applying the quadratic formula.
Arithmetic Progression
Key Formulas
- nth term: an = a + (n−1)d
- Sum: Sn = n/2 [2a + (n−1)d]
Concept Explanation
Arithmetic Progression deals with sequences where each term increases or decreases by a constant value. Many real-life problems, such as patterns and series, are based on AP, making this chapter highly practical.
Exam Insight
Word problems are very common and test your ability to translate statements into formulas.
Common Mistake
Students often use incorrect values of n or d, which leads to wrong answers even if the formula is correct.
Triangles
Key Theorems
- Basic Proportionality Theorem (BPT)
- Pythagoras Theorem
Concept Explanation
Triangles is a theorem-based chapter where logical reasoning is more important than formulas. You must understand why a theorem works, not just memorize it. This helps in writing clear and correct proofs.
Exam Insight
Proof-based questions carry significant marks, and step-wise presentation is very important.
Coordinate Geometry
Key Formulas
- Distance formula: √[(x2 − x1)² + (y2 − y1)²]
- Section formula
- Midpoint formula
Concept Explanation
This chapter converts geometric problems into algebraic ones, making calculations easier. Once you know the formulas, most questions become direct substitutions.
Exam Insight
These are among the easiest scoring questions because they are purely formula-based.
Exam Tip
Always write the formula before substituting values. This improves clarity and helps you gain step marks.
Trigonometry
Important Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
Standard Values
0°, 30°, 45°, 60°, 90°
Concept Explanation
Trigonometry may seem difficult at first, but it becomes easy once you understand identities and standard values. These identities help simplify complex expressions quickly.
Exam Insight
Identity-based questions are very common and scoring if practiced well.
Common Mistake
Students often mix up sine and cosine values or forget standard angle values during exams.
Applications of Trigonometry
Key Concept
- Angle of elevation and depression
Concept Explanation
This chapter applies trigonometry to real-life situations like finding the height of buildings or distance of objects. Visualization is key here.
Exam Insight
tan values are used most frequently in these problems.
Exam Tip
Always draw a diagram before solving. It reduces confusion and improves accuracy.
Circles
Key Theorems
- Tangent is perpendicular to radius
- Tangents from same external point are equal
Concept Explanation
This chapter is based on theorems and logical reasoning. Understanding the properties of tangents and radii is essential to solve problems correctly.
Exam Insight
Proof-based questions are commonly asked from this chapter.
Areas Related to Circles
Key Formulas
- Area = πr²
- Circumference = 2πr
- Arc length = (θ/360) × 2πr
Concept Explanation
This chapter focuses on calculating areas and lengths of sectors and segments. It combines geometry with formulas.
Exam Insight
Application-based problems are very common.
Surface Areas & Volumes
Shapes Covered
- Cube, Cuboid
- Cylinder, Cone
- Sphere, Hemisphere
Concept Explanation
This chapter deals with three-dimensional shapes and their measurements. Questions often combine multiple shapes, requiring careful understanding of formulas.
Exam Insight
Mixed solid problems are frequently asked in board exams.
Common Mistake
Students often forget to write units or use incorrect formulas for different shapes.
Statistics
Key Formulas
- Mean (assumed mean method)
- Median
- Mode
Important Relation
Mode = 3 Median − 2 Mean
Concept Explanation
Statistics involves analyzing grouped data and calculating averages. Proper table formation is crucial in solving these problems accurately.
Exam Insight
Questions are mostly step-based and require careful calculation.
Probability
Key Formula
Probability = Favourable outcomes / Total outcomes
Important Cases
- Coin toss
- Dice
- Playing cards (52 cards)
Concept Explanation
Probability helps measure the likelihood of events. Listing all possible outcomes ensures accuracy.
Exam Insight
Simple yet scoring chapter if concepts are clear.
Final Tips for Board 2026
- Revise formulas daily for 10–15 minutes
- Focus more on weak chapters
- Practice previous year questions
- Avoid last-minute new topics
- Use this sheet before entering exam hall
FAQs
Q1. Is this formula sheet enough for boards?
Yes, if you understand and practice applying these formulas properly.
Q2. Which chapters are most important?
Quadratic equations, trigonometry, arithmetic progression, and geometry.
Q3. How many times should I revise formulas?
At least twice daily during the last week before exams.
Conclusion
This extended formula sheet is your complete revision partner for CBSE Boards 2026. With proper understanding, consistent revision, and practice, you can improve your performance, boost confidence, and achieve excellent marks in your Maths exam.
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