This is your ultimate premium revision guide designed specifically for Class 10 CBSE students who want to score high in board exams. This is not just a formula sheet – it is a complete learning + revision toolkit.
This guide helps you:
- Understand concepts deeply
- Remember formulas easily with logic
- Apply formulas quickly in exams
- Avoid common mistakes students make
If you revise this strategically, you can revise the entire Maths syllabus in 10–15 minutes before the exam and boost your confidence instantly.
Real Numbers
Why This Chapter Matters
This chapter is one of the easiest scoring areas in the CBSE board exam. Most questions are direct, concept-based, and require very little calculation if you know the formulas well.
Key Formulas
| Concept | Formula |
| HCF & LCM | HCF × LCM = Product of two numbers |
| Euclid’s Lemma | a = bq + r (0 ≤ r < b) |
Concept Understanding
Euclid’s Division Lemma helps break numbers into smaller parts, making it easier to find HCF. This is often used in proof-based questions.
Exam Hack
Always reduce numbers using HCF before solving – this saves time and reduces calculation errors.
Common Mistake
Students often forget to check remainder conditions in Euclid’s Lemma.
Polynomials
Why Important
This chapter is frequently asked in short-answer questions and builds the base for algebra.
Key Formulas
| Concept | Formula |
| Sum of zeros | −b/a |
| Product of zeros | c/a |
Must-Learn Identities
- (a + b)² = a² + b² + 2ab
- (a − b)² = a² + b² − 2ab
- a² − b² = (a + b)(a − b)
- (a + b)³ = a³ + b³ + 3ab(a + b)
Concept Insight
These identities are not just formulas – they are shortcuts that reduce long calculations into quick steps.
Memory Trick
Think of identities as “calculation shortcuts” that can save up to 50% time in algebra questions.
Common Mistake
Sign errors while expanding expressions.
Pair of Linear Equations
Concept Overview
This chapter helps you understand relationships between two equations graphically and algebraically.
Quick Concept Table
| Condition | Solution Type | Graph |
| a1/a2 ≠ b1/b2 | Unique solution | Intersecting lines |
| a1/a2 = b1/b2 = c1/c2 | Infinite solutions | Coincident lines |
| a1/a2 = b1/b2 ≠ c1/c2 | No solution | Parallel lines |
Concept Insight
Understanding these conditions helps you identify answers without solving equations fully.
Exam Hack
Use coefficient comparison to directly answer 2-mark questions in seconds.
Common Mistake
Confusing infinite solutions with no solution cases.
Quadratic Equations
Most Important Chapter
This is one of the highest-weightage chapters in the board exam.
Key Formulas
| Concept | Formula |
| Discriminant | D = b² − 4ac |
| Roots | x = [−b ± √D] / 2a |
Root Nature Shortcut
- D > 0 → Two real and distinct roots
- D = 0 → Equal roots
- D < 0 → No real roots
Concept Insight
The discriminant gives you information about roots even before solving the equation.
Exam Hack
Always calculate D first – it helps you choose the correct solving method quickly.
Common Mistake
Forgetting to simplify under-root values.
Arithmetic Progression (AP)
Concept Overview
AP is a sequence where the difference between consecutive terms is constant.
Key Formulas
| Concept | Formula |
| nth term | a + (n−1)d |
| Sum of n terms | n/2 [2a + (n−1)d] |
Concept Insight
AP questions often combine logic and formulas, especially in word problems.
Memory Trick
Remember: “First term + repeated difference pattern”
Common Mistake
Using wrong value of n or d.
Triangles
Concept Overview
This chapter focuses on similarity, proportionality, and geometric reasoning.
Important Theorems
- Basic Proportionality Theorem (BPT)
- Pythagoras Theorem: a² + b² = c²
Concept Insight
Similarity is heavily used in proofs and numerical problems.
Exam Tip
Write steps clearly in proofs to get full marks.
Coordinate Geometry
Concept Overview
This chapter converts geometry into algebra, making calculations easier.
Key Formulas
| Concept | Formula |
| Distance | √[(x2 − x1)² + (y2 − y1)²] |
| Midpoint | [(x1+x2)/2, (y1+y2)/2] |
| Section | [(mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)] |
Concept Insight
These formulas help solve geometry problems using coordinates.
Exam Hack
Always write formula before solving – improves presentation and accuracy.
Trigonometry
Concept Overview
This is one of the most scoring and important chapters.
Most Important Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
Standard Values Table
| θ | sinθ | cosθ | tanθ |
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
Memory Trick
Visualize a triangle – helps remember values faster.
Common Mistake
Mixing up sine and cosine values.
Applications of Trigonometry
Concept Overview
Used in real-life problems involving heights and distances.
Formula
- tanθ = height/base
Exam Hack
Always draw a diagram before solving – reduces errors significantly.
Circles
Concept Overview
Focuses on tangents and circle properties.
Key Theorems
- Tangent is perpendicular to radius
- Tangents from same external point are equal
Exam Tip
Draw neat diagrams – helps in scoring better marks.
Areas Related to Circles
Key Formulas
| Concept | Formula |
| Area of circle | πr² |
| Circumference | 2πr |
| Arc length | (θ/360) × 2πr |
Concept Insight
Used in sector and segment problems.
Surface Areas & Volumes
Important Shapes
| Shape | Volume |
| Cylinder | πr²h |
| Cone | 1/3 πr²h |
| Sphere | 4/3 πr³ |
Concept Insight
Understanding shapes helps in solving mixed solid problems.
Exam Hack
Always check units – missing units can cost marks.
Statistics
Concept Overview
Deals with analyzing grouped data.
Key Formulas
| Concept | Formula |
| Mean | a + (Σfiui / Σfi) × h |
| Median | L + [(N/2 − cf)/f] × h |
| Mode | L + [(f1 − f0)/(2f1 − f0 − f2)] × h |
Concept Insight
Questions often involve tables and step calculations.
Exam Tip
Maintain proper table format to avoid mistakes.
Probability
Concept Overview
Probability measures the chance of an event occurring.
Basic Formula
- Probability = Favourable outcomes / Total outcomes
Common Cases
- Coins
- Dice
- Playing Cards
Exam Hack
Always list all outcomes – prevents calculation mistakes.
Final Revision Strategy (Most Important Section)
- Revise formulas twice daily during last week
- Focus on weak chapters first
- Practice at least 2 questions per formula
- Avoid learning new topics in final days
- Use this sheet for quick revision before exam
FAQs
Q1. How can I revise Maths formulas in one day effectively?
Focus on formula tables and revise chapter-wise with quick examples and practice.
Q2. Which formulas are most important for CBSE boards?
Quadratic equations, trigonometry identities, arithmetic progression, and geometry formulas.
Q3. Is memorizing formulas enough to score high?
No, understanding and application of formulas are equally important.
Conclusion
This premium formula sheet is your complete revision companion. With proper understanding, regular practice, and smart revision, you can significantly improve your speed, accuracy, and confidence in the Class 10 Maths board
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