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📘 CBSE Class 10 Maths - Chapter-wise Study Notes

Comprehensive revision notes, theorem proofs, and concept explanations for all 14 chapters.

Chapter 1: Real Numbers
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Chapter 2: Polynomials
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Chapter 3: Pair of Linear Equations
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Chapter 4: Quadratic Equations
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Chapter 5: Arithmetic Progressions
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Chapter 6: Triangles
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Chapter 7: Coordinate Geometry
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Chapter 8: Trigonometry
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Chapter 9: Appl. of Trigonometry
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Chapter 10: Circles
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Chapter 11: Areas Related to Circles
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Chapter 12: Surface Areas & Volumes
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Chapter 13: Statistics
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Chapter 14: Probability
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📐 CBSE Class 10 Maths - All Chapters Formula Sheets

Quick revision formula sheets and core concepts for Class 10 board exams!

Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Trigonometry
Chapter 9: Appl. of Trigonometry
Chapter 10: Circles
Chapter 11: Areas Related to Circles
Chapter 12: Surface Areas & Volumes
Chapter 13: Statistics
Chapter 14: Probability
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Class 10 - Chapter 1: Real Numbers

1. Fundamental Theorem of Arithmetic: Every composite number can be uniquely factorized into primes.
2. HCF & LCM: HCF(a, b) × LCM(a, b) = a × b.

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Class 10 - Chapter 2: Polynomials

1. Quadratic Polynomial: ax² + bx + c
2. Sum of Zeroes (α + β): -b / a
3. Product of Zeroes (αβ): c / a

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Class 10 - Chapter 3: Pair of Linear Equations

1. Unique solution: a₁/a₂ ≠ b₁/b₂
2. Infinitely many solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
3. No solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂

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Class 10 - Chapter 4: Quadratic Equations

1. Standard Form: ax² + bx + c = 0 (a ≠ 0)
2. Discriminant: D = b² - 4ac
3. Quadratic Formula: x = (-b ± √D) / 2a

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Class 10 - Chapter 5: Arithmetic Progressions

1. nth Term: aₙ = a + (n - 1)d
2. Sum of n Terms: Sₙ = (n / 2) × [2a + (n - 1)d] or Sₙ = (n / 2) × (a + l)

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Class 10 - Chapter 6: Triangles

1. BPT (Thales Theorem): Parallel line divides sides proportionally.
2. Similarity Criteria: AAA, SSS, SAS criteria.

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Class 10 - Chapter 7: Coordinate Geometry

1. Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]
2. Section Formula: ((m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂))
3. Mid-point: ((x₁ + x₂)/2, (y₁ + y₂)/2)

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Class 10 - Chapter 8: Trigonometry

1. Ratios: sin θ = Opp/Hyp, cos θ = Adj/Hyp, tan θ = Opp/Adj
2. Identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ

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Class 10 - Chapter 9: Some Applications of Trigonometry

1. Angle of Elevation: Angle formed when viewing above horizontal line.
2. Angle of Depression: Angle formed when viewing below horizontal line.

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Class 10 - Chapter 10: Circles

1. Tangent Theorem: Tangent is perpendicular to radius at point of contact.
2. Length of Tangents: Tangents from external point are equal.

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Class 10 - Chapter 11: Areas Related to Circles

1. Area of Sector: (θ / 360°) × πr²
2. Length of Arc: (θ / 360°) × 2πr
3. Area of Segment: Area of Sector - Area of Triangle

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Class 10 - Chapter 12: Surface Areas and Volumes

1. Cylinder: CSA = 2πrh, Volume = πr²h
2. Cone: CSA = πrl, Volume = (1/3)πr²h
3. Sphere: Surface Area = 4πr², Volume = (4/3)πr³

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Class 10 - Chapter 13: Statistics

1. Mean (x̄): Σfᵢxᵢ / Σfᵢ
2. Mode: L + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h
3. Median: L + [(n/2 - cf)/f] × h

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Class 10 - Chapter 14: Probability

1. Probability P(E): Favourable Outcomes / Total Outcomes
2. Complementary Events: P(E) + P(not E) = 1
3. Range: 0 ≤ P(E) ≤ 1