1. Trigonometry
Trigonometry is one of the most fascinating topics in Class 10. Here are the must-know formulas:
- Trigonometric Ratios:
- sinα = Opposite / Hypotenuse
- cosα = Adjacent / Hypotenuse
- tanα = Opposite / Adjacent
- cotα = 1 / tanα
- secα = 1 / cosα
- cosecα = 1 / sinα
- Trigonometric Identities:
- sin²A + cos²A = 1
- 1 + tan²A = sec²A
- 1 + cot²A = cosec²A
- Complementary Angles:
- sin(90° − θ) = cosθ
- cos(90° − θ) = sinθ
- tan(90° − θ) = cotθ
- cot(90° − θ) = tanθ
- sec(90° − θ) = cosecθ
- cosec(90° − θ) = secθ
2. Quadratic Equations
Quadratic equations appear frequently in exams. Here’s the standard formula to solve them:
- Quadratic Formula: x = (-b ± √(b² – 4ac)) / 2a
- Sum of Roots: -b / a
- Product of Roots: c / a
3. Arithmetic Progressions (AP)
Sequences and series form the basis of Arithmetic Progressions:
- nth Term of AP: aₙ = a + (n − 1)d
- Sum of First n Terms: Sₙ = n / 2 [2a + (n − 1)d]
Where a is the first term, d is the common difference, and n is the number of terms.
4. Statistics
Statistics is all about analyzing data. These formulas help you calculate key measures:
- Mean (Direct Method): Mean = Σf * x / Σf
- Median Formula: Median = l + [(N/2 − cf) / f] * h
- Mode Formula: Mode = l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] * h
5. Coordinate Geometry
Coordinate Geometry links algebra and geometry beautifully:
- Distance Between Two Points: √[(x₂ − x₁)² + (y₂ − y₁)²]
- Midpoint Formula: [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
- Slope Formula: m = (y₂ − y₁) / (x₂ − x₁)
- Centroid Formula: [(x₁ + x₂ + x₃) / 3, (y₁ + y₂ + y₃) / 3]
6. Mensuration
Mensuration involves formulas for finding areas, perimeters, and volumes of 2D and 3D shapes:
- 2D Figures:
- Square: Area = a², Perimeter = 4a
- Rectangle: Area = l * b, Perimeter = 2(l + b)
- Circle: Area = πr², Circumference = 2πr
- 3D Figures:
- Cube: Volume = a³, TSA = 6a²
- Cuboid: Volume = l * b * h, TSA = 2(lb + bh + hl)
- Sphere: Volume = (4/3)πr³, TSA = 4πr²
- Cylinder: Volume = πr²h, TSA = 2πr(h + r)
- Cone: Volume = (1/3)πr²h, CSA = πrl
7. Algebraic Identities
Algebraic identities simplify complex expressions. Here are some key ones:
- (a + b)² = a² + 2ab + b²
- (a − b)² = a² − 2ab + b²
- a² − b² = (a + b)(a − b)
- (x + a)(x + b) = x² + (a + b)x + ab
8. Logarithms
Logarithms are an essential topic for simplifying large numbers:
- log(ab) = loga + logb
- log(a/b) = loga − logb
- logaⁿ = n * loga
- logₐa = 1, logₐ1 = 0
9. Pair of Linear Equations
- General Form: ax + by + c = 0
- Condition for Consistency:
- Consistent and Independent: (a₁/a₂) ≠ (b₁/b₂)
- Consistent and Dependent: (a₁/a₂) = (b₁/b₂) = (c₁/c₂)
- Inconsistent: (a₁/a₂) = (b₁/b₂) ≠ (c₁/c₂)
10. Real Numbers
aᵐ / aⁿ = aᵐ⁻ⁿ
Euclid’s Division Lemma: a = bq + r (0 ≤ r < b)
Laws of Exponents:
aᵐ * aⁿ = aᵐ⁺ⁿ
(aᵐ)ⁿ = aᵐⁿ
Conclusion
This comprehensive list of formulas covers every crucial aspect of Class 10 mathematics. Understanding these formulas and practicing their application is key to mastering the subject and excelling in exams. Bookmark this blog for quick revision and share it with your friends to help them prepare as well.
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