Class 10 Maths Important Formulas – Complete A to Z Formula Sheet

This post contains all important Class 10 Maths formulas with proper symbols, as written in board exam answer sheets.

Chapter 1: Real Numbers

• Euclid Division Algorithm: a = bq + r, where 0 ≤ r < b
• HCF × LCM = Product of two positive integers

Chapter 2: Polynomials

• For quadratic polynomial ax² + bx + c:
• α + β = −b / a
• αβ = c / a

Chapter 3: Pair of Linear Equations in Two Variables

• a₁/a₂ = b₁/b₂ = c₁/c₂ → Infinitely many solutions
• a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → No solution
• a₁/a₂ ≠ b₁/b₂ → Unique solution

Chapter 4: Quadratic Equations

• Standard form: ax² + bx + c = 0
• Discriminant, D = b² − 4ac
• D > 0 → roots are real and distinct
• D = 0 → roots are real and equal
• D < 0 → no real roots
• x = (−b ± √D) / 2a

Chapter 5: Arithmetic Progressions (AP)

• a_n = a + (n − 1)d
• S_n = n/2 [2a + (n − 1)d]

Chapter 6: Triangles (Complete Theorems and Formulas)

• Basic Proportionality Theorem (Thales Theorem):
• If a line is drawn parallel to one side of a triangle to intersect the other two sides, then it divides the two sides in the same ratio.
• Similar Triangles:
• Ratio of corresponding sides of two similar triangles is constant.
• Ratio of the areas of two similar triangles = (Ratio of corresponding sides)²
• Pythagoras Theorem:
• In a right-angled triangle, (Hypotenuse)² = (Base)² + (Perpendicular)²
• Converse of Pythagoras Theorem:
• If in a triangle, the square of one side equals the sum of squares of the other two sides, then the triangle is right-angled.

Chapter 7: Coordinate Geometry (All Important Formulas)

• Distance Formula: √[(x₂ − x₁)² + (y₂ − y₁)²]
• Midpoint Formula: ((x₁ + x₂)/2 , (y₁ + y₂)/2)
• Section Formula (Internal): ((mx₂ + nx₁) / (m + n) , (my₂ + ny₁) / (m + n))
• Area of triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃) is:
• Area = (1/2) | x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) |

Chapter 8: Trigonometric Identities

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
• sinθ = 1 / cosecθ
• cosθ = 1 / secθ
• tanθ = 1 / cotθ
• cosecθ = 1 / sinθ
• secθ = 1 / cosθ
• cotθ = 1 / tanθ

Chapter 9: Trigonometric Ratios (Right Triangle)

• sinθ = Perpendicular / Hypotenuse
• cosθ = Base / Hypotenuse
• tanθ = Perpendicular / Base
• cosecθ = Hypotenuse / Perpendicular
• secθ = Hypotenuse / Base
• cotθ = Base / Perpendicular

Chapter 10: Trigonometric Values

• sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
• sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1
• sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3

Chapter 11: Circles

• Area of circle = πr²
• Circumference of circle = 2πr
• Radius ⟂ Tangent at point of contact

Chapter 12: Surface Areas and Volumes (All Important Formulas)

• Cuboid:
• Lateral Surface Area (LSA) = 2h(l + b)
• Total Surface Area (TSA) = 2(lb + bh + hl)
• Volume = lbh
• Cube:
• Lateral Surface Area (LSA) = 4a²
• Total Surface Area (TSA) = 6a²
• Volume = a³
• Right Circular Cylinder:
• Curved Surface Area (CSA) = 2πrh
• Total Surface Area (TSA) = 2πr(r + h)
• Volume = πr²h
• Right Circular Cone:
• Slant height, l = √(r² + h²)
• Curved Surface Area (CSA) = πrl
• Total Surface Area (TSA) = πr(l + r)
• Volume = (1/3)πr²h
• Sphere:
• Curved Surface Area (CSA) = 4πr²
• Total Surface Area (TSA) = 4πr²
• Volume = (4/3)πr³
• Hemisphere:
• Curved Surface Area (CSA) = 2πr²
• Total Surface Area (TSA) = 3πr²
• Volume = (2/3)πr³

Chapter 13: Statistics

• Mean = (Σf_ix_i) / (Σf_i)

Chapter 14: Probability

• P(E) = Number of favourable outcomes / Total number of outcomes
• 0 ≤ P(E) ≤ 1

Tip: Revise this formula sheet daily. Save this page for last day revision before board exams.