All Important Math Formulas for Class 10 and 12 – Complete Chapter-wise List & Memory Tips

Explore the complete list of essential math formulas for Class 10 & 12 with easy memory tricks. Perfect for CBSE, ICSE, ISC & IGCSE board exam preparation.

🔍 Introduction: Why Formulas Are the Key to Cracking Board Maths

If you're preparing for Class 10 or Class 12 board exams—whether CBSE, ICSE, ISC, or IGCSE—you know this one truth:

You can’t solve maths without knowing the right formulas.

Formulas are like weapons in your exam arsenal. Whether you're tackling Geometry, Algebra, Trigonometry, or Calculus, formulas speed up problem-solving and boost accuracy.

In this article, we’ll cover:

  • ✅ Chapter-wise formula lists for Class 10 & 12

  • ✅ Tips to memorize formulas faster

  • ✅ Tricks to retain them during exams

📘 1. Chapter-Wise Important Math Formulas for Class 10

🔹 Real Numbers

  • Euclid’s Division Lemma:
    a = bq + r, where 0 ≤ r < b

  • LCM × HCF = Product of Two Numbers

🔹 Polynomials

  • (x – a)(x – b) = x² – (a + b)x + ab

  • If ax² + bx + c = 0, then:
    Sum of roots = –b/a, Product of roots = c/a

🔹 Linear Equations in Two Variables

  • General form: ax + by + c = 0

  • Solution = Intersection point of two lines

🔹 Quadratic Equations

  • General form: ax² + bx + c = 0

  • Discriminant: D = b² – 4ac

  • Roots: x = (–b ± √D) / 2a

🔹 Arithmetic Progression (AP)

  • nth term: aₙ = a + (n – 1)d

  • Sum of n terms: Sₙ = (n/2)[2a + (n – 1)d]

🔹 Triangles

  • Pythagoras Theorem: a² + b² = c² (right-angled triangle)

  • Area (Heron’s Formula):
    √[s(s–a)(s–b)(s–c)], where s = (a + b + c)/2

🔹 Coordinate Geometry

  • Distance formula:
    √[(x₂ – x₁)² + (y₂ – y₁)²]

  • Midpoint: [(x₁ + x₂)/2 , (y₁ + y₂)/2]

  • Section formula:
    (mx₂ + nx₁)/(m + n) , (my₂ + ny₁)/(m + n)

🔹 Trigonometry

  • Basic Ratios:

    sin θ = Opp/Hyp
cos θ = Adj/Hyp
tan θ = Opp/Adj

  • Identities:

    • sin²θ + cos²θ = 1

    • 1 + tan²θ = sec²θ

    • 1 + cot²θ = cosec²θ

🔹 Circles

  • Angle in semicircle = 90°

  • Tangent ⊥ Radius at point of contact

  • Only one tangent possible at a point on a circle

🔹 Surface Areas and Volumes

  • Cylinder:

    • Surface Area = 2πr(h + r)

    • Volume = πr²h

  • Cone:

    • Surface Area = πr(l + r)

    • Volume = (1/3)πr²h

  • Sphere:

    • Surface Area = 4πr²

    • Volume = (4/3)πr³

🔹 Statistics

  • Mean = Σfᵢxᵢ / Σfᵢ

  • Median using ogives or formula (Grouped data)

🔹 Probability

  • Probability =
    Favorable outcomes / Total outcomes

📘 2. Chapter-Wise Important Math Formulas for Class 12

🔹 Relations and Functions

  • Cartesian Product: A × B = {(a, b) | a ∈ A, b ∈ B}

  • Types: One-one, Onto, Bijective

🔹 Inverse Trigonometry

  • sin⁻¹(sin x) = x,
    cos⁻¹(cos x) = x, within domain

  • sin⁻¹x + cos⁻¹x = π/2

🔹 Matrices

  • Addition: A + B = [aᵢⱼ + bᵢⱼ]

  • Transpose: Row ↔ Column

  • Inverse: A⁻¹ = adj(A)/|A| when |A| ≠ 0

🔹 Determinants

  • Determinant of 2×2: |a b| = ad – bc
    |c d|

  • Properties of determinants & Cramer's Rule

🔹 Continuity and Differentiability

  • dy/dx of:

    • xⁿ = nxⁿ⁻¹

    • sin x = cos x

    • cos x = –sin x

    • eˣ = eˣ, ln x = 1/x

🔹 Applications of Derivatives

  • Tangent, Normal

  • Increasing/Decreasing functions

  • Maxima/Minima using f'(x) = 0 and sign chart

🔹 Integrals

  • ∫xⁿ dx = (xⁿ⁺¹)/(n + 1) + C, n ≠ –1

  • ∫eˣ dx = eˣ + C

  • ∫1/x dx = ln|x| + C

🔹 Differential Equations

  • General + Particular solutions

  • Variable separable method

🔹 Vectors and 3D Geometry

  • Dot product: a·b = |a||b|cosθ

  • Cross product: Vector perpendicular to both

  • Equation of Line/Plane

🔹 Probability

  • Bayes’ Theorem

  • Independent events

  • P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

🧠 3. Tips to Remember Formulas Easily

🎓 1. Use Mnemonics

  • E.g., “Some People Have Curly Black Hair Through Proper Brushing”
    (for Trigonometric Ratios)

📝 2. Make a Formula Chart

  • Paste it on your wall, door, or desk

  • Revise it twice a day

📱 3. Use Flashcards or Apps

  • Quizlet, Anki, or custom index cards

🔄 4. Practice Daily

  • Apply formulas while solving examples or past papers

  • Don’t just read them—use them

🧪 4. How to Retain Formulas During Exams

  • Revise formulas early morning before your exam

  • Solve 5–10 questions based on key formulas

  • Don’t try to learn new ones during the last minute

  • Use rough sheets to scribble quick notes before you start answering

🎯 Conclusion: Know Them. Use Them. Own Them.

Formulas are the foundation of mathematics. Whether you're preparing for your board exams or competitive tests, these formulas will save time, reduce errors, and boost your confidence.

✔️ Bookmark this article
✔️ Revise formulas weekly
✔️ Practice questions from xMathCop.com with these formulas in action

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