Maths Formulas for Class 12 – All Chapters

Class 12 students, want to know the easiest way to score more marks in Maths? It’s none other than knowing all formulas of Maths class 12. Yes, it’s not at all difficult! It’s easier than most subjects. Having all formulas in one place also revises exams and builds a strong base for future entrance exams. This blog is perfect if you’re a Class 12 CBSE student looking for a complete list of Maths formulas for Class 12 and tips on how to learn them easily. Plus, we’ve added some practice questions to help you apply what you’ve learnt. So, let’s get started with Class 12, all formulas chapter-wise!

List of Important Class 12 Maths Formulas

Before we begin sharing all the Maths formulas for class 12, here’s a quick list of the most important ones. These formulas are frequently asked, easy to apply, and learning them by heart can help you score well. While these are high-weightage and commonly tested, this doesn’t mean the other formulas can be skipped; you must memorise all formulas to aim for a perfect 100. We’re sure you don’t wanna miss out on any, so here’s the shorter list first:

• |A| = a₁₁(a₂₂a₃₃ – a₂₃a₃₂) – a₁₂(a₂₁a₃₃ – a₂₃a₃₁) + a₁₃(a₂₁a₃₂ – a₂₂a₃₁)
• A⁻¹ = (1/|A|) × Adj(A) (if |A| ≠ 0)
• (AB)ᵗ = BᵗAᵗ
• 
• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• 2tan⁻¹x = sin⁻¹(2x / (1 + x²))
• ∫eˣ dx = eˣ + C
• ∫1/x dx = ln|x| + C
• ∫ xn dx = (xn + 1) / (n + 1) + C
• Slope of tangent = dy/dx
• P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
• P(A|B) = P(A ∩ B) / P(B), P(B) ≠ 0

Chapter-Wise List of Maths Formulas for Class 12

Looking for a complete, easy-to-revise, and well-explained list of Maths formulas for class 12? You’ve landed at the right place. Below is a chapter-wise breakdown of all the formulas from the CBSE Class 12 Maths syllabus. These are meant for quick revision and strengthening your foundation for CBSE board exams and competitive entrances.

1. Relations and Functions

This chapter forms the foundation for later chapters and is often used for MCQs and short questions. Questions from this topic typically involve identifying the relation type, finding domains, and evaluating composite functions.

The class 12 Maths formulas from this chapter are stated as follows:

• Domain of f/g = Domain of f ∩ Domain of g, provided g(x) ≠ 0
• Composite Function: (f ∘ g)(x) = f(g(x))
• Binary Operation: A binary operation *: A × A → A

2. Inverse Trigonometric Functions

This chapter usually has only one question in the exam, typically based on simplification using identities. Thus, it carries only 4 marks in total. However, the formulas are important in calculus.

Formulas from this chapter are stated as follows:

• sin⁻¹x + cos⁻¹x = π/2
• tan⁻¹x + cot⁻¹x = π/2
• 2tan⁻¹x = sin⁻¹(2x / (1 + x²))
• tan⁻¹x − tan⁻¹y = tan⁻¹((x − y)/(1 + xy)) when xy > −1

3. Matrices

Matrices is a direct and scoring chapter of 5 marks. Usually, one question focusing on matrix operations, transposition, and finding inverse matrices is asked in the exam. 

The Maths formulas for class 12 from this chapter are stated as follows:

• (AB)ᵗ = BᵗAᵗ
• A⁻¹ = (1/|A|) × adj(A), if |A| ≠ 0
• A · A⁻¹ = I
• adj(A) = Transpose of cofactor matrix
• If A = [aᵢⱼ], then Aᵗ = [aⱼᵢ]

4. Determinants

This chapter carries 5 marks in the CBSE board exam. You can expect 1 question, usually formula-based, which may involve calculating a 3×3 determinant, applying properties, or solving using Cramer’s Rule. It’s direct, primarily and highly scoring if you know the formulas well.

The class 12 Maths Formulas from this chapter are stated as follows:

• Determinant of 3×3 matrix:

|A| = a₁₁(a₂₂a₃₃ − a₂₃a₃₂) − a₁₂(a₂₁a₃₃ − a₂₃a₃₁) + a₁₃(a₂₁a₃₂ − a₂₂a₃₁)

• Area of triangle using determinant:

(1/2)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

• Cramer’s Rule: x = |Aₓ| / |A|

Properties: Interchanging rows changes sign, multiplying row by scalar multiplies determinant by that scalar

5. Continuity and Differentiability

One of Calculus’s most conceptual and significant chapters, this chapter usually carries around 9 marks. You can expect 2 to 3 questions, often a mix of proving continuity, checking differentiability, and applying derivative formulas (including chain, product, and quotient rules). This chapter forms the backbone for upcoming Calculus topics like derivatives and integrals, so practice well!

Formulas from this chapter are stated as follows:

• A function f(x) is continuous at x = a if: limₓ→a⁻ f(x) = limₓ→a⁺ f(x) = f(a)
• A function is differentiable at x = a if:
• limₕ→0⁻ [f(a+h) − f(a)]/h = limₕ→0⁺ [f(a+h) − f(a)]/h

• (xⁿ)’ = nxⁿ⁻¹
• (eˣ)’ = eˣ
• (aˣ)’ = aˣ·ln a
• (logₐx)’ = 1/(x ln a)
• (sin x)’ = cos x, (cos x)’ = −sin x

6. Applications of Derivatives

This chapter tests your ability to apply derivatives in real-life scenarios such as maxima, minima, rate of change, and tangents. It is generally application-based, so a good grasp of concepts and formulas is important. You must keep in mind that only 4 marks have been allotted to this chapter. 

The Maths formulas for class 12 from this chapter are stated as follows:

• Rate of change of quantity: dy/dx
• Equation of tangent: y − y₁ = m(x − x₁), where m = f'(x₁)
• Increasing/decreasing function:
• f'(x) > 0 ⇒ increasing
• f'(x) < 0 ⇒ decreasing

Maxima/Minima:

• If f'(x) = 0 and f”(x) < 0 ⇒ local maxima
• If f'(x) = 0 and f”(x) > 0 ⇒ local minima

7. Integrals

A high-weightage chapter of 9 marks that deals with indefinite and definite integration. Questions are both conceptual and formula-based. Suppose you learn integration as the reverse process of differentiation, and practice its types like substitution, partial fractions, and by parts. In that case, you can solve all the questions this chapter asks. 

Formulas from this chapter are stated as follows:

• ∫xⁿ dx = (xⁿ⁺¹)/(n + 1) + C, for n ≠ −1
• ∫eˣ dx = eˣ + C
• ∫1/x dx = ln|x| + C
• ∫aˣ dx = aˣ/ln a + C
• ∫sin x dx = −cos x + C
• ∫cos x dx = sin x + C
• ∫1/(x² + a²) dx = (1/a)·tan⁻¹(x/a) + C
• ∫1/√(a² − x²) dx = sin⁻¹(x/a) + C
• Properties of definite integrals:
• ∫ₐᵇ f(x) dx = ∫ₐᵇ f(a + b − x) dx
• ∫ₐᵇ f(x) dx = −∫ᵇₐ f(x) dx

8. Applications of Integrals

This chapter uses definite integrals to find the area under and between curves. It generally carries 6 marks, usually as 1 long-form question. You’ll be required to interpret graphs and apply area formulas. Though it looks graphical, the calculation is formula-driven. This chapter is a scoring one with straightforward methods once the concept is clear.

The class 12 Maths formulas from this chapter are stated as follows:

• Area under curve and x-axis: A = ∫ₐᵇ f(x) dx
• Area between two curves: A = ∫ₐᵇ [f(x) − g(x)] dx, where f(x) ≥ g(x)

9. Differential Equations

This is a moderately challenging yet important chapter. You must practice reducing differential equations to separable or linear form to make this chapter easy and highly scoreable.

Formulas from this chapter are stated as follows:

Order and degree: Order is the highest derivative; degree is the power of the highest derivative (no fractional powers).

• General solution: y + C
• Particular solution: When a specific condition is applied
• Linear DE: dy/dx + P(x)y = Q(x)
• Integrating factor (IF): IF = e^(∫P dx)
• Solution: y·IF = ∫Q·IF dx + C

10. Vectors

This chapter is based on the geometric interpretation of vector operations. Operations like the dot and cross products are frequently asked, formula-based, and direct.

Formulas from this chapter are stated as follows:

• a·b = |a||b|cosθ (dot product)
• a × b = |a||b|sinθ·n̂ (cross product)
• Magnitude: |a| = √(a₁² + a₂² + a₃²)
• Direction Cosines: l = a/|a|, m = b/|a|, n = c/|a|
• Vector projection: Proj of a on b = (a·b/|b|²)·b

11. Three-Dimensional Geometry

Questions are primarily based on line and plane equations and angles between them. You must also practice interpreting direction ratios and cosines. It carries 7 marks and often includes 1–2 questions. 

The Maths formulas for class 12 from this chapter are stated as follows:

• Distance between two points: √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]
• Direction cosines: cos α = l, cos β = m, cos γ = n
• Line in vector form: r = a + λb
• Plane equation: ax + by + cz + d = 0
• Angle between two lines: cosθ = (a·b)/|a||b|

12. Linear Programming

A simple and scoring chapter of 5 marks. Forming equations from word problems and solving graphically using the corner point method is the trick. Tip: Always shade the feasible region carefully.

Mathematics formula of class 12 from this chapter are stated as follows:

• Objective function: Z = ax + by (to maximise or minimise)
• Constraints: Linear inequalities
• Feasible region: Graphical intersection of inequalities
• Optimal value: Corner point method

13. Probability

This chapter carries 8 marks, so you expect one story-based question and another direct formula-based application. The key to scoring here lies in understanding the nature of events and applying the correct probability formula accordingly. Tip: Practice problems involving tree diagrams and Venn diagrams. 

Formulas from this chapter are stated as follows:

• P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
• P(A | B) = P(A ∩ B) / P(B)
• Bayes’ Theorem:
• P(Eᵢ | A) = [P(Eᵢ)·P(A | Eᵢ)] / Σ P(Eⱼ)·P(A | Eⱼ)
• Independent events: P(A ∩ B) = P(A)·P(B)

Also Learn: Physics Formulas for Class 12

Class 12 Maths Formulas Examples with Solutions

If you’ve completed the chapters or feel ready to test yourself, we’ve shared 5 practice questions with answers based on Maths formulas for class 12. Let’s get started and see how many you get correct! 

Example 1: If P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2

Find P(A ∪ B).

Solution:

To find P(A ∪ B), let’s use the formula,

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Thus, P(A ∪ B) = 0.4 + 0.5 – 0.2 

P(A ∪ B) = 0.9 – 0.2 

Answer: P(A ∪ B) = 0.7 

Example 2: Evaluate ∫ x·eˣ dx

Solution:

Use the integration by parts formula:

∫ u·dv = u·v – ∫ v·du

Let u = x ⇒ du = dx

dv = eˣ dx ⇒ v = eˣ

Then,

∫ x·eˣ dx = x·eˣ – ∫ eˣ dx

= x·eˣ – eˣ + C

Answer: ∫ x·eˣ dx = eˣ(x – 1) + C

Example 3: Find the slope of the tangent to y = x³ – 5x² at x = 1

Solution:

Differentiate: dy/dx = 3x² – 10x

The formula of a slope = dy/dx at x = a

At x = 1, dy/dx = 3(1)² – 10(1) = 3 – 10 = –7

Answer: Slope = –7

Example 4: Evaluate ∫ (3x + 1)/(x² + x) dx

Solution:

First, factor the denominator: x² + x = x(x + 1)

To integrate, we break it using partial fractions.

The formula used is:

(3x + 1)/(x(x + 1)) = A/x + B/(x + 1)

Now solve:

(3x + 1) = A(x + 1) + Bx

⇒ A + B = 3 and A = 1 ⇒ B = 2

So,

∫ (3x + 1)/(x(x + 1)) dx = ∫ (1/x + 2/(x + 1)) dx

Answer: ln|x| + 2ln|x + 1| + C

Example 5: The volume of a sphere increases at a rate of 100 cm³/sec. Find the rate of change of radius when the radius is 5 cm.

Solution:

Let the volume of the sphere be V = (4/3)πr³.

To relate volume and radius, we differentiate both sides for time t.

The formula used is:

dV/dt = 4πr²·dr/dt

We are given dV/dt = 100 and r = 5.

Substitute:

100 = 4π(5²)·dr/dt

100 = 100π·dr/dt

Answer: dr/dt = 1/π ≈ 0.318 cm/sec

Tips to Memorise Maths Formulas for Class 12 Students

Looking for simple ways to remember all formulas of Maths class 12 CBSE? Well, remembering formulas isn’t about repeating them in a loop. You must understand when and how to apply them correctly to get the correct answer. To help you figure this out, here are 5 tips:

• Always keep a formula sheet beside you when solving a particular chapter. As you work through the exercises, you’ll notice which formulas are used more often and which are less important. This approach helps you identify which formulas you cannot miss. 

• The best way to learn a formula is by applying it to different types of sums. So, you must solve a variety of questions using the same formula. By the end of your practice session, you’ll remember the formula and understand precisely where and how to use it.

• Make it a habit to write down the formula every time you use it while solving a question. You will remember it well this way. Plus, marks are often awarded in board exams for writing the correct formula, so it’s a habit worth developing.

• Try to revise using a formula sheet, which you can easily create by compiling the chapter-wise formulas listed below. Combine them into a single PDF so you have all the crucial formulas in one place for quick revision before every exam.

• Print out the class 12 Maths formula all chapters PDF you have created for daily revision. Stick it on the wall above your desk. Glance through it before and after solving questions to keep it fresh in your memory.

FAQs