CBSE Class 12 Mathematics Quick Revision

One of the most testing times for students is their final year in school where they will be facing their board exams to complete their school life. Taking down the right CBSE class 12 Maths notes does enable students to evaluate what they have learnt on a daily basis in entire year for the examinations. The examinations are never easy and it can be stressful if students are not able to understand what they are learning

AUTHOR: KRISHNA MURTHY

SIZE OF FILE: 6MB

NUMBER OF PAGES: 205

LANGUAGE:  ENGLISH

CATEGORY : MATHEMATICS

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Mathematics XII Quick Revision Full Course Download Link

Quick revision for CBSE Class 12 Mathematics requires summarizing key formulas, concepts, and tips for each chapter to prepare efficiently. Here's a chapter-wise breakdown to help you revise:

1. Relations and Functions

• Key Concepts:
  • Types of relations: Reflexive, Symmetric, Transitive, and Equivalence.
  • Types of functions: One-one, Onto, Bijective.
  • Composition of functions and Inverse of a function.
• Important Formulas:
  • For a bijective function f:A→Bf: A \to B, f−1(f(x))=xf^{-1}(f(x)) = x.

2. Inverse Trigonometric Functions

• Key Concepts:
  • Principal values of inverse trigonometric functions.
  • Properties and identities like sin⁡−1(x)+cos⁡−1(x)=π2\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}.
• Important Formulae:
  • tan⁡−1(x)+tan⁡−1(y)=tan⁡−1(x+y1−xy), if xy<1\tan^{-1}(x) + \tan^{-1}(y) = \tan^{-1}\left(\frac{x + y}{1 - xy}\right), \text{ if } xy < 1.

3. Matrices

• Key Concepts:
  • Types of matrices: Square, Diagonal, Identity, Zero.
  • Operations: Addition, Subtraction, Scalar Multiplication, Matrix Multiplication.
• Key Formulae:
  • (AB)T=BTAT(AB)^T = B^T A^T
  • A−1=adj(A)∣A∣A^{-1} = \frac{\text{adj}(A)}{|A|} (if ∣A∣≠0|A| \neq 0).

4. Determinants

• Key Concepts:
  • Properties of determinants.
  • Area of a triangle using determinants.
• Key Formulae:
  • ∣A∣=∣AT∣|A| = |A^T|
  • Cramer's Rule for solving linear equations.

5. Continuity and Differentiability

• Key Concepts:
  • Continuity of a function at a point.
  • Differentiability implies continuity, but not vice versa.
  • Derivatives of inverse trigonometric, exponential, and logarithmic functions.
• Important Formulae:
  • Chain rule: dydx=dydu⋅dudx\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.
  • ddx[sin⁡−1(x)]=11−x2\frac{d}{dx}[\sin^{-1}(x)] = \frac{1}{\sqrt{1 - x^2}}.

6. Applications of Derivatives

• Key Topics:
  • Increasing and decreasing functions.
  • Maxima and minima of functions.
  • Tangents and normal to curves.

7. Integrals

• Key Topics:
  • Indefinite integrals as the reverse of differentiation.
  • Integration by substitution, parts, and partial fractions.
• Important Formulae:
  • ∫exdx=ex+C\int e^x dx = e^x + C
  • ∫1a2+x2dx=1atan⁡−1(xa)+C\int \frac{1}{a^2 + x^2} dx = \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C.

8. Applications of Integrals

• Key Topics:
  • Area under curves using definite integrals.
  • Area between y=f(x) and y=g(x):∫ab[f(x)−g(x)]dx\text{Area between } y = f(x) \text{ and } y = g(x): \int_{a}^{b} [f(x) - g(x)] dx.

9. Differential Equations

• Key Concepts:
  • Formation of differential equations.
  • General and particular solutions.
  • Methods: Variable separable, Homogeneous, Linear.

10. Vector Algebra

• Key Topics:
  • Scalar (Dot) Product: A⃗⋅B⃗=∣A⃗∣∣B⃗∣cos⁡θ\vec{A} \cdot \vec{B} = |\vec{A}||\vec{B}|\cos\theta.
  • Vector (Cross) Product: A⃗×B⃗=∣A⃗∣∣B⃗∣sin⁡θ n^\vec{A} \times \vec{B} = |\vec{A}||\vec{B}|\sin\theta \, \hat{n}.

11. Three-Dimensional Geometry

• Key Concepts:
  • Equation of a line and plane.
  • Angle between two lines, a line and a plane, or two planes.

12. Linear Programming

• Key Topics:
  • Graphical method to solve linear inequalities.
  • Optimize objective functions (Maximize/Minimize).

13. Probability

• Key Topics:
  • Conditional probability.
  • Bayes' theorem.
  • Probability distribution of a random variable.

Quick Revision Tips

1. Create a formula sheet for all chapters.
2. Focus on solving sample papers and previous years' question papers.
3. Revise derivations for important results.
4. Solve NCERT problems thoroughly.

Would you like a specific chapter explained in detail?

CBSE Class 12 Mathematics Quick Revision

CBSE Class 12 Mathematics Revision Notes

“Mathematics rightly viewed possesses not only truth,but supreme beauty” - Bertrand Russell