CBSE Class 12 Mathematics Important Topics and Tips

Mathematics is a scoring subject for CBSE class 12 students where you can even score 100 out of 100. However, it is possible only when you clearly understand the topics and practice them before the exam. Additionally, students must have a strong grip on the basics of this subject to solve the difficult questions. Since CBSE Class 12 Mathematics has more weightage, it is also important for engineering entrance exams like IIT JEE. You need to revise the important concepts and formulas regularly. It ensures their application for solving the most difficult questions in these exams.

We advise studying the NCERT 12 Mathematics textbook thoroughly before moving to any other study material. You should dedicate at least 1 hour daily from your study schedule to solving NCERT textbook problems. When preparing for IIT-JEE, try to solve as many questions from various study materials and take mock tests. Infinity Learn provides mock tests that will help you prepare for competitive exams like IIT-JEE. Keep a positive mindset and approach during preparation, and excel at this subject.

All the topics are important when preparing for IIT-JEE or CBSE Exam. However, below are some crucial topics that require more emphasis.

Chapter 1 – Relations and Functions

Important Topics:

1. Types of Relations
2. Composition of Two Functions
3. Invertible Functions

Chapter 2 – Inverse Trigonometric Functions

Important Topics:

1. Properties of Inverse Trigonometric Functions

Chapter 3 – Matrices

Important Topics:

1. Multiplication of Matrices and Related Properties
2. Symmetric and Skew Symmetric Matrices
3. Using Elementary Transformations to find Inverse of a Matrix

Chapter 4 – Determinants

Important Topics:

1. Properties of Determinants
2. Adjoint and Inverse of a Matrix
3. Solution of System of Linear Equations

Chapter 5 – Continuity and Differentiability

Important Topics:

1. Continuity of a Function
2. Logarithmic Differentiation
3. Differentiation of Functions in Parametric Form
4. Second Order Derivatives

Chapter 6 – Application of Derivatives

Important Topics:

1. Rate of Change of Quantities
2. Increasing and Decreasing Functions
3. Tangents and Normals to Curves
4. Finding Points of Local Maxima and Minima using First and Second Derivative Tests 

Chapter 7 – Integrals 

Important Topics:

1. Integration by Method of Substitution
2. Integration by Method of Partial Fractions
3. Integration by Parts
4. Definite Integral (as Limit of a Sum)
5. Properties of Definite Integrals

Chapter 8 – Application of Integrals

Important Topics:

1. Area under Simple Curves
2. Area Bounded by a Curve and Line
3. Area Bounded by Two Curves

Chapter 9 – Differential Equations 

Important Topics:

1. Formation of Differential Equations
2. Method of Solving Differential Equations using Variable Separable
3. Homogeneous Differential Equations
4. Linear Differential Equations

Chapter 10 – Vector Algebra

Important Topics:

1. Scalar Product of Vectors

2. Projection of Vector on a Line

3. Vector Product of Vectors

Chapter 11 – Three-Dimensional Geometry

Important Topics:

1. Direction Cosines & Direction Ratios of Line
2. Equation of a Line
3. Coplanarity of Lines
4. Angle between Two Lines
5. Shortest Distance between Two Skew Lines
6. Equation for a Plane 
7. Equation for a Plane Perpendicular to Given Vector & Passing through a Given Point
8. Equation for a Plane Passing through Three Non-collinear Points
9. Equation for a Plane Passing through the Intersection of Two Planes
10. Angle between Two Planes
11. Distance of a Point from a Plane
12. Angle between a Line and Plane

Chapter 12 – Linear Programming

Important Topics:

1. Graphical Solution of Linear Programming Problems

Chapter 13 – Probability

Important Topics:

1. Multiplication Theorem on Probability
2. Independent Events
3. Bayes’ Theorem
4. Random Variable and Its Probability Distribution
5. Mean and Variance of Random Variable
6. Binomial Distribution

CBSE Class 12th Maths Exam Pattern 2024

Class 12th Maths Exam Preparation Tips

1. Understand the Syllabus and Exam Pattern

• Familiarize yourself with the entire syllabus and the weightage of each topic.
• Prioritize topics based on their marks distribution, giving more time to high-weightage units.

2. Build a Strong Foundation with NCERT

• NCERT is the most important book for Class 12 Maths. Make sure you thoroughly understand and practice all the exercises and examples in the NCERT textbook.
• Practice each concept until you're confident, as the board exam often includes direct questions from NCERT.

3. Make a Study Schedule

• Create a realistic timetable that allocates time for each topic.
• Divide time between learning new concepts, practicing problems, and revising completed topics.
• Spend extra time on challenging chapters like Calculus, which often carry more weight in exams.

4. Practice Previous Year Papers and Sample Papers

• Solving previous years' papers and sample papers gives you an idea of the exam pattern and helps you manage time better during the exam.
• Set a timer and attempt these papers as if in an actual exam setting to improve your speed and accuracy.

5. Focus on Important Topics

• Chapters like Calculus (Differentiation, Integration), Vectors, 3D Geometry, and Probability are crucial for Class 12 Maths.
• Spend more time mastering these high-weightage topics but do not skip any smaller topics that may appear in short questions.

6. Clear Your Doubts Regularly

• Never leave any doubt unresolved. Clear up difficult concepts right away with the help of teachers, classmates, or online resources.
• Practice problems related to the concepts you're uncertain about to strengthen your understanding.

7. Use Formula Sheets and Flashcards

• Keep a formula sheet or flashcards handy with all the important formulas, theorems, and shortcuts.
• Regularly revise these to ensure they stay fresh in your memory, which will be especially helpful during last-minute revision.

8. Work on Time Management and Accuracy

• While practicing, pay attention to both accuracy and speed.
• Avoid spending too much time on a single problem. Move on if you’re stuck and return to it later if time permits.

9. Revise Regularly

• Schedule revision sessions weekly to revisit previously covered topics and practice questions.
• Focus on strengthening weak areas but also ensure you don’t forget the topics you are already confident in.

10. Stay Calm and Take Care of Your Health

• Keep a balanced routine, including breaks, exercise, and adequate sleep.
• Avoid stress, especially before the exam, by practicing relaxation techniques like deep breathing or meditation.