CBSE Class 12 Maths Important Questions for 2024-25 Exam

CBSE Class 12 Maths Important Questions for 2024-25 Exam: Getting ready for the CBSE Class 12 Maths exam doesn’t have to be scary! Focusing on CBSE Class 12 Maths important questions for exams can make your preparation much easier. These questions are from the most important topics and often appear in the exam. This post will guide you through these questions, explain why they’re important, and help you prepare smartly.

Check out:

• CBSE Class 12th Books
• CBSE Class 12 Question Bank

Important CBSE Class 12 Maths Questions by Chapter

Chapter 1: Relations and Functions

Important Concepts

1.Types of Relations

• Reflexive relations

• Symmetric relations

• Transitive relations

• Equivalence relations

2. Functions

• Domain and range

• Types of functions

• Composite functions

• Inverse functions

Important Questions

1. If R is a relation on set A = {1, 2, 3, 4} given by R = {(a,b): |a-b| ≤ 1}, find whether R is reflexive, symmetric, and transitive.

2. Find the domain of the function f(x) = √(x-1)/(x²-4)

3. If f(x) = x²-2x+3 and g(x) = 2x+1, find (f∘g)(x) and (g∘f)(x)

Chapter 2: Inverse Trigonometric Functions

Concepts

1. Basic Properties

• Domain and range

• Principal values

• Graphs

2. Identities and Equations

• Basic identities

• Complex identities

• Solving equations

Important Questions

1. Write the principal value of cos-1 [cos(680)°]. (Delhi 2014C)

Answer: First we check the given angle lies in the principal value branch. If it is so, then use the property cos1 (cos θ) = θ, ∀θ ∈ [0, 180°]. Otherwise reduce the angle such that it lies in the principal value branch.

We know that, principal value branch of cos-1 x is [0, 180°].
Since, 680° ∉ [0, 180°], so write 680° as 2 × 360° – 40°

Now, cos-1 [cos(680)°] = cos-1 [cos(2 × 360° – 40°)]

= cos-1 (cos 4o°) [∵ cos(4π – θ) = cos θ]

Since, 40° ∈ [0, 180°]

∴ cos-1[cos(680°)] = 40° [∵ cos-1 (cos θ) = θ; ∀ θ ∈ [0, 1 80°]]

which is the required principal value.

Check out: CBSE Class 12 Science Stream Sample Papers

Chapter 3: Matrices

Concepts

1. Matrix Operations

• Addition and subtraction

• Multiplication

• Transpose

2. Special Matrices

• Singular matrix

• Non-singular matrix

• Adjoint matrix

• Inverse matrix

Important Questions

1. If A = [2 3; 1 4] and B = [1 0; 2 1], find AB and BA.

2. Find the inverse of matrix A = [3 2; 5 4]

3. Solve the system of equations using matrix method: 2x + 3y = 7 4x + 5y = 13

Chapter 4: Determinants

Concepts

1. Properties of Determinants

• Basic properties

• Expansion

• Cramer's rule

2. Applications

• Area of triangle

• Solving equations

• Consistency of equations

Important Questions

1. Using determinants, find the area of a triangle with vertices (1,1), (2,3), and (4,2)

2. Solve using Cramer's rule: 3x + 2y = 8 5x - 2y = 4

Chapter 5: Continuity and Differentiability

Key Concepts

1. Continuity

• Definition

• Types of discontinuity

• Checking continuity

2. Differentiability

• Rules of differentiation

• Chain rule

• Implicit differentiation

Important Questions

1. Check the continuity of f(x) = |x-1|/x-1 at x = 1

2. Find dy/dx if y = (x²+1)/(x-2)

3. If y = sin(ax), prove that y'' + a²y = 0

Chapter 6: Applications of Derivatives

Concepts

1. Rate of Change

• Instantaneous rate

• Average rate

• Related rates

2. Maxima and Minima

• Critical points

• Local maxima/minima

• Absolute maxima/minima

Important Questions

1. Find the maximum and minimum values of f(x) = x³ - 6x² + 9x + 1

2. Find the points on the curve y = x³ where the tangent is parallel to x-axis

Check out: CBSE Class 12 Mathematics Question Banks

Chapter 7: Integration

Key Concepts

1. Basic Integration

• Standard integrals

• Integration by substitution

• Integration by parts

2. Definite Integration

• Properties

• Fundamental theorem

• Applications

Important Questions

1. Evaluate ∫(x²+1)/(x-2)dx

2. Find ∫sin²x dx

3. Calculate ∫₀π/2 sin x cos x dx

Why Practice Important Math Questions?

1. Builds Confidence: Practicing important math questions in class 12 helps you get familiar with the exam style and commonly asked problems. It ensures that you don’t get surprised during the exam.

2. Saves Time: Instead of learning everything, focus on key topics that matter the most. This targeted approach helps you study smarter, not harder.

3. Reduces Mistakes: Solving these questions improves accuracy and understanding of concepts, giving you an edge in avoiding common errors.

4. Spot Exam Trends: Solving math PYQ class 12 (past year questions) helps you see which questions are often repeated. This lets you focus on areas that can fetch maximum marks.

Moreover, practicing regularly ensures that you develop speed, which is crucial for completing the paper on time. It’s not just about studying hard—it’s about studying the right way.

How to Use Sample Papers

1. Find weak points:

• Use math important questions from the class 12 PDF to figure out which topics you need to study more. Highlight the areas where you’re making mistakes and focus on them during revision.

2. Practice Under Time Limits:

• Solve questions within a set time to get used to the exam. This helps you manage time effectively and reduces panic during the actual exam.

3. Check Your Answers:

• Compare your answers with the solutions to 12th grade math important questions. Understanding the correct steps ensures that you learn from your mistakes and refine your problem-solving techniques.

4. Simulate Exam Conditions:

• Treat sample papers like real exams. This prepares you for the pressure and helps you stay calm and focused.

Check out: Class 12th Sample Papers

Most Repeated Board Exam Questions

Some questions keep coming back in CBSE exams. Here are a few examples:

• Questions about eigenvalues and eigenvectors in matrices.

• Problems with Rolle’s Theorem and Mean Value Theorem, which are critical in understanding calculus applications.

• Word problems in linear programming, are often related to optimizing resources.

• Integration questions using trigonometric substitutions, are a common favorite among examiners.

• Probability questions about rolling dice or picking cards. These questions test your ability to calculate probabilities in various scenarios.

By solving these repeatedly asked questions, you can boost your confidence and score higher. Get the whole question related to this in Physics wala math sample paper.

Easy Tips to Score Full Marks

1. Start with NCERT: Make sure you’ve solved every question in your NCERT textbook. It’s the foundation of the syllabus and is often directly linked to board exam questions.

2. Use Sample Papers: Look for patterns and practice similar questions. This helps you become familiar with the exam structure.

3. Solve Past Year Papers: Focus on PW maths PYQ class 12 to see what examiners like to ask. This is an excellent way to identify important topics. 

4. Understand Marking Rules: Know how much time and effort to spend on different sections. Follow the marking scheme while writing answers.

5. Practice Graphs and Diagrams: Work on visual problems, especially in 3D geometry. Neat and labeled diagrams can fetch you extra marks.

6. Revise Smartly: Create short notes for formulas and key concepts. Use them for quick revision before the exam.

Resources for Maths Preparation

To prepare well, use resources like mock tests and solve maths important questions in class 12 PDFs. They help you understand tough problems and prepare completely.

What to Look for in Study Materials:

• Full coverage of all topics with detailed solutions.

• Answers that follow CBSE’s marking scheme.

• Updated with the newest syllabus to ensure relevancy.

• Includes practice questions, short revision notes, and tips for time management.

Benefits of Maths PDFs for Class 12

1. Study Offline: Print them out and study anywhere without distractions.

2. Clear Solutions: Step-by-step explanations make tough questions easier. You can use these solutions to learn the correct way to answer questions.

3. Find Trends: Helps you see most repeated questions in board exams class 12 and focus on high-priority topics.

Practicing CBSE Class 12 Maths important questions for the 2024-25 exam can help you feel confident and perform better. Use maths important questions class 12 PDFs and solve sample papers regularly. Keep studying maths PYQ class 12 to understand what’s important. With practice and the right tools, you can score good marks in your Class 12 Maths exam!

By focusing on these strategies, you’ll not only improve your preparation but also ensure success. Start early, stay consistent, and believe in your efforts.

CBSE Class 12 Question Bank for All Subjects

Important CBSE Class 12 Maths Questions FAQs

1. How can I score well in CBSE Class 12 Maths?

Focus on NCERT textbooks and solve all examples and exercises. Use sample papers and past year questions(PYQ) to understand exam patterns and frequently asked topics.

2. How can I avoid making silly mistakes in Maths exams?

Try to practice regularly, double-check calculations, and make sure that you’re following the steps correctly. Time management is also important to avoid rushing through problems.

3. How can I score full marks in lengthy questions?

Think of solving a lengthy mathematics question like telling a story – it needs a clear beginning, logical progression, and satisfying conclusion. Here's how to craft your solution: