CBSE Class 12 Mathematics Exam 2026: Important Questions for Last Week Prep
BoardsWallah Expert Team
Published 17 March 2026 · 8 min read
CBSE Class 12 Mathematics Exam 2026: Important Questions for Last Week Prep
Hello, dear Class 12 students! The CBSE Class 12 Mathematics exam is just five days away, and we know you're in the final stretch of your preparation. To help you make the most of this last week, we've compiled a set of important questions that focus on the key areas of calculus, algebra, and probability. These questions are designed to boost your confidence and ensure you're well-prepared for the exam. Let's dive in!
Marks Weightage and Syllabus Overview
Understanding the marks distribution is crucial for strategic preparation. According to the CBSE Class 12 Mathematics syllabus, the marks are distributed as follows:
| Unit | Topic | Marks |
|---|---|---|
| I | Relations and Functions | 10 |
| II | Algebra | 13 |
| III | Calculus | 44 |
| IV | Vectors and Three-Dimensional Geometry | 17 |
| V | Linear Programming | 6 |
| VI | Probability | 10 |
As you can see, calculus carries the highest weightage, followed by algebra and probability. Therefore, these areas should be your top priority in the last few days. Let's break down some important questions from each of these sections.
Calculus
Calculus is a vast and important topic that covers limits, derivatives, integrals, and differential equations. Here are some key questions to focus on:
1. Evaluate the following limit: \( \lim_{x \to 0} \frac{\sin(3x)}{x} \)
2. Find the derivative of \( f(x) = \log(\sin x) \) with respect to \( x \).
3. Evaluate the integral: \( \int \frac{1}{1 + \sin x} \, dx \)
4. Solve the differential equation: \( \frac{dy}{dx} = \frac{x + y}{x - y} \)
5. Find the area enclosed by the curve \( y = x^2 \) and the line \( y = 2x \).
6. Determine the volume of the solid generated by revolving the region bounded by the curve \( y = \sqrt{x} \) and the x-axis from \( x = 0 \) to \( x = 4 \) about the x-axis.
These questions cover a range of concepts and techniques in calculus. Make sure you practice these and understand the underlying principles. For more in-depth practice, refer to the NCERT textbooks and CBSE sample papers. NCERT and CBSE are your best resources for theory and practice.
Algebra
Algebra is another critical area that includes matrices, determinants, and quadratic equations. Here are some important questions to tackle:
1. If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \), find the matrix \( (A + B)^2 \).
2. Solve the system of linear equations using the matrix method: \( 2x + 3y = 8 \) and \( 4x + 5y = 14 \).
3. Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \).
4. If \( f(x) = x^2 - 5x + 6 \), find the roots of the equation and verify them.
5. Prove that the function \( f(x) = x^3 - 3x + 1 \) is strictly increasing on the interval \( (1, \infty) \).
Algebra questions often test your understanding of matrix operations, determinants, and quadratic equations. Practice these questions to ensure you can handle a variety of problems. For additional practice, consider solving questions from the NCERT exemplar problems and CBSE sample papers.
Probability
Probability is a fascinating topic that is relatively easier to score in. Here are some important questions to help you prepare:
1. A bag contains 5 red, 7 blue, and 8 green balls. Two balls are drawn at random. What is the probability that both balls are of the same color?
2. A die is rolled twice. What is the probability that the sum of the numbers on the two dice is 8?
3. If two events A and B are independent, and \( P(A) = 0.4 \) and \( P(B) = 0.5 \), find \( P(A \cap B) \).
4. A random variable X has the following probability distribution:
| X | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| P(X) | 0.1 | 0.3 | 0.4 | 0.2 |
Find the mean and variance of X.
5. A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability that the card drawn is a king or a queen?
Probability questions can be tricky, but with practice, you can master them. Focus on understanding the concepts of independent and dependent events, and practice solving problems involving random variables. The NCERT textbook and CBSE sample papers are excellent resources for additional practice.
Practice with Previous Year Papers
Solving PYQs is the fastest way to prepare. Download free PDFs:
CBSE Class 12 Mathematics Previous Year Question Papers →Tips for Last Week Prep
With just five days left, here are some tips to help you make the most of your time:
- Revise the Syllabus: Go through the entire syllabus and ensure you have a clear understanding of all the concepts. Focus on the areas where you feel less confident.
- Solve Sample Papers: Solve at least 3-4 CBSE sample papers to get a feel for the exam pattern and the types of questions that might be asked.
- Practice Important Formulas: Make a list of all important formulas and practice applying them to different problems. This will help you recall them quickly during the exam.
- Review Past Papers: Look at the previous year's question papers to identify recurring topics and question patterns.
- Time Management: Practice solving questions within the time limit to improve your speed and accuracy. Allocate time for each section based on its marks weightage.
- Stay Healthy: Ensure you get enough sleep, eat well, and take short breaks to avoid burnout. A healthy body and mind are crucial for exam success.
- Seek Help: If you're struggling with a particular topic, don't hesitate to ask your teachers or peers for help. Sometimes, a fresh perspective can make all the difference.
Stay calm, stay focused, and trust your preparation. You've got this!
Official Statistics and Trends
According to the official CBSE results, the pass percentage for the Class 12 Mathematics exam has been steadily increasing over the years. Here are the pass percentages for the past five years:
- 2021: 88.9%
- 2022: 86.7%
- 2023: 91.5%
- 2024: 89.0%
- 2025: 92.8%
"The increasing pass percentage is a testament to the hard work and dedication of students, teachers, and the CBSE board. Stay focused and consistent in your preparation to join the ranks of successful candidates this year." — CBSE Official Statement
These statistics show that with the right preparation and approach, you can achieve a high score in your Class 12 Mathematics exam. Use the time wisely to review and practice, and you'll be well-prepared for the exam.
📊 CBSE Mathematics — Pass % Trend
Source: CBSE Official Results
FAQs
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Q1: How can I manage my time effectively during the exam?
A1: Start by allocating time based on the marks weightage of each section. For instance, spend more time on calculus problems since they carry the highest marks. Practice solving sample papers within the time limit to improve your speed and accuracy. Also, make sure to leave some time at the end for revision and checking your answers.
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Q2: What are the most important topics in calculus for the exam?
A2: Key topics in calculus include limits and derivatives, integrals, and differential equations. Make sure you are thorough with the concepts of differentiation and integration, and practice solving a variety of problems, including application-based questions.
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Q3: How should I approach probability questions?
A3: Probability questions often involve understanding the sample space and the events. Start by identifying the type of probability (independent, dependent, conditional) and then apply the appropriate formula. Practice solving problems involving random variables and their distributions to gain confidence.
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Q4: Are there any specific chapters in algebra that I should focus on?
A4: Yes, focus on chapters like matrices, determinants, and quadratic equations. These topics are fundamental and often carry significant marks in the exam. Make sure you understand the properties of matrices and determinants, and practice solving quadratic equations using different methods.
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Q5: What is the best way to prepare for the Mathematics board exam?
A5: The best way to prepare is to practice regularly, solve previous year question papers, and revise the syllabus thoroughly. Make a study schedule that allows you to cover all topics and allocate time for solving sample papers and revising important formulas. Stay consistent and focused in your preparation.
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Q6: How can I reduce exam anxiety?
A6: Reducing exam anxiety involves a combination of mental and physical strategies. Practice deep breathing and relaxation techniques. Stay organized and follow a well-planned study schedule. Ensure you get enough sleep and eat a balanced diet. Positive affirmations and maintaining a positive mindset can also help reduce anxiety.
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Q7: What should I do the night before the exam?
A7: The night before the exam, avoid studying new topics. Instead, review your notes and important formulas. Get a good night's sleep to ensure you're well-rested and alert on the day of the exam. Avoid caffeine and other stimulants that might affect your sleep. Pack your stationery and other exam essentials in advance to avoid last-minute stress.
We hope these important questions and tips help you prepare effectively for your CBSE Class 12 Mathematics exam. Stay focused, stay positive, and give your best. Good luck!