Important Questions for CBSE Class 12 Maths – Chapter-Wise
Are you searching for Important Questions for CBSE Class 12 Maths to strengthen your board exam preparation? You have landed on the right page. CBSE Class 12 Maths is one of the most scoring subjects if a student practices the right questions from every unit instead of trying to cover the entire textbook randomly. This guide brings you a complete, chapter-wise list of important topics, unit-wise weightage, and the key formulas that are asked most frequently in the CBSE board exam.
Every year, thousands of students look for CBSE Class 12 Maths important questions before their final exams, and for good reason. Whether it is Relations and Functions, Matrices and Determinants, Continuity and Differentiability, Integrals, Vectors, Three-Dimensional Geometry, Linear Programming, or Probability, this page covers the high-weightage questions that repeat in previous year papers and CBSE sample papers.
Maths rewards consistent practice more than last-minute memorising. By focusing on important questions for Class 12 Maths, students save time and target the chapters that carry maximum marks. This guide also includes simple formula tables so you can revise quickly. Keep reading to know which chapters to prioritise and how to aim for full marks in your CBSE Class 12 Maths board exam.
CBSE Class 12 Maths Important Questions: Chapter-wise PDF Download
Why Practicing Important Questions Helps
The CBSE Class 12 Maths paper follows a fixed pattern every year, and a large portion of questions are based on standard concepts repeated across previous years. Practising important questions for Class 12 Maths helps students recognise question patterns, manage exam time better, and avoid silly mistakes in calculation-heavy chapters like Calculus and Vectors. It also builds confidence, since most board questions are variations of the same core formulas explained below. Before Solving the Important Questions one must solve NCERT solutions with the help of NCERT solutions for Class 12.
Unit-Wise Weightage in CBSE Class 12 Maths
Knowing the marks distribution helps students decide where to invest more revision time.
Unit / Chapters Covered | Approx. Marks |
Relations & Functions, Inverse Trigonometric Functions | 8 |
Algebra: Matrices, Determinants | 10 |
Calculus: Continuity, Differentiability, Applications, Integrals, Differential Equations | 35 |
Vectors & Three-Dimensional Geometry | 14 |
Linear Programming Problems | 5 |
Probability: Conditional Probability, Bayes' Theorem, Random Variables | 8 |
Relations and Functions – Important Questions
This unit tests whether a student can identify reflexive, symmetric, and transitive relations, and check if a function is one-one, onto, or bijective. Common important questions ask students to prove a given relation is an equivalence relation, or to find the principal value of inverse trigonometric expressions.
Concept | Formula |
Reflexive Relation | (a, a) ∈ R for every a ∈ A |
Equivalence Relation | R is reflexive, symmetric, and transitive |
sin⁻¹x + cos⁻¹x | π/2 |
tan⁻¹x + cot⁻¹x | π/2 |
tan⁻¹x + tan⁻¹y | tan⁻¹[(x+y)/(1−xy)], xy < 1 |
Matrices and Determinants – Important Questions
Matrices and Determinants is a high-scoring unit because questions follow a predictable structure: finding the inverse of a matrix, solving a system of linear equations using matrices, or proving properties of determinants. Students should practice questions on adjoint and inverse of a matrix, and solving equations using the matrix method, since these appear almost every year.
Concept | Formula |
Inverse of Matrix A | A⁻¹ = (1/|A|) · adj(A) |
Condition for Inverse | |A| ≠ 0 |
Area of Triangle (Determinant) | (1/2) |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)| |
System of Equations | X = A⁻¹B (Matrix Method) |
Continuity, Differentiability and Applications of Derivatives
This is part of Calculus, the highest weightage section in CBSE Class 12 Maths. Important questions here include checking continuity at a point, finding derivatives of implicit and parametric functions, and solving applications of derivatives questions such as rate of change, increasing-decreasing functions, and maxima-minima problems, which are almost guaranteed in every board paper.
Concept | Formula |
Derivative of eˣ | eˣ |
Derivative of logₑx | 1/x |
Second Derivative Test (Maxima) | f'(x)=0 and f''(x) < 0 |
Second Derivative Test (Minima) | f'(x)=0 and f''(x) > 0 |
Rate of Change | dy/dt = (dy/dx) × (dx/dt) |
Integrals and Differential Equations – Important Questions
Integrals carry the maximum individual weightage in the exam. Frequently asked important questions involve integration by parts, integration using partial fractions, and definite integrals using properties. In Differential Equations, students are commonly tested on forming a differential equation and solving variable-separable and linear differential equations.
Concept | Formula |
∫ 1/(x²+a²) dx | (1/a) tan⁻¹(x/a) + C |
∫ 1/√(a²−x²) dx | sin⁻¹(x/a) + C |
Integration by Parts | ∫u v dx = u∫v dx − ∫(du/dx)(∫v dx) dx |
Linear Differential Equation | dy/dx + Py = Q → y·e^∫Pdx = ∫Q·e^∫Pdx dx + C |
Vectors and Three-Dimensional Geometry – Important Questions
This unit frequently asks students to find the angle between two lines or planes, the shortest distance between two skew lines, and the equation of a plane passing through given points. Practising the dot product and cross product formulas thoroughly is essential, since almost every question in this unit depends on them.
Concept | Formula |
Dot Product | a·b = |a||b| cosθ |
Cross Product | a×b = |a||b| sinθ n̂ |
Distance Between Skew Lines | d = |(b1×b2)·(a2−a1)| / |b1×b2| |
Equation of Plane | r·n = d |
Linear Programming Problems – Important Questions
Linear Programming questions usually ask students to formulate the objective function and constraints from a word problem, then find the optimal (maximum or minimum) value using the corner point method on the feasible region. These questions are direct and scoring if the graph is plotted correctly.
Probability – Important Questions
Important questions from Probability revolve around conditional probability, Bayes' Theorem, and the probability distribution of a random variable, along with its mean and variance. Word problems involving bags of balls, dice, or cards are extremely common in this chapter.
Concept | Formula |
Conditional Probability | P(A|B) = P(A∩B) / P(B) |
Bayes' Theorem | P(Ai|A) = P(Ai)P(A|Ai) / ΣP(Aj)P(A|Aj) |
Mean of a Random Variable | Σ x·P(x) |
Variance | Σx²P(x) − [Σx·P(x)]² |
Preparation Tips for CBSE Class 12 Maths
Solve at least five years of previous CBSE Class 12 Maths question papers along with the current year's sample paper to understand the exact question pattern. Keep a separate formula notebook for Calculus, Vectors, and Probability, since these units carry the most marks. Practice NCERT exemplar questions for extra application-based problems, and always attempt CBSE sample papers under timed conditions before the final exam.
Final Words
Preparing with important questions for CBSE Class 12 Maths helps students study smart instead of studying everything with equal focus. Use the chapter-wise breakdown, formula tables, and weightage list above to plan your last few weeks of revision. For more chapter-wise notes, sample papers, and subject guides for CBSE Class 12, keep following MyClass24.