Master the CBSE Class 12 Mathematics syllabus 2026-27 with this comprehensive guide covering Calculus, Algebra, Vector Algebra, Three-Dimensional Geometry, Linear Programming, Probability, and Application of Derivatives and Integrals. This detailed syllabus includes complete chapter breakdown, exam pattern, marking scheme, scoring strategies, and expert tips to score 95+ marks in your board examination.

Course Structure & Marking Scheme

Total Marks Distribution:

Unit-wise Marks Distribution (Theory - 80 Marks)

Complete Syllabus - All Units & Chapters

Unit I: Relations and Functions (8 Marks)

Chapter 1: Relations and Functions

•        Types of relations: Reflexive, symmetric, transitive and equivalence relations

•        One to one and onto functions: Composite functions, inverse of a function

•        Binary operations: Properties of binary operations

Chapter 2: Inverse Trigonometric Functions

•        Definition, range, domain, principal value branch

•        Graphs of inverse trigonometric functions

•        Elementary properties of inverse trigonometric functions

Unit II: Algebra (10 Marks)

Chapter 3: Matrices

•        Concept, notation, order, equality, types of matrices: Row and column matrices, square matrix, diagonal matrix, scalar matrix, identity matrix, zero matrix

•        Transpose of a matrix: Symmetric and skew symmetric matrices

•        Operations on matrices: Addition and multiplication, multiplication with a scalar

•        Simple properties of addition, multiplication and scalar multiplication

•        Non-commutativity of multiplication of matrices

•        Concept of elementary row and column operations

•        Invertible matrices: Existence of non-singular square matrices

•        Proof of the uniqueness of inverse, if it exists

(Here all matrices will have real entries)

Chapter 4: Determinants

•        Determinant of a square matrix (up to 3 × 3 matrices)

•        Properties of determinants: Minor, cofactor

•        Adjoint and inverse of a square matrix

•        Applications of determinants and matrices: Consistency and inconsistency of system of linear equations by examples

•        Solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

Unit III: Calculus (35 Marks)

Chapter 5: Continuity and Differentiability

•        Continuity and differentiability: Derivative of composite functions, chain rule

•        Derivatives of inverse trigonometric functions

•        Derivatives of implicit functions: Concept of explicit and implicit functions

•        Logarithmic differentiation: Derivative of functions expressed in parametric forms

•        Second order derivatives

•        Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation

Chapter 6: Applications of Derivatives

•        Applications of derivatives: Rate of change of bodies, increasing/decreasing functions

•        Tangents and normals: Approximations

•        Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)

•        Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)

Chapter 7: Integrals

•        Integration as inverse process of differentiation

•        Integration of a variety of functions by substitution, by partial fractions and by parts

•        Evaluation of simple integrals of the following types and problems based on them:

∫dx/(x² ± a²), ∫dx/√(x² ± a²), ∫dx/√(a² - x²)

∫dx/(ax² + bx + c), ∫dx/√(ax² + bx + c)

∫(px + q)/(ax² + bx + c)dx, ∫(px + q)/√(ax² + bx + c)dx

∫√(a² ± x²)dx, ∫√(x² - a²)dx, ∫√(ax² + bx + c)dx

•        Definite integrals as a limit of a sum

•        Fundamental Theorem of Calculus (without proof)

•        Basic properties of definite integrals and evaluation of definite integrals

Chapter 8: Applications of the Integrals

•        Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only)

•        Area between any of the two above said curves (the region should be clearly identifiable)

Chapter 9: Differential Equations

•        Definition, order and degree: General and particular solutions of a differential equation

•        Formation of differential equation whose general solution is given

•        Solution of differential equations by method of separation of variables

•        Solutions of homogeneous differential equations of first order and first degree

•        Solutions of linear differential equation of the type: dy/dx + py = q, where p and q are functions of x or constants

dx/dy + px = q, where p and q are functions of y or constants

Unit IV: Vectors and Three-Dimensional Geometry (14 Marks)

Chapter 10: Vectors

•        Vectors and scalars: Magnitude and direction of a vector

•        Direction cosines and direction ratios of a vector

•        Types of vectors (equal, unit, zero, parallel and collinear vectors)

•        Position vector of a point: Negative of a vector, components of a vector

•        Addition of vectors, multiplication of a vector by a scalar: Position vector of a point dividing a line segment in a given ratio

•        Scalar (dot) product of vectors: Projection of a vector on a line

•        Vector (cross) product of vectors: Scalar triple product

Chapter 11: Three-dimensional Geometry

•        Direction cosines and direction ratios of a line joining two points

•        Cartesian equation and vector equation of a line

•        Coplanar and skew lines

•        Shortest distance between two lines

•        Cartesian and vector equation of a plane

•        Angle between two lines, two planes, a line and a plane

•        Distance of a point from a plane

Unit V: Linear Programming (5 Marks)

Chapter 12: Linear Programming

•        Introduction, related terminology such as constraints, objective function, optimization

•        Different types of linear programming (L.P.) problems

•        Mathematical formulation of L.P. problems

•        Graphical method of solution for problems in two variables

•        Feasible and infeasible regions (bounded and unbounded)

•        Feasible and infeasible solutions: Optimal feasible solutions (up to three non-trivial constraints)

Unit VI: Probability (8 Marks)

Chapter 13: Probability

•        Conditional probability: Multiplication theorem on probability

•        Independent events: Total probability

•        Bayes' theorem

•        Random variable and its probability distribution

•        Mean and variance of random variable

•        Repeated independent (Bernoulli) trials and Binomial distribution

CBSE Class 12 Mathematics Exam Pattern 2026-27

Theory Examination Pattern (80 Marks, 3 Hours)

Important: Internal choice is provided in 2-mark, 3-mark, and 5-mark questions. No internal choice in MCQs and case studies. All questions are compulsory.

Internal Assessment (20 Marks)

Important Dates & Academic Calendar 2026-27

Note: Visit the official CBSE website (cbse.gov.in) for date sheet, sample papers, and marking scheme updates.

Expert Study Tips for 95+ Score in Mathematics

1. Unit-wise Preparation Strategy

•        Relations and Functions (8 marks): Focus on types of relations, inverse functions, and inverse trigonometric properties

•        Algebra (10 marks): Master matrix operations, determinant properties, and solving linear equations

•        Calculus (35 marks - Highest weightage): This is the most important unit

Practice differentiation and integration daily

Master application problems: maxima-minima, rate of change, area under curves

Solve differential equations by separation of variables

•        Vectors & 3D Geometry (14 marks): Learn vector operations, direction cosines, and equations of lines/planes

•        Linear Programming (5 marks): Practice graphical method problems, easy scoring unit

•        Probability (8 marks): Understand conditional probability, Bayes' theorem, and binomial distribution

2. Daily Practice Routine

•        Practice minimum 10-15 problems daily from different chapters

•        Dedicate 2-3 hours daily specifically for Mathematics

•        Solve NCERT exercises thoroughly - most important resource

•        Practice NCERT Exemplar problems for conceptual clarity

•        Maintain a formula sheet with all important formulas, theorems, and identities

•        Create an error log - note down mistakes and revise them weekly

•        Time yourself while solving - practice speed and accuracy

•        Focus more time on Calculus (35 marks) - highest weightage

3. Concept Mastery Techniques

•        Understand, don't memorize: Focus on understanding concepts rather than rote learning

•        Learn derivations: Many times derivation steps can help solve problems

•        Connect concepts: Link related topics (e.g., differentiation and integration are inverse)

•        Visualization: Draw graphs for functions, curves, 3D geometry problems

•        Theorem application: Know when and how to apply theorems (LMVT, Rolle's theorem)

•        Integration techniques: Master substitution, partial fractions, by parts

•        Standard formulas: Memorize all integration formulas, trigonometric identities

4. Revision Strategy

•        First revision: Within 24 hours of learning a chapter

•        Second revision: After one week

•        Third revision: After one month, then monthly

•        Solve previous year question papers - last 10 years minimum

•        Practice CBSE sample papers released by board

•        Take mock tests under timed conditions (3 hours)

•        Revise formula sheet daily before sleeping

•        Focus on high-weightage chapters: Calculus, Vectors, Algebra

Scoring Tips & Answer Writing Strategies

General Answer Writing Guidelines

•        Read the entire question paper in first 15 minutes - mark easy, moderate, difficult

•        Attempt questions in order: Easy → Moderate → Difficult

•        Show all steps clearly - step marks are awarded even if final answer is wrong

•        Write in neat, legible handwriting - examiners appreciate organized work

•        Use blue or black pen only - pencil only for graphs and diagrams

•        Leave proper margins and space between answers

•        Box or underline final answers - makes them easily identifiable

•        Draw neat diagrams with pencil and ruler - earn presentation marks

Section-wise Strategy

Section A: MCQs & Assertion-Reason (20 Marks)

•        No negative marking - attempt all MCQs

•        Use elimination method for difficult questions

•        Don't spend more than 1.5 minutes per MCQ

•        Mark difficult ones and return later if time permits

•        Assertion-Reason: Read both statements carefully, understand the logic

•        Time allocation: 25-30 minutes maximum for entire Section A

Section B: 2-Mark Questions (10 Marks)

•        Keep answers concise and direct

•        3-4 steps are usually sufficient

•        Write formula first, then substitute values

•        Show one intermediate step between formula and answer

•        Use internal choice wisely - attempt the easier option

•        Time: 3-4 minutes per question

Section C: 3-Mark Questions (18 Marks)

•        Write 5-7 clear steps

•        Show all intermediate calculations

•        If proof is asked, write 'To Prove:' statement first

•        Use proper mathematical notation and symbols

•        Draw diagram if question involves geometry/graphs

•        Time: 5-6 minutes per question

Section D: 5-Mark Questions (20 Marks)

•        These carry maximum individual weightage - be thorough

•        Write 8-10 detailed steps

•        Start with 'Given:' and 'To Find:' statements

•        Show all working: substitutions, simplifications, calculations

•        Verify answer if time permits (especially in maxima-minima, area problems)

•        Use proper theorem names where applicable

•        Time: 8-10 minutes per question

Section E: Case Study Questions (12 Marks)

•        Read the case study carefully 2-3 times

•        Underline key information - numbers, conditions, requirements

•        Usually 4 sub-questions: 3 MCQs (1 mark each) + 1 subjective (1 mark)

•        Case studies test application of concepts in real-life situations

•        Draw diagram from given information if helpful

•        Time: 6-8 minutes per case study

Time Management in Exam

•        Reading & Planning: 15 minutes

•        Section A (MCQs): 25-30 minutes

•        Section B (2-marks): 20 minutes (5 questions)

•        Section C (3-marks): 35 minutes (6 questions)

•        Section D (5-marks): 35 minutes (4 questions)

•        Section E (Case studies): 20-25 minutes (3 case studies)

•        Revision & Checking: 20-25 minutes

•        Total: 180 minutes (3 hours)

•        Stick to time limits - don't get stuck on any single question

Common Mistakes to Avoid in Mathematics Exam

Calculation & Arithmetic Errors

•        Silly calculation mistakes - double-check arithmetic operations

•        Sign errors: Negative signs, plus-minus in quadratic formulas

•        Fraction mistakes: Adding, multiplying fractions incorrectly

•        Decimal errors: Misplacing decimal points

•        Square root errors: √(a² + b²) ≠ a + b

•        Algebraic simplification mistakes: (a + b)² ≠ a² + b²

Conceptual Errors

•        Derivative errors: d/dx(uv) ≠ (du/dx)(dv/dx), use product rule correctly

•        Integration confusion: Forgetting constant C in indefinite integrals

•        Limits of integration: Interchanging upper and lower limits changes sign

•        Matrix multiplication: Not commutative, AB ≠ BA

•        Determinant properties: Det(AB) = Det(A) × Det(B), not Det(A) + Det(B)

•        Probability errors: P(A∪B) = P(A) + P(B) - P(A∩B), not just P(A) + P(B)

•        Vector operations: Cross product not commutative, a×b = -b×a

Formula & Theorem Errors

•        Using wrong formula: Quadratic formula, distance formula, section formula

•        Trigonometric identities: sin²θ + cos²θ = 1, not sin²θ + cos²θ = 0

•        Integration formulas: ∫1/x dx = ln|x| + C, not 1/x² + C

•        Differentiation formulas: d/dx(sin x) = cos x, not -cos x

•        Theorem misapplication: Using Rolle's theorem when conditions aren't satisfied

Presentation Errors

•        Not showing steps: Even with correct answer, marks deducted for missing steps

•        Skipping important steps: Integration by substitution without showing substitution

•        Poor handwriting: Examiners can't read, may award lower marks

•        Not drawing diagrams: Especially in geometry, vectors, linear programming

•        Missing units: In application problems, always write units

•        Not labeling graphs: Axes, points, curves must be labeled

•        Crossing out excessively: Makes paper look messy

Time Management Errors

•        Spending too much time on difficult questions - move on and return later

•        Not attempting all MCQs - no negative marking, always attempt

•        Leaving questions blank - partial marks better than zero

•        Not managing time per section - leads to incomplete paper

•        No time left for revision - always reserve 20 minutes at end

Specific Chapter Mistakes

•        Matrices: Forgetting matrix is non-commutative, order matters in multiplication

•        Determinants: Sign errors in cofactor expansion

•        Continuity: Checking only LHL = RHL, forgetting to check f(a) = limit

•        Differentiation: Chain rule errors, forgetting to differentiate inner function

•        Integration: Forgetting dx, wrong substitution, limits not changed after substitution

•        Differential Equations: Not including +C, wrong variable separation

•        Vectors: Dot product gives scalar, cross product gives vector - confusion

•        3D Geometry: Direction ratios and direction cosines confusion

•        Linear Programming: Checking corner points but missing optimal solution

•        Probability: Confusing P(A|B) with P(B|A)

High-Scoring Chapters & Topics

Focus on these for maximum marks with smart preparation:

•        Matrices & Determinants (10 marks): Formulaic, practice-based, high scoring if concepts clear

•        Differentiation (Applications): Maxima-minima, rate of change - straightforward if practiced

•        Integration: Definite integrals, area under curves - standard problems, good scoring

•        Differential Equations: Variable separable type - follow steps, easy marks

•        Vectors: Dot product, cross product - formula-based, less conceptual confusion

•        Linear Programming (5 marks): Graphical method - practice 10-15 problems, guaranteed full marks

•        Probability: Binomial distribution, Bayes' theorem - formula application, scoring

•        Inverse Trigonometric Functions: Properties-based questions, moderate difficulty

Must-Remember Formulas & Theorems

Differentiation Formulas

•        Basic: d/dx(xⁿ) = nxⁿ⁻¹, d/dx(sin x) = cos x, d/dx(cos x) = -sin x, d/dx(eˣ) = eˣ, d/dx(ln x) = 1/x

•        Product Rule: d/dx(uv) = u(dv/dx) + v(du/dx)

•        Quotient Rule: d/dx(u/v) = [v(du/dx) - u(dv/dx)]/v²

•        Chain Rule: dy/dx = (dy/du) × (du/dx)

Integration Formulas

•        Basic: ∫xⁿdx = xⁿ⁺¹/(n+1) + C (n≠-1), ∫1/x dx = ln|x| + C

•        ∫sin x dx = -cos x + C, ∫cos x dx = sin x + C, ∫eˣ dx = eˣ + C

•        ∫1/(x²+a²) dx = (1/a)tan⁻¹(x/a) + C

•        ∫1/√(a²-x²) dx = sin⁻¹(x/a) + C

•        By Parts: ∫u dv = uv - ∫v du

•        Definite Integral Properties: ∫ₐᵇ f(x)dx = ∫ₐᵇ f(a+b-x)dx

Vector Formulas

•        Dot Product: a⃗·b⃗ = |a⃗||b⃗|cos θ = a₁b₁ + a₂b₂ + a₃b₃

•        Cross Product: |a⃗×b⃗| = |a⃗||b⃗|sin θ

•        Scalar Triple Product: [a⃗ b⃗ c⃗] = a⃗·(b⃗×c⃗)

Probability Formulas

•        Conditional Probability: P(A|B) = P(A∩B)/P(B)

•        Multiplication Theorem: P(A∩B) = P(A) × P(B|A)

•        Bayes' Theorem: P(A|B) = [P(B|A) × P(A)]/P(B)

•        Binomial Distribution: P(X = r) = ⁿCᵣ pʳ qⁿ⁻ʳ where q = 1-p

Last 30 Days Preparation Strategy

•        Days 30-25: Complete final revision of all chapters - focus on formulas and theorems

•        Days 24-20: Solve 5-7 CBSE sample papers under timed conditions (3 hours)

•        Days 19-15: Chapter-wise practice - solve 20-25 problems from each chapter

•        Days 14-10: Solve previous year question papers (last 10 years minimum)

•        Days 9-7: Revision of formulas - spend 2 hours daily on formula sheet

•        Days 6-4: Take 3-4 full-length mock tests - simulate actual exam conditions

•        Day 3: Light revision - go through formula sheet, important theorems, common mistakes

•        Day 2: Revise high-weightage chapters: Calculus, Vectors, Algebra

•        Day 1: Complete rest - light reading of formulas only, sleep well

•        Exam Day: Reach center 30 minutes early, stay calm, manage time wisely