Syllabus class 12 maths

CLASS XII COURSE STRUCTURE (2025-26)

CLASS XII COURSE STRUCTURE (2025-26) One Paper \| Max. Marks: 80
No.	Units	Marks
I.	Relations and Functions	08
II.	Algebra	10
III.	Calculus	35
IV.	Vectors and Three-Dimensional Geometry	14
V.	Linear Programming	05
VI.	Probability	08
Total		80
Internal Assessment		20

UNIT-WISE DETAILED SYLLABUS

Chapter	Topics Covered
UNIT I: RELATIONS AND FUNCTIONS
1. Relations and Functions	Types of relations: reflexive, symmetric, transitive, equivalence relations One-one and onto functions
2. Inverse Trigonometric Functions	Definition, range, domain, principal value branch Graphs of inverse trigonometric functions

Chapter	Topics Covered
UNIT II: ALGEBRA
1. Matrices	Types of matrices, operations, transpose, symmetric/skew-symmetric Invertible matrices, uniqueness of inverse
2. Determinants	Determinants up to 3×3, minors, co-factors, area of triangle Adjoint, inverse, solving linear equations

Chapter	Topics Covered
UNIT III: CALCULUS (35 Marks – Highest Weightage)
1. Continuity & Differentiability	Chain rule, derivatives of composite/inverse trig functions Implicit functions, logarithmic differentiation, parametric forms
2. Applications of Derivatives	Rate of change, increasing/decreasing functions Maxima and minima, first & second derivative tests
3. Integrals	Integration as inverse of differentiation Methods: substitution, partial fractions, by parts Standard integrals, Fundamental Theorem of Calculus
4. Application of Integrals	Area under simple curves: lines, circles, parabolas, ellipses
5. Differential Equations	Order and degree, general/particular solutions Separation of variables, homogeneous equations, linear equations

Chapter	Topics Covered
UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY
1. Vectors	Vectors and scalars, magnitude/direction Direction cosines/ratios, types of vectors Scalar (dot) and vector (cross) products
2. Three-dimensional Geometry	Direction cosines/ratios of line Cartesian and vector equations of line Skew lines, shortest distance, angle between lines

Chapter	Topics Covered
UNIT V: LINEAR PROGRAMMING (5 Marks – Lowest Weightage)
Linear Programming	Introduction, terminology: constraints, objective function Graphical method for two variables Feasible/infeasible regions and solutions

Chapter	Topics Covered
UNIT VI: PROBABILITY
Probability	Conditional probability, multiplication theorem Independent events, total probability, Bayes’ theorem

MATHEMATICS QUESTION PAPER DESIGN – CLASS XII (2025-26)

Mathematics (Code No. – 041) Time: 3 hours \| Max. Marks: 80
S. No.	Typology of Questions	Marks & Weightage
1.	Remembering & Understanding	44 Marks (55%)
2.	Applying	20 Marks (25%)
3.	Analysing, Evaluating & Creating	16 Marks (20%)
TOTAL		80 Marks (100%)

INTERNAL ASSESSMENT – 20 MARKS

PERIODIC TESTS SCHEDULE
Test	Tentative Month
Pre-Mid-term (PT-I)	July-August
Mid-Term (PT-II)	November
Post Mid-Term (PT-III)	December-January

INTERNAL ASSESSMENT DISTRIBUTION
Periodic Tests (Best 2 out of 3 tests)	10 Marks
Mathematics Activities	10 Marks

ACTIVITY WORK ASSESSMENT
Activities performed & record keeping	5 Marks
Assessment of activity during year-end test	3 Marks
Viva-voce	2 Marks
GRAND TOTAL (Theory + Internal)	100 Marks

PRESCRIBED BOOKS

NCERT TEXTBOOKS & MANUALS
1.	Mathematics Textbook for Class XI, NCERT Publications
2.	Mathematics Part I – Textbook for Class XII, NCERT Publication
3.	Mathematics Part II – Textbook for Class XII, NCERT Publication
4.	Mathematics Exemplar Problem for Class XI, Published by NCERT
5.	Mathematics Exemplar Problem for Class XII, Published by NCERT
6.	Mathematics Lab Manual class XI, published by NCERT
7.	Mathematics Lab Manual class XII, published by NCERT

IMPORTANT NOTES
• No chapter-wise weightage. All chapters to be covered • 33% internal choice in all sections • Best 2 out of 3 periodic tests considered • NCERT Lab Manual to be used for activities • Calculus has highest weightage (35 marks = 43.75% of theory) • Linear Programming has lowest weightage (5 marks = 6.25% of theory)