GUJCET Maths Syllabus 2027 PDF - Complete Topic List

CLASS XI

UNIT I: Sets and Functions

Sets

Representation, empty, finite & infinite sets, equal sets, subsets, subsets of ℝ (intervals & notations), power set, universal set, Venn diagrams, union, intersection, difference, complement, properties of complements

Relations & Functions

Ordered pairs, Cartesian product, number of elements in Cartesian product, R × R × R, definition of relation, pictorial diagrams, domain, co-domain, range, functions as special relations, real-valued functions, graphs of constant, identity, polynomial, rational, modulus, signum, greatest integer functions, sum, difference, product & quotient of functions

Trigonometric Functions

Angles (positive/negative), radians & degrees, conversion, unit circle definition, identity sin²x + cos²x = 1, signs of functions, graphs, sin(x ± y), cos(x ± y), tan(x ± y), trigonometric identities (sin x ± sin y, cos x ± cos y, etc.), multiple angle identities (sin2x, cos2x, tan2x, sin3x, cos3x, tan3x), general solution of trigonometric equations (sinθ=sinα, cosθ=cosα, tanθ=tanα), sine & cosine rules

UNIT II: Algebra

Mathematical Induction

Principle & applications

Complex Numbers & Quadratic Equations

Need for √−1, algebraic properties, Argand plane, polar representation, Fundamental Theorem of Algebra, quadratic equations in ℂ, square root of complex number

Linear Inequalities

Algebraic solution (1 variable), number line representation, graphical solution (2 variables), system of inequalities

Permutations & Combinations

Counting principle, factorial n, derivation of formulae, connections & applications

Binomial Theorem

History, statement, proof (positive integer index), Pascal’s triangle, general & middle term, applications

Sequences & Series

A.P., A.M., G.P., nth term, sum of n terms, infinite G.P., G.M., relation between A.M. & G.M., special series (∑n, ∑n², ∑n³)

UNIT III: Coordinate Geometry

1. Straight Lines

Recall of 2D, shifting of origin, slope & angle between lines, forms of equations: parallel to axes, point-slope, slope-intercept, two-point, intercept, normal, general equation, family of lines through intersection, distance from point to line

2. Conic Sections

Circle, parabola, ellipse, hyperbola, degenerate cases (point, line, intersecting lines), standard equations & properties

3. 3D Geometry (Intro)

Axes & planes, coordinates of a point, distance between 2 points, section formula

UNIT IV: Calculus

Limits & Derivatives: Concept of derivative as rate of change, intuitive idea of limit, standard limits, derivative definition, slope of tangent, derivative of sum, difference, product, quotient, polynomial & trigonometric functions

UNIT V: Mathematical Reasoning

Statements, connecting words (if & only if, implies, and/or, implied by, there exists), use in real life, validating statements, contradiction, converse, contrapositive

UNIT VI: Statistics & Probability

1. Statistics

Dispersion, mean deviation, variance, standard deviation (ungrouped & grouped), frequency distribution analysis

2. Probability

Experiments, outcomes, sample space, events (‘not’, ‘and’, ‘or’), exhaustive & mutually exclusive, axiomatic probability, probability rules

CLASS XII

UNIT I: Relations and Functions

1. Relations & Functions

Types: reflexive, symmetric, transitive, equivalence, one-one, onto, composite, inverse functions, binary operations

2. Inverse Trigonometric Functions

Definition, range, domain, principal values, graphs, properties

UNIT II: Algebra

1. Matrices

Concept, notation, order, equality, types (zero, symmetric, skew-symmetric), operations, non-commutativity, zero product, elementary operations, invertible matrices & uniqueness

2. Determinants

Up to 3×3, properties, minors, cofactors, applications (area of triangle), adjoint, inverse, system of linear equations (2–3 variables), solution via inverse matrix

UNIT III: Calculus

1. Continuity & Differentiability

Continuity, differentiability, chain rule, inverse trigonometric derivatives, implicit functions, exponential & logarithmic functions, log differentiation, parametric forms, 2nd order derivatives, Rolle’s & Lagrange’s Mean Value Theorems (geometric interpretation)

2. Applications of Derivatives

Rate of change, monotonicity, tangents & normals, approximation, maxima & minima (first & second derivative tests)

3. Integrals

As inverse of differentiation, substitution, partial fractions, by parts, standard integrals, definite integrals as limit of sum, Fundamental Theorem of Calculus, properties, evaluation

4. Applications of Integrals

Area under curves (lines, circles, parabolas, ellipses), area between curves

5. Differential Equations

Definition, order & degree, general/particular solutions, formation, solution (separation of variables, homogeneous, linear)

UNIT IV: Vectors & 3D Geometry

1. Vectors

Scalars & vectors, magnitude, direction cosines/ratios, types (equal, unit, zero, parallel, collinear), position vector, components, operations, scalar (dot) & vector (cross) product, scalar triple product

2. Three-Dimensional Geometry

Line equations (Cartesian & vector), coplanar & skew lines, shortest distance, plane equations, angles (line-line, plane-plane, line-plane), distance of point from plane

UNIT V: Linear Programming

Terminology (constraints, objective function, optimization), LPP formulation, graphical solution (2 variables), feasible region/solution, optimal solutions

UNIT VI: Probability

Multiplication theorem, conditional probability, independence, total probability, Bayes’ theorem, random variable, probability distribution, mean & variance, Bernoulli trials, Binomial distribution

Mode of GUJCET 2027 Exam

OMR-based Offline Exam

Papers

Paper 1 - Physics and Chemistry

Paper 2 - Mathematics

Duration

Physics and Chemistry - 120 Minutes

Mathematics - 60 Minutes

Marking Scheme

One mark for 1 correct answer

0.25 mark deducted for 1 wrong answer