JEE Main Maths Syllabus
Maths is an important subject in the JEE Main exam. The JEE Main Maths syllabus covers
a wide range of topics, from fundamental principles to advanced concepts. Students must
understand these concepts to perform well on the exam and achieve a high ranking. Here’s
the content restructured into a clear table format, summarising the units, topics, and
subtopics for the JEE Mains Maths syllabus:
Syllabus for JEE Main Paper 1 (B.E./B.Tech.)- Mathematics, Paper 2A (B.Arch.), and
Paper 2B (B.Planning) Unit
Title
Content
UNIT 1
SETS, RELATIONS
AND FUNCTIONS
Sets and their representation; Union,
intersection and complement of sets and their
algebraic properties; Power set; Relations,
type of relations, equivalence relations,
functions; one-one, into and onto functions,
the composition of functions.
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UNIT 2
COMPLEX NUMBERS
AND QUADRATIC
EQUATIONS
Complex numbers as ordered pairs of reals,
Representation of complex numbers in the
form a + ib and their representation in a plane,
Argand diagram, algebra of complex numbers,
modulus and argument (or amplitude) of a
complex number, Quadratic equations in real
and complex number systems and their
solutions; Relations between roots and
coefficients, nature of roots, the formation of
quadratic equations with given roots.
UNIT 3
MATRICES AND
DETERMINANTS
Matrices, algebra of matrices, type of
matrices, determinants and matrices of order
two and three, evaluation of determinants,
area of triangles usingdeterminants; Adjoint
and inverse of a square matrix; Test of
consistency andsolution of simultaneous linear
equations in two or three variables using
matrices.
UNIT 4
PERMUTATIONS AND
COMBINATIONS
The fundamental principle of counting,
permutations and combinations; Meaningof
P(n, r) and C(n, r). Simple applications.
UNIT 5
BINOMIAL THEOREM
AND ITS SIMPLE
APPLICATIONS
Binomial theorem for a positive integral
index, general term and middle termandsimple
applications
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UNIT 6
SEQUENCE AND
SERIES
Arithmetic and Geometric progressions,
insertion of arithmetic, geometric means
between two given numbers, Relation between
A.M and G.M.
UNIT 7
LIMIT, CONTINUITY
AND
DIFFERENTIABILITY
Real–valued functions, algebra of functions;
polynomial, rational, trigonometric,
logarithmic and exponential functions; inverse
functions. Graphs of simple functions. Limits,
continuity and differentiability. Differentiation
of the sum, difference, product and quotient of
two functions. Differentiation of
trigonometric, inverse trigonometric,
logarithmic, exponential, composite
andimplicit functions; derivatives of order
upto two, Applications of derivatives: Rate of
change of quantities, monotonic-Increasing
and decreasing functions, Maxima and
minima of functions of one variable
UNIT 8
INTEGRAL
CALCULUS
Integral as an anti-derivative, Fundamental
integrals involving algebraic, trigonometric,
exponential and logarithmic functions.
Integration by substitution, by parts and by
partial fractions. Integration using
trigonometric identities. Evaluation of simple
integrals of the type The fundamental theorem
of calculus, properties of definite integrals.
Evaluation of definite integrals, determining
areas of the regions bounded bysimple curves
by simple curves in standard forms.
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UNIT 9
DIFFERENTIAL
EQUATIONS
Ordinary differential equations, their order and
degree, the solution of differential equation by
the method of separation of variables, solution
of a homogeneous and linear differential
equation of the type.
UNIT
10
CO-ORDINATE
GEOMETRY
Cartesian system of rectangular coordinates in
a plane, distance formula, sections formula,
locus and its equation, the slope of a line,
parallel and perpendicular lines, intercepts of
a line on the co-ordinate axis. Straight line:
Various forms of equations of a line,
intersection of lines, angles between two lines,
conditions for concurrence of three lines, the
distance of a point form a line, co-ordinate of
the centroid, orthocentre and circumcentre of
a triangle. Circle, conic sections: A standard
form of equations of a circle, the general form
of the equation of a circle, its radius and
centre, equation of a circle whenthe endpoints
of a diameter are given, points of intersection
of a line and a circle with the centre at the
origin and sections of conics, equations of
conic sections (parabola, ellipse and
hyperbola) in standard forms.
UNIT
11
THREE
DIMENSIONAL
GEOMETRY
Coordinates of a point in space, the distance
between two points, sectionformula, direction
ratios and direction cosines and the angle
between twointersecting lines. Equation of a
line; Skew lines, the shortest distance
betweenthem and its equation.
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UNIT
12
VECTOR ALGEBRA
Vectors and scalars, the addition of vectors,
components of a vector in twodimensions and
three-dimensional spaces, scalar and vector
products.
UNIT
13
STATISTICS AND
PROBABILITY
Measures of dispersion; calculation of mean,
median, mode of grouped andungrouped data,
calculation of standard deviation, variance and
meandeviation for grouped and ungrouped
data. Probability: Probability of an event,
addition and multiplication theorems of
probability, Baye's theorem,
probabilitydistribution of a random variable.
UNIT
14
TRIGONOMETRY
Trigonometrical identities and trigonometrical
functions, inverse trigonometrical functions
their properties.
Part –II APTITUDE TEST - Paper 2A (B.Arch.)
UNIT - 1 Awareness of persons: Buildings, Materials. Objects, Texture related to
Architecture and Build-environment, Visualizing three- dimensional objectsfrom twodimensional drawings. Visualizing. Different sides of three- dimensional objects.
Analytical Reasoning Mental Ability (Visual, Numerical and Verbal)
UNIT – 2 Three dimensional- perception: Understanding and appreciation of scale and
proportions ofobjects, building forms and elements, colour texture harmony and contrast
Design and drawingofgeometrical or abstract shapes and patterns in pencil.
Transformation of forms both 2Dand 3Dunion, subtraction rotation, development of
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surfaces and volumes, Generation of plans, elevations and 3Dviewsof objects, creating
two-dimensional and three-dimensional compositions using given shapes and forms.
Part – III DRAWING TEST
Sketching of scenes and activities from memory of urbanscape (public space, market,
festivals, street scenes, monuments, recreational spaces, etc.). landscape (riverfronts.
Jungle. Gardens, trees. Plants, etc.)and rural life. To be conducted in a Drawing sheet.
Note: Candidates are advised to bring pencils, own geometry box set, crasets and colour
pencils andcrayons for the Drawing Test.
Part –II APTITUDE TEST - Paper 2B (B.Planning) UNIT - 1 Awareness of persons, Buildings, Materials, Objects and Textures related to
Architecture andBuild-environment, Visualizing three-dimensional objects from twodimensional drawings.Visualizing different sidesof three-dimensional objects, Analytical
Reasoning Mental Ability (Visual, Numerical and Verbal)
UNIT – 2 Three dimensional- perception: Understanding and appreciation of scale and
proportions of objects,building forms and elements, colour texture harmony and contrast
Design and drawing of geometrical orabstract shapes and patterns in pencil.
Transformation of forms both 2D and 3D union, subtractionrotation,development of
surfaces and volumes, Generation of plans, elevations and 3D views of objects,
creatingtwo-dimensional and three-dimensional compositions using given shapes and
forms.
Part – III PLANNING
UNIT-1 GENERAL AWARENESS. General knowledge questions and knowledge about
prominent cities, development issues, governmentprograms etc.
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UNIT-2 SOCIAL SCIENCES The idea of nationalism, nationalism in India, pre-modern
world, 19 th-century global economy, colonialismandcolonial cities, industrialization,
resources and development, types of resources, agriculture, water, mineralresources,
industries, national economy; Human Settlements. Power-sharing, federalism, political
parties, democracy, the constitution of India. Economic development- economic sectors,
globalization, the concept of development, poverty; Populationstructure, social exclusion
and inequality, urbanization, rural development, colonial cities.
UNIT-3 THINKING SKILLS Comprehension (unseen passage); map reading skills, scale,
distance, direction, area etc.; critical reasoning;understanding of charts, graphs and tables;
basic concepts of statistics and quantitative reasoning.
Overview of JEE Main Maths Topics
The syllabus for JEE Main Maths typically covers a wide range of topics from classical
algebra to advanced calculus. To help you navigate through the vast JEE Main Maths
syllabus, we have organised the topics into sections. Here are the key topics that you need
to cover:
Algebra:
•
Polynomials: Understanding polynomial functions, their properties, and solutions,
including factoring polynomials, finding the roots of polynomials, and using the
Remainder Theorem and Factor Theorem.
•
Quadratic Equations: Solving quadratic equations and analysing their properties,
including the discriminant, the quadratic formula, and vertex-form equations.
•
Complex Numbers: Exploring complex numbers, arithmetic operations, and their
applications, including the modulus and argument of complex numbers, DeMoivre's
Theorem, and complex solutions to quadratic equations.
•
Sequences and Series: Studying arithmetic and geometric progressions and their sum
formulas, as well as infinite series and their convergence tests.
•
Permutations and Combinations: Analysing arrangements and selections in various
situations, including using the factorial function and Pascal's Triangle.
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•
Binomial Theorem: Exploring binomial expansions and their properties, including
using the Binomial Theorem to expand binomial expressions and find approximate
values.
•
Mathematical Induction: Understanding the principle of mathematical induction and
its applications to proving theorems.
•
Matrices and Determinants: Dealing with matrix operations, determinants, and their
properties, including finding the inverse of a matrix and solving systems of linear
equations using matrices.
Calculus:
•
Functions and Limits: Grasping the concepts of functions, limits, and their continuity,
including understanding the different types of discontinuities and using L'Hôpital's
rule to evaluate limits.
•
Differentiation: Calculating derivatives, including applying derivatives to finding the
maximum and minimum values of functions, solving related rates problems, and
sketching the graphs of functions.
•
Integration: Solving definite and indefinite integrals, along with applications,
including finding the area under a curve and the volume of a solid of revolution.
•
Differential Equations: Studying ordinary differential equations and their solutions,
including first-order equations and separable equations
Trigonometry:
•
Trigonometric Functions: Understanding trigonometric functions and their properties,
including the trigonometric identities, the unit circle, and inverse trigonometric
functions.
•
Trigonometric Equations: Solving trigonometric equations and inequalities, including
using trigonometric identities and inverse trigonometric functions.
Coordinate Geometry:
•
Coordinate Systems: Analysing coordinate systems, including the rectangular
coordinate system and the polar coordinate system.
•
Lines: Understanding the properties and equations of lines, including slope-intercept
form and point-slope form.
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•
Circles: Exploring the properties and equations of circles, including the standard
equation of a circle and the equation of a circle in parametric form.
•
Conic Sections: Understanding the properties and equations of conic sections,
including the parabola, ellipse, and hyperbola.
Three-Dimensional Geometry and Vector Algebra:
•
Vectors: Understanding vectors and three-dimensional space, including vector
operations, the dot product, and the cross product.
•
Vector Operations: Exploring vector operations, including addition, subtraction, scalar
multiplication, the dot product, and the cross product.
Probability:
•
Probability Theory: Delving into probability theory, events, and probability
distributions, including conditional probability, Bayes' theorem, and the binomial
distribution.
Statistics:
•
Analysing Data: Analysing data, measures of central tendency, and dispersion,
including the mean, median, mode, and standard deviation.
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JEE Main Maths Section Wise Weightage
Topics
No. of Questions
Marks
Coordinate Geometry
5
20
Limits, Continuity, and Differentiability
3
12
Integral Calculus
3
12
Complex Numbers and Quadratic Equations
2
8
Matrices and Determinants
2
8
Statistics and Probability
2
8
Three-Dimensional Geometry
2
8
Vector Algebra
2
8
Sets, Relations, and Functions
1
4
Permutations and Combinations
1
4
Binomial Theorem and Its Applications
1
4
Sequences and Series
1
4
Trigonometry
1
4
Differential Equations
1
4
Statics and Dynamics
1
4
Differential Calculus
1
4
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