# JEE Mains Math Syllabus 2018

## Math Syllabus JEE Mains 2018

Mathematics is considered to be the most important subject for JEE Mains 2018 since the most of the foundation of Physics and Chemistry develops from Mathematics. Candidates aspiring for JEE Mains 2018 exam must have an in-depth knowledge of JEE Mains Math Syllabus 2018 which will help them to plan their preparation strategy accordingly. Candidates must have a thorough knowledge of each and every chapter from JEE mains 2018 Math Syllabus since a question from any topic could be asked in the examination. Mathematics is a subject that requires hard work and rigorous practice. So the candidate must go through the topics mentioned in Math Syllabus JEE Mains 2018 and then practice the questions related to that topic. This would also help the candidate by increasing their speed and accuracy.

The chapter-wise weightage and important topics of the entire JEE Mains Math Syllabus 2018 is given below:

## JEE Mains Math Syllabus 2018 | |||

S. No. | Topics from Syllabus of JEE Mains 2018 | Marking Weightage | Important Topics |

1 | Sets, Relations & Functions | 3-4% | – |

2 | Complex Numbers and Quadratic Equations | 5-6% | Important |

3 | Permutation and Combination | 3-4% | – |

4 | Mathematical Induction | 1-2% | – |

5 | Binomial Theorem and its Applications | 3-4% | – |

6 | Sequence and Series | 6-7% | Important |

7 | Matrices and Determinants | 6-7% | Important |

8 | Statistics and Probability | 4-5% | Important |

9 | Trigonometry | 6-7% | Important |

10 | Mathematical Reasoning | 3-4% | – |

11 | Coordinate Geometry | 10-12% | Important |

12 | Limits, Continuity and Differentiability | 7-8% | Important |

13 | Integral Calculus | 10-12% | Important |

14 | Differential Equations | 6-7% | – |

15 | 3D Geometry | 5-6% | Important |

16 | Vector Algebra | 3-4% | Important |

17 | Application of Derivatives | 1% | – |

## JEE Mains Math Syllabus 2018 (Official)

The detailed analysis of each and every topic and subtopic in JEE Mains Math Syllabus 2018 is given below. The candidates are advised to go through the Maths syllabus thoroughly before starting their JEE Exam preparation.

### UNIT I: Sets, Relations and Functions

• Sets and their representation

• Union, intersection and complement of sets and their algebraic properties

• Powerset

• Relation, Types of relations, equivalence relations, functions

• one-one, into and onto functions, composition of functions

### UNIT II: 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

• square root of a complex number

• triangle inequality

• Quadratic equations in real and complex number system and their solutions

• Relation between roots and co-efficient, nature of roots, formation of quadratic equations with given roots.

### UNIT III: Matrices and Determinants

• Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three.

• Properties of determinants, evaluation of determinants, area of triangles using determinants.

• Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations

• Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.

### UNIT IV: Permutations and Combinations

• Fundamental principle of counting

• permutation as an arrangement and combination as selection

• Meaning of P (n,r) and C (n,r), simple applications.

### UNIT V: Mathematical Induction

• Principle of Mathematical Induction and its simple applications.

### UNIT VI: Binomial Theorem

• Binomial theorem for a positive integral index

• general term and middle term

• properties of Binomial coefficients and simple applications.

### UNIT VII: Sequences and Series

• Arithmetic and Geometric progressions

• insertion of arithmetic

• geometric means between two given numbers.

• Relation between A.M. and G.M. Sum upto n terms of special series: Sn, Sn2, Sn3.

• Arithmetic – Geometric progression.

### UNIT VIII: Limit, Continuity and Differentiability

• Real – valued functions, algebra of functions, polynomials, 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 and implicit functions

• derivatives of order upto two.

• Rolle’s and Lagrange’s Mean Value Theorems.

• Applications of derivatives: Rate of change of quantities, monotonic – increasing and decreasing functions

• Maxima and minima of functions of one variable, tangents and normals.

### UNIT IX: 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

• Integral as limit of a sum.

• Fundamental Theorem of Calculus.

• Properties of definite integrals.

• Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.

### UNIT X: Differential Equations

• Ordinary differential equations, their order and degree.

• Formation of differential equations.

• Solution of differential equations by the method of separation of variables,

• solution of homogeneous and linear differential equations of the type:

### UNIT XI: Co-ordinate Geometry

• Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

Straight lines

• Various forms of equations of a line,

• intersection of lines,

• angles between two lines,

• conditions for concurrence of three lines,

• distance of a point from a line,

• equations of internal and external bisectors of angles between two lines,

• coordinates of centroid, orthocentre and circumcentre of a triangle,

• equation of family of lines passing through the point of intersection of two lines.

Circles, conic sections

• Standard form of equation of a circle,

• general form of the equation of a circle,

• its radius and centre,

• equation of a circle when the endpoints of a diameter are given,

• points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle,

• equation of the tangent.

• Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.

### UNIT XII: Three Dimensional Geometry

• Coordinates of a point in space,

• distance between two points,

• section formula,

• direction ratios and direction cosines,

• angle between two intersecting lines.

• Skew lines, the shortest distance between them and its equation.

• Equations of a line and a plane in different forms,

• intersection of a line and a plane, coplanar lines.

### UNIT XIII: Vector Algebra

• Vectors and scalars,

• addition of vectors,

• components of a vector in two dimensions and three dimensional space,

• scalar and vector products,

• scalar and vector triple product.

### UNIT XIV: Statistics and Probability

Measures of Dispersion

• Calculation of mean, median, mode of grouped and ungrouped data.

• Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.

Probability

• Probability of an event,

• addition and multiplication theorems of probability,

• Baye’s theorem,

• Probability distribution of a random variate,

• Bernoulli trials

• Binomial distribution.

### UNIT XV: Trigonometry

• Trigonometrical identities and equations.

• Trigonometrical functions.

• Inverse trigonometrical functions and their properties.

• Heights and Distances.

### UNIT XVI: Mathematical Reasoning

• Statements, logical operations and, or, implies, implied by, if and only if.

• Understanding of tautology, contradiction, converse and contrapositive.

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