**KEAM Mathematics** **Syllabus 2021**– Commissioner of entrance exam (CEE) is the conducting body of KEAM. With the help of the KEAM entrance exam applicants can take admission through various courses such as engineering, Medical, Accenture and many more for that applicant to read this article. This article is totally base on the KEAM Mathematics syllabus 2021. There are two more important subjects Physics and chemistry. To view KEAM chemistry syllabus 2021 and KEAM physics syllabus 2021 applicants must click on the button that is given below. This will directly help the applicant to make a road map to get good marks in the KEAM entrance exam. Applicants also click on the direct link that is given below to download the KEAM syllabus pdf 2021.

*Latest Updates for KEAM 2021 *

**01 June 2021- **Online application form has been released by the organization. Click Here to apply online for KEAM 2021.

## KEAM Mathematics Syllabus 2021

According to our expert research, it is proven that if any applicants make a road map of exam preparation by observing syllabus and exam pattern then that applicants score good marks. This is because the speed of attempting questions during the exam will increase and the accuracy of attempting the questions will help to score good marks in KEAM 2021. KEAM syllabus 2021 contains three subjects are Physics, Chemistry and Mathematics.

If we look towards the KEAM exam pattern then applicants need to face two papers. i.e. paper 1 and paper 2. After completing the KEAM syllabus applicants need to look towards the KEAM model test paper or the KEAM question paper. Applicants need to follow only a single author book. If any applicants follow different author books to cover all the topics then applicants face so much difficulty to complete the KEAM syllabus and there is a lot of confusion created in their mind.

### KEAM 2021 Exam Pattern

Particulars | Details |
---|---|

Mode of Exam | Offline (Pen and Paper Based Test) |

Number of Papers | Two (2): Paper 1 – Physics and ChemistryPaper 2 – Mathematics |

Language | English |

Total Number of Questions | 120 Questions – Paper 1120 Questions – Paper 2 |

Type of Questions | Multiple Choice Question (MCQ) |

Duration of Exam | 2 hours 30 minutes for each paper |

Marking Scheme | 4 marks will be awarded for every correct answer1 mark will be deducted for an incorrect answer |

### KEAM Exam Pattern 2021 – Subject-Wise Distribution

Papers | Subjects | Number of Questions | Marks per question | Marks | Time Allotted |
---|---|---|---|---|---|

Paper 1 | Physics & Chemistry | 120 | 4 | 120X4=480 | 2 hours 30 minutes |

Paper 2 | Mathematics | 120 | 4 | 120X4=480 | 2 hours 30 minutes |

Total | 240 | 960 |

### KEAM Exam Pattern important points & Highlights

- All the question to be asked in the exam that is in the format of multiple-choice questions
- KEAM 2021 is an offline mode exam for or pen-paper test. Applicants need to mark their answers in the OMR sheet that has been given by the examiner.
- The applicant will get zero marks if the applicant marks more than 1 answer for the same question even if the answer marked by the applicant is correct.
- Negative marking is present in this exam for every incorrect answer there will be 1 negative mark detected.
- Paper 1 and Paper 2 is going to be contested on a different day but the user needs to fill a single slot for both papers.

### KEAM 2021 Mathematics Syllabus | Download pdf of KEAM Mathematics syllabus

The Paper-II of Mathematics in KEAM will comprise a total of 120 questions to be answered in 150 minutes. The question papers will carry a total of 480 marks. The KEAM question paper for mathematics will comprise questions from the following topics.

#### UNIT I: ALGEBRA

**Sets, Relations and Functions**:-

Sets and their representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams; Complement of a set; Operations on Sets (Union, Intersection and Difference of Set); Applications of sets: Ordered Pairs, Cartesian Product of Two sets; Relations, reflexive, symmetric, transitive and equivalence relations. Domain, Co-domain and Range: Functions: into, onto, one – one into, one-one onto Functions; Constant Function; Identity Function; composition of Functions; Invertible Functions; Binary Operations.

**Complex Numbers**

Complex Numbers in the form a + i b; Real and Imaginary Parts of a Complex Number; Complex Conjugate, Argand Diagram, Representation of Complex Number as a point in the plane; Modulus and The argument of a Complex Number; Algebra of Complex Numbers; Triangle Inequality; Polar Representation of a Complex Number and square root of a complex number. Solution of a Quadratic Equation in the Complex Number System.

**Sequences and Series**

Sequence and Examples of Finite and Infinite Sequences; Arithmetic Progression (A..P): First Term, Common Difference, nth Term and sum of n terms of an A.P.; Arithmetic Mean (A.M); Insertion of Arithmetic Means between any Two given Numbers; Geometric Progression (G.P): first Term, Common Ratio and nth term, Sum to n Terms, infinite GP and its sum. Geometric Mean (G.M); Insertion of Geometric Means, Relation between AM and GM. between any two given numbers. The formula for finding the sum of first n natural numbers, sum of the squares of first n natural numbers and sum of the cubes of first n natural numbers.

**Permutations, Combinations, Binomial Theorem and Mathematical Induction**

Fundamental Principle of Counting; The Factorial Notation; Permutation as an Arrangement; Meaning of P(n, r); Combination: Meaning of C(n,r); Applications of Permutations and Combinations. Statement of Binomial Theorem; Proof of Binomial Theorem for positive integral Exponent using Principle of Mathematical Induction and also by combinatorial Method; General and Middle Terms in Binomial Expansions; Properties of Binomial Coefficients; Binomial Theorem for any Index (without proof); Application of Binomial Theorem. The Principle of Mathematical Induction, simple Applications.

**Matrices and Determinants**

Concept of a Matrix; Types of Matrices; Equality of Matrices (only real entries may be considered): Operations of Addition, Scalar Multiplication and Multiplication of Matrices; Statement of Important Results on operations of Matrices and their Verifications by Numerical Problem only; Determinant of a Square Matrix; Minors and Cofactors; singular and non-singular Matrices; Applications of Determinants in finding the Area of a Triangle. Concept of elementary row and column operations.

Transpose, Adjoint and Inverse of a Matrix; Consistency and Inconsistency of a system of Linear Equations; Solving System of Linear Equations in Two or Three variables using Inverse of a Matrix (only up to 3X3 Determinants and Matrices should be considered).

**Linear Inequalities**

Solutions of Linear Inequalities in one variable and its Graphical Representation; solution of system of Linear Inequalities in one variable; Graphical solutions of Linear Inequalities in two variables; solution of system of Linear Inequalities in two variables.

**Mathematical Reasoning**

Mathematically acceptable statements and their Negation. Connecting words /phrases consolidating the understanding of if and only if condition, implies, and/or, implied by, there exists. Validating the statements involving the connecting words, difference among contradiction, converse and contrapositive.

#### UNIT II : TRIGONOMETRY

**Trigonometric functions and Inverse Trigonometric functions**

Degree measures and Radian measure of positive and negative angles; relation between degree measure and radian measure, definition of trigonometric functions with the help of a unit circle, periodic functions, concept of periodicity of trigonometric functions, value of trigonometric functions of x for x. Trigonometric functions of multiple and submultiples of numbers. Conditional identities for the angles of a triangle, solution of trigonometric equations of the type Sin x = Sin a ; Cos x = Cos a; Tan x = Tan a and equations reducible to these forms. Proofs and simple application of sine and cosine formulae.Inverse Trigonometric functions. Range, domain, principal value branch and graphs of inverse trigonometric functions.

Simple problems Graph of the following trigonometric functions; y = Sin x ; y = Cos x ; y = Tan x ; y = a Sin x ;y = a Cos x, y = a Sin bx ; y = a Cos bx;

#### UNIT III: GEOMETRY

**Lines and Family of lines**

Cartesian system of coordinates in a plane, shifting of origin. Distance formula, Slope of line, parallel and perpendicular lines. Various forms of equations of a line parallel to axes, slope-intercept form, The Slope point form, Intercept form, Normal form, General form, Intersection of lines. Equation of bisectors of the angle between two lines, Angles between two lines, condition for concurrency of three lines, Distance of a point from a line, Equations of family of lines through the intersection of two lines.

**Conic sections**

Sections of a cone. Circles, standard form of the equation of a circle, its radius and centre. Equations of conic sections [Parabola, Ellipse and Hyperbola] in standard form and simple properties.

**Vectors**

Vectors and scalars, Magnitude and Direction of a vector, Types of vectors (Equal vectors, unit vector, Zero vector). Position vector of a point, Localized and free vectors, parallel and collinear vectors, Negative of a vector, components of a vector, Addition of vectors, multiplication of a vector by a scalar, position vector of point dividing a line segment in a given ratio, Application of vectors in geometry. Scalar product of two vectors, projection of a vector on a line, vector product of two vectors.

**Three-Dimensional Geometry**

Coordinate axes and coordinate planes in three dimensional space, coordinate of a point in space, distance between two points, section formula, direction cosines, and direction ratios of a line joining two points, projection of the join of two points on a given line, Angle between two lines whose direction ratios are given,

**Cartesian and vector equation of a line through**

- A point and parallel to a given vector
- Through two points, Collinearity of three points, coplanar and skew lines, Shortest distance between
- Two lines, Condition for the intersection of two lines,

**Cartesian and vector equation of a plane**

- When the normal vector and the distance of the plane from the origin is given.
- Passing through a point and perpendicular to a given vector.
- Passing through a point and parallel to two given lines through the intersection of two other planes
- Containing two lines.
- Passing through three points,

**Angle between**

- Two lines
- Two planes
- A line and a plane,

Condition of coplanarity of two lines in vector and Cartesian form, length of perpendicular of a point from a plane by both vector and Cartesian methods.

#### Unit IV: STATISTICS

**Statistics and probability**

Mean deviation, variance, standard deviation for grouped an ungrouped data. Analysis of frequency distributions with equal means but different variances. Random experiments and sample space, Events as subset of a sample space, occurrence of an event, sure and impossible events, Exhaustive events, Algebra of events, Meaning of equality likely outcomes, mutually exclusive events. Probability of an event; Theorems on probability; Addition rule, Multiplication rule, Independent experiments and events. Finding P (A or B), P (A and B), Bayes’ theorem, random variables, Probability distribution of a random variable and its mean and variance. Repeated independent (Bernoulli) trials and Binomial distribution.

#### UNIT V : CALCULUS

**Functions, Limits and continuity**

Concept of a real function; its domain and range; Modulus Function, Greatest integer function: Signum functions; Trigonometric functions and inverse trigonometric functions and their graphs; composite functions, Inverse of a function. Limit of a function; meaning and related notations; Left and right hand limits; Fundamental theorems on limits without proof. Continuity of a function at a point, over an open/ closed interval; Sum, Product and quotient of continuous functions; Continuity of special functions- Polynomial, Trigonometric, exponential, Logarithmic and Inverse trigonometric functions.

**Differentiation**

Derivative of a function; its geometrical and physical significance; Relationship between continuity and differentiability; Derivatives of polynomial, basic trigonometric, exponential, logarithmic and inverse trigonometric functions from first principles; derivatives of sum, difference, product and quotient of functions; derivatives of polynomial, trigonometric, exponential, logarithmic, inverse

trigonometric and implicit functions; Logarithmic differentiation; derivatives of functions expressed in parametric form; chain rule and differentiation by substitution; Derivatives of Second order.

Application of Derivatives Rate of change of quantities; Tangents and Normals; increasing and decreasing functions and sign of the derivatives; maxima and minima; Greatest and least values; Rolle’s theorem and Mean value theorem; Approximation by differentials. Simple problems.

**Indefinite Integrals**

Integration as inverse of differentiation; properties of integrals; Integrals involving algebraic, trigonometric, exponential and logarithmic functions; Integration by substitution; Integration by parts; Integrals of the type, Integration of rational functions; Partial fractions and their use in integration; Integrals of the type

**Definite Integrals**

Definite integral as a limit of a sum; Fundamental theorems of integral calculus without proof; Evaluation of definite integrals by substitution and by using the following properties. Application of definite integrals in finding areas bounded by a curve, circle, parabola and ellipse in standard form between two ordinates and x-axis; Area between two curves, line and circle; line and

parabola: line and ellipse

**Differential Equations**

Definition; order and degree; general and particular solutions of a differential equation; formation of differential equations whose general solution is given; solution of differential equations by method of Separation of variables; Homogeneous differential equations of the first order and their solutions; Solution of linear differential equations of the types

**Linear Programming**

Introduction, related terminology such as constraints, 0bjective function, optimisation, different types of linear programming problems, mathematical formulation of Linear Programming Problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions ( up to three non-trivial constraints).

### Important topics in KEAM Mathematics Syllabus

- Sets, Relation & Functions
- Complex Numbers
- Quadratic Equations
- Linear Inequations
- 3D Geometry
- Differential Equations
- Application of Derivatives
- Indefinite Integrals
- Lines & Family of Lines
- Mathematical Logic & Boolean Algebra
- Trigonometric Functions & Inverse Trigonometric Functions

### Best Books for Mathematics

Book name | Publication/ Author |
---|---|

Mathematics XI & XII | R. D Sharma |

Problems in Calculus in One Variable | I. A Maron |

### KEAM Mathematics Syllabus 2021 Quick Links

KEAM Mathematics syllabus events | Quick Links |
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KEAM Chemistry Syllabus pdf | Download Now |

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KEAM Application Form 2021 | Apply now |

KEAM Result 2021 | Click Here |

KEAM 2021 official website | cee.kerala.gov.in |