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**Best Coaching Classes **are given to **12th** Students for **MATHS**. We have **Expert and Experienced** faculties having more than **25 years of Experience**. Students from **VIP Road , Zirakpur, Mohali, ****Chandigarh and **

**Panchkula**are already taking the advantage and returning the productivity of our efforts and hard work in the form of

**Excellent Results.**

We assist our students to perform better and achieve desired results in their exams. Our faculty applies the self –learning and assessment tools for the growth of students, along with this we work on the student’s over all personality grooming by giving PD sessions time to time. We ensure one to one attention to be given to our each student, to boost up their performance. We apply the following tools in Quality and well programmed classroom coaching to meet the targets of Teacher, Students and Parents.

**1. Personalized Learning:** Our faculties are highly experienced hence they enables and enhance a student’s learning skills which includes the use of expertise and statistics to resolve complex issues, running collaboratively, communicating efficiently, mastering how to analyze, and growing instructional mindsets. They empower students to be actively involved in the processes of their own learning, rather than passively receptive.

**2. Weekly Mock tests: **We conduct tests on weekly basis, to have strong command on the covered topics and to clear the doubts related to subject if any. This helps in developing self confidence and performance in the exams.

**3. Timely completion of syllabus:** We ensure to complete the syllabus timely so that student have enough time left for the revision and doubts clearing sessions can be conducted before final examinations.

**4. Educational videos: **The videos are made for important topics and same has been uploaded for the convenience of students which helps them to revise those topics being taught in class.

**5. Free Educational App:** Online educational app is available for our foundation group of students covering all the important area of their syllabus. Students can take help to make handy notes from the app and can use them for further competitive exams.

**6. Get Online Assignments:** We provide multiple assignments covering each topic which is helpful in examinations and class room tests.

**For students to learn, they must feel safe, engaged, connected, and supported in their classrooms. It enables them to succeed further in their respective careers and life.**

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**Mathematics Syllabus**

**Mathematics Syllabus**

### Course Structure

Unit |
Topic |
Marks |

I. | Relations and Functions | 10 |

II. | Algebra | 13 |

III. | Calculus | 44 |

IV. | Vectors and 3-D Geometry | 17 |

V. | Linear Programming | 6 |

VI. | Probability | 10 |

Total |
100 |

### Unit I: Relations and Functions

**1. Relations and Functions**

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

**2. Inverse Trigonometric Functions**

Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

### Unit II: Algebra

**1. Matrices**

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

**2. Determinants**

Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.

### Unit III: Calculus

**1. Continuity and Differentiability**

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.

Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.

**2. Applications of Derivatives**

Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

**3. Integrals**

Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof definite integrals and evaluation of definite integrals.

**4. Applications of the Integrals**

Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).

**5. Differential Equations**

Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

dy/dx + py = q, where p and q are functions of x or constants.

dx/dy + px = q, where p and q are functions of y or constants.

### Unit IV: Vectors and Three-Dimensional Geometry

**1. Vectors**

Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.

**2. Three - dimensional Geometry**

Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.

### Unit V: Linear Programming

**1. Linear Programming**

Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

### Unit VI: Probability

**1. Probability**

Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.

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