**Gurgaon Academy **provides academic coaching to students to enhance their academic skills, gain confidence, discover motivation, and improve performance in their test examination. Our academic coaching students usually schedule classes twice or thrice weekly depending on their individual need. Academic coaching is available year round for any subject, any level.

We at **Gurgaon Academy** follow some fundamental principles which encourage contact between students and faculty. We always try to develop reciprocity and cooperation among students to encourage active learning. We are very prompt in giving feedback. Our faculties, trainers, mentors, tutors, teachers and professionals are very punctual and they emphasize time on task. We respect diverse talents and ways of learning at our institute.

We set common goals for academic coaching to deliver our best. We develop study skills, prepare students for tests and reduce anxiety. We focus and improve time management skills. We encourage the students, motivate them and help them to learn self-discipline and self-efficacy.

At our coaching centre **Gurgaon Academy** you meet with an academic skills coach who will observe your strategies and techniques, suggest changes to your approach, and provide encouragement as you implement new ways of learning.

**Gurgaon Academy** is Learner-centered teaching institute/coaching centre that encourages collaboration. It sees classrooms (online or face-to-face) as communities of learners. Learner-centered teachers recognize, and research consistently confirms, that students can learn from and with each other. Certainly the teacher has the expertise and an obligation to share it, but teachers can learn from students as well. Learner-centered teachers work to develop structures that promote shared commitments to learning. They see learning individually and collectively as the most important goal of any educational experience. Learner-centered teaching motivates students by giving them some control over learning processes.

**About Our Teachers**

Our teachers have an engaging personality and teaching style which holds the attention of students in all discussions. They have clear objectives for lessons and work hard to meet those specific objectives during each class. Our teachers have effective discipline skills and promote positive behaviors and change in the classroom. Our trainers understand the importance of good classroom management skills that can ensure good student behavior, effective study and work habits, and an overall sense of respect in the classroom. Teachers at Gurgaon Academy maintain open communication with parents and keeps them informed of what is going on in the classroom as far as curriculum, discipline, and other issues. They make themselves available for phone calls, meetings, and email. Our professional trainers and faculties are highly educated and well experienced in delivering classroom coaching. Here at Gurgaon Academy teachers have incredible knowledge of the subject matter they are teaching. They are prepared to answer questions and keep the material interesting for the students. Our teachers and faculty members have **“Passion for Children and Teaching”.** A great teacher is passionate about teaching and working with children. They are excited about influencing students’ lives and understand the impact they have. A great teacher develops a strong rapport with students and establishes trusting relationships.

**Mathematics coaching at Gurgaon Academy:**

We organise group coaching for Mathematics for 9^{th},10^{th},11^{th} & 12^{th} classes. We do offer Maths tutoring service/group coaching for different boards and different syllabus. The boards may include

**CBSE**

**ICSE**

**ISC**

**IGCSE**

**IB(Maths HL/SL/Studies)**

**GMAT**

**GRE**

**SAT**

**SAT II**

**ACT**

**MCAT**

Apart from group and classroom coaching, we also offer home tutoring services for Maths.

## Mathematics Class 12 Syllabus:CBSE Board

**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**

**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.

**Inverse Trigonometric Functions**

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

**Unit II: Algebra**

**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. Non commutativity 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).

**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**

**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.

**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).

**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.

**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).

**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**

**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.

**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**

**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**

**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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**Gurgaon Academy**

**Phone:** +91 99996 50006, 99996 40006

**Email:** gurgaon.tutor@gmail.com

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