Course Description

Language of Instruction:English|Category: AIEEE: AIEEE Aptitude Test for B Arch and B Planning, AIEEE Chemistry, AIEEE Mathematics, AIEEE Physics; IIT JEE: IIT JEE Aptitude Test for B Arch B Des, IIT JEE Chemistry, IIT JEE Mathematics, IIT JEE Physics

Success isn’t always about hard work. It is also about Smart Work!

With APT you get to prepare smartly by focusing on portions which are most important for AIEEE/ IIT-JEE Mathematics examinations

This course will teach you key concepts and short cuts for AIEEE/ IIT-JEE and other Engineering Entrance Exams. The course is supported by online tests and regular assessment of rank through RPI (Rank Potential Index) - a key online innovation from APT Academy.

• Lowest Price Guarantee: You will not find such a course anywhere else at this price by a reputed training organization with great success record in Engineering Entrance Exams for last 5 years.

Why APT Academic Solutions (AAS) Pvt. Ltd.?

APT Academic Solutions believe in people who deliver the right solutions, and it proudly possesses them. AAS is an Indian based e-teaching initiative, working to provide quality education to the needy students globally through the Internet. Here is why students around the country trust AAS to prepare online for AIEEE:

• You will experience significant improvement in grades
• APT supports Progress at your own pace
• Boost your emotional development
• Develop a strong foundation
• Enhance self-confidence
• Enhance your analytical skills
• APT is less expensive

AIEEE Success Stories from 2010 Exam:

What's in the box:

• 30 LIVE online classes
• 30 hours of academic delivery in Mathematics @ an Introductory Price
• Access to online test for practice through TopTrigger
• Rank assessment through periodic online tests

About the instructor:

Doctorate in Applied Mathematics with over 20 years of experience in teaching and content development, Dr. Vidyamanohar Sharma has a proven track record in designing curriculum, setting up patterns for many well-known institutions in India and abroad. He has also been a visiting faculty to many educational institutes in Europe and U.S.A. His innovative thinking , professionalism and creativity is helping the company in scaling new frontiers

Course outline:

Complex Numbers:

• Algebra of complex numbers, various forms of complex numbers, square root of complex numbers
• De Moivre's Theorem and cube roots of unity

Quadratic Equations:

• Quadratic formula, relation between roots and coefficients, nature of roots, symmetric function of roots, equations reducible to quadratic equations, applications

Matrices:

• Algebra of Matrices, determinants, properties of determiniants, inverse of matrices, system of linear equations
• Binomial Theorem, Exponential and logarithmic series - Binomial Theorem for positive integral index, general term, middle term

Limits & continuity:

• Various types of functions, standard limits, indeterminate forms, continuity

Differentiation:

• Application of Differentiation, Successive Differentiation - Rules of differentiation, logarithmic, implicit differentiation, rate change, errors, tangent and normals
• Monotonic functions, Maxima and Minima, Rolle's theorem, Lagrange's mean value theorem, derivatives of order up to two

Integration:

• Integrals involving algebraic, trigonometric, exponential, irrational functions, integration by parts, methods of integration
• Problems, properties of definite, evaluation of definite integrals, definite integral as a limit of sum, areas under curves

 

Differential equations:

 

• Formation, solution of differential equations, methods of solving them, homogeneous, linear differential equations

 

Straight Lines:

 

• Various forms of equations of line, intersections of lines, angle between lines, concurrent lines, bisectors of lines, family of lines

 

Circles:

 

• Various forms of the equation to circle, equation to tangent, family of circles, intersecting circles, orthogonal circles

 

Conics:

 

• Standard form, condition for y=mx+c to be a tangent, point of tangency, focal chord, standard equation to ellipse, condition for y=mx+c to be a tangent, point of tangency
• Ellipse contd. Standard equation to hyperbola, condition for y=mx+c to be a tangent, point of tangency, asymptotes

 

3-D and Vectors:

 

• Direction ratios, direction cosines, equation of line in different forms, angle between lines, skew lines, shortest distance between them,
• Equation to plane in different forms, intersection with line, equation to sphere, diameter form, scalar product contd. Cross product, triple products and applications

Trigonometry:

 

• Transformations - Trigonometric identities, trigonometric functions and their properties, transformations

Trig. Eqns & Inv Trig functions:

 

• Trigonometric equations, general solutions, inverse trigonometric functions, their properties

 

Properties of Triangles, Heights and distances:

 

• Cosine rule, sine rule, tangent rule, area and circumference radius formulae
• In and ex radii formulae, heights and distances, problems

 

Permutations &Combinations, Statistics and Probability:

 

• Meaning of P(n, r) , C(n, r) and simple applications, Mean, median, mode for unwrapped data, standard deviation, variance

 

Probability of an event, addition theorem, conditional probability, Baye's theorem, binomial and Poisson distribution

 

Sets Relations and functions:

Algebra of sets, relations equivalence relations, cartesian product, Functions, types of functions, composition of functions

 

Progressions :

 

• Types of progressions, Arithmetic, geometric and harmonic means

 

Pair of Straight Lines:

 

• Homogeneous equation of second degree, condition for pair of lines, point of intersection, angle between pair of lines