Classroom Course
Mathematics for NIMCET, XIth & XIIth
A strong mathematics foundation for MCA and B-Tech entrance exams.
Overview
It is the one-year regular course of KIM India Institute™. The duration is approximately 8–9 months, with classes usually conducted 4 days a week for 1 hour 30 minutes each (this may increase depending on the course curriculum). The coverage is exhaustive and prepares students for all the leading B-Tech entrance examinations in India.
Course Features
- Printed material & assignments
- Support in acquiring and filling entrance exam forms
- Regular feedback from students on satisfaction
- Timely completion of syllabus
- Regular tests — weekly / monthly
- Strong foundation in core mathematics
Syllabus
Learning Path
The complete mathematics syllabus we cover, unit by unit. Tap any unit to see the topics.
1 Sets, Relations and Functions +
Sets and their representation; union, intersection and complement of sets and their algebraic properties; power set; relations, types of relations, equivalence relations; functions — one-one, into and onto functions, composition of functions.
2 Complex Numbers and Quadratic Equations +
Complex numbers in the form a+ib and their representation; Argand diagram; algebra of complex numbers, modulus and argument; square root of a complex number; quadratic equations and their solutions; relation between roots and coefficients, nature of roots.
3 Matrices and Determinants +
Algebra and types of matrices; determinants and their properties, evaluation, area of triangles; adjoint and inverse of a square matrix; consistency and solution of simultaneous linear equations using determinants and matrices.
4 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.
5 Mathematical Induction +
The principle of mathematical induction and its simple applications.
6 Binomial Theorem +
Binomial theorem for a positive integral index; general and middle terms; properties of binomial coefficients and simple applications.
7 Sequence and Series +
Arithmetic and geometric progressions; arithmetic and geometric means; relation between A.M. and G.M.; sums of special series; arithmetico-geometric progression.
8 Limit, Continuity and Differentiability +
Algebra of functions; polynomial, rational, trigonometric, logarithmic and exponential functions; limits, continuity and differentiability; differentiation rules; Rolle’s and Lagrange’s Mean Value Theorems; applications of derivatives — rates of change, monotonicity, maxima and minima, tangents and normals.
9 Integral Calculus +
Integral as an antiderivative; integration by substitution, by parts and by partial fractions; integration using trigonometric identities; definite integrals and their properties; Fundamental Theorem of Calculus; area of regions bounded by simple curves.
10 Differential Equations +
Order and degree of differential equations; formation of differential equations; solution by separation of variables; solution of homogeneous and linear differential equations.
11 Coordinate Geometry +
Cartesian coordinates, distance and section formulae, locus; straight lines in various forms; circles and conic sections (parabola, ellipse, hyperbola) in standard forms, and conditions for tangency.
12 3D Geometry +
Coordinates of a point in space and distance between two points; section formula, direction ratios and cosines; angle between lines; skew lines and shortest distance; equations of lines and planes in different forms.
13 Vector Algebra +
Scalars and vectors; addition, subtraction and multiplication of vectors; components in 2D and 3D; scalar and vector products and triple products.
14 Statistics and Probability +
Measures of dispersion — mean, mode, median, variance, standard deviation and mean deviation; probability of events, addition and multiplication theorems, Bayes’ theorem, Bernoulli trials and binomial distribution.
15 Trigonometry +
Trigonometric identities and equations; trigonometric functions; inverse trigonometric functions and their properties; heights and distances.
16 Mathematical Reasoning +
Statements and logical operations — and, or, implies, implied by, if and only if; tautology, contradiction, converse and contrapositive.