Math Tutoring for Grade 12
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XII
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Affordable Math Test Preperation Programs
MLK Home and Online Tutoring Service 's Math Refresher course is designed to build a strong foundation in the basic math skills essential for success on the following tests:
Topics Covered by our Math Home Tutoring Program:
MATHEMATICS SYLLABUS FOR Grade XII
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 branches
 Graphs of inverse trigonometric functions
 Elementary properties of inverse trigonometric functions
UNIT II: ALGEBRA
Matrices
 Concept, notation, order, equality
 types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices
 Addition, multiplication and scalar multiplication of matrices
 simple properties of addition, multiplication and scalar multiplication
 Noncommutativity of multiplication of matrices and existence of nonzero 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 × 3 matrices)
 properties of determinants, minors, cofactors
 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 function
 Concepts of exponential, logarithmic functions
 Derivatives of loge x and ex
 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 interpretations
Applications of Derivatives
 Applications of derivatives: Rate of change
 increasing/decreasing functions
 tangents and normals
 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 reallife situations)
Integrals
 Integration as inverse process of differentiation
 Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals to be evaluated
 Definite integrals as a limit of a sum
 Fundamental Theorem of Calculus (without proof)
 Basic properties of definite integrals and evaluation of definite integrals
Applications of the Integrals
 Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses(in standard form only)
 area between the two above said curves (the region should be cleraly 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
 homogeneous differential equations of first order and first degree
 Solutions of linear differential equations
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UNIT IV: VECTORS AND THREEDIMENSIONAL GEOMETRY
Vectors
 Vectors and scalars
 magnitude and direction of a vector
 Direction cosines/ratios of vectors
 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
 Scalar (dot) product of vectors
 projection of a vector on a line
 Vector (cross) product of vectors
 scalar triple product
Threedimensional Geometry
 Direction cosines/ratios of a line joining two points
 Cartesian 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
 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
 feasible and infeasible solutions
 optimal feasible solutions (up to three nontrivial constrains)
Unit VI: Probability
 Multiplications theorem on probability
 Conditional probability
 independent events
 total probability
 Baye’s theorem
 Random variable and its probability distribution
 mean and variance of haphazard variable
 Repeated independent (Bernoulli) trials and Binomial distribution
