Sonam
Online
About
Sonam is an online Mathematics tutor who teaches students from Class 10 to Class 12, including A Level and Further Mathematics. She focuses on explaining concepts in a clear and st...
Sonam
Online
Sonam is an online Mathematics tutor who teaches students from Class 10 to Class 12, including A Level and Further Mathematics. She focuses on explaining concepts in a clear and st...
Courses by: Sonam
Mathematics Class 12
What You Will Learn
Unit 1: Relations and Functions
Types of relations
Functions and types of functions
Composition of functions
Inverse of functions
Binary operations
Unit 2: Inverse Trigonometric Functions
Definition and properties of inverse trigonometric functions
Principal value branches
Basic identities and problem solving
Unit 3: Matrices
Types of matrices
Matrix operations (addition, multiplication)
Transpose of a matrix
Determinant of matrices
Adjoint and inverse of matrices
Solving system of linear equations using matrices
Unit 4: Determinants
Properties of determinants
Evaluation of determinants
Minors and cofactors
Applications of determinants
Area of triangle using determinants
Unit 5: Continuity and Differentiability
Continuity of functions
Differentiability
Derivatives of composite functions
Chain rule
Logarithmic differentiation
Implicit differentiation
Unit 6: Applications of Derivatives
Rate of change
Increasing and decreasing functions
Tangents and normals
Maxima and minima
Approximation
Unit 7: Integrals
Indefinite integrals
Definite integrals
Fundamental theorem of calculus
Substitution method
Integration by parts
Integration using partial fractions
Unit 8: Applications of Integrals
Area under curves
Area between two curves
Unit 9: Differential Equations
Formation of differential equations
Methods of solving differential equations
Variable separable method
Homogeneous differential equations
Unit 10: Vectors
Vector algebra
Direction cosines and ratios
Scalar (dot) product
Vector (cross) product
Applications in geometry
Unit 11: Three Dimensional Geometry
Direction cosines
Equation of line in space
Shortest distance between lines
Angle between lines
Equation of plane
Unit 12: Linear Programming
Formulation of LPP
Graphical method
Feasible region
Optimization problems
Unit 13: Probability
Conditional probability
Multiplication theorem
Bayes’ theorem
Random variables
Probability distributions
Mathematics Class 11
What You Will Learn
Unit 1: Sets
Types of sets
Subsets and power sets
Union, intersection, complement of sets
Venn diagrams
De Morgan’s Laws
Unit 2: Relations and Functions
Cartesian product of sets
Types of relations
Types of functions
Domain and range of functions
Composition of functions
Unit 3: Trigonometric Functions
Trigonometric ratios
Trigonometric identities
Trigonometric equations
Graphs of trigonometric functions
General solutions of trigonometric equations
Unit 4: Complex Numbers and Quadratic Equations
Complex numbers
Algebra of complex numbers
Modulus and conjugate
Quadratic equations and roots
Nature of roots
Unit 5: Linear Inequalities
Solution of linear inequalities
Graphical representation on number line
System of linear inequalities
Unit 6: Permutations and Combinations
Fundamental principle of counting
Permutations
Combinations
Applications in counting problems
Unit 7: Binomial Theorem
Expansion of binomial expressions
General term
Middle term
Properties of binomial coefficients
Unit 8: Sequences and Series
Arithmetic Progression (AP)
Geometric Progression (GP)
Sum of n terms
Arithmetic Mean (AM)
Applications of sequences
Unit 9: Straight Lines
Slope of a line
Various forms of equation of a line
Distance between two points
Angle between lines
Unit 10: Conic Sections
Circle
Parabola
Ellipse
Hyperbola
Standard equations and properties
Unit 11: Introduction to Three-Dimensional Geometry
Coordinate axes in space
Distance between two points in space
Section formula
Unit 12: Limits and Derivatives
Introduction to limits
Basic derivative concepts
Derivative of simple functions
Unit 13: Statistics
Measures of central tendency
Mean, median, mode
Variance and standard deviation
Unit 14: Probability
Basic probability concepts
Events and outcomes
Addition theorem of probability
Mathematics Class 10
What You Will Learn
Unit 1: Real Numbers
Euclid’s Division Lemma
Fundamental Theorem of Arithmetic
Finding HCF and LCM
Decimal expansion of rational numbers
Unit 2: Polynomials
Zeros of polynomials
Relationship between zeros and coefficients
Division algorithm for polynomials
Graphs of polynomials
Unit 3: Pair of Linear Equations in Two Variables
Graphical method of solving equations
Algebraic methods (substitution and elimination)
Consistency of linear equations
Applications in word problems
Unit 4: Quadratic Equations
Standard form of quadratic equation
Solution using factorization
Solution using quadratic formula
Nature of roots
Applications of quadratic equations
Unit 5: Arithmetic Progressions (AP)
nth term of AP
Sum of first n terms
Applications of AP in daily life
Unit 6: Triangles
Similarity of triangles
Criteria for similarity
Pythagoras theorem and its converse
Applications of similarity
Unit 7: Coordinate Geometry
Distance formula
Section formula
Area of triangle using coordinates
Unit 8: Trigonometry
Trigonometric ratios
Trigonometric identities
Heights and distances
Applications of trigonometry
Unit 9: Circles
Tangents to a circle
Properties of tangents
Number of tangents from a point
Unit 10: Constructions
Division of line segments
Construction of tangents to circles
Unit 11: Areas Related to Circles
Area of circle
Area of sectors and segments
Applications of areas
Unit 12: Surface Areas and Volumes
Surface area and volume of solids
Combination of solids
Frustum of a cone
Unit 13: Statistics
Mean, median, mode
Cumulative frequency
Graphical representation of data
Unit 14: Probability
Classical probability
Finding probability of events
Location
H. No. 45, Govt. Employees Colony, Ghari Bolni Road, Rewari, Gurgaon, Haryana
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