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MATHEMATICS UNIT 1: SETS, RELATIONS AND FUNCTIONS:

Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relations, type of relations, equivalence relations, functions; one-one, into and onto functions, the composition of functions.

UNIT 2: COMPLEX NUMBERS AND QUADRATIC EQUATIONS:

Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a + ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, Quadratic equations in real and complex number systems and their solutions; Relations between roots and coefficients, nature of roots, the formation of quadratic equations with given roots.

UNIT3: MATRICES AND DETERMINANTS:

Matrices, algebra of matrices, type of matrices, determinants and matrices of order two and three, evaluation of determinants, area of triangles using determinants; Adjoint and inverse of a square matrix; Test of consistency and solution of simultaneous linear equations in two or three variables using matrices.

UNIT 4: PERMUTATIONS AND COMBINATIONS:

The fundamental principle of counting, permutations and combinations; Meaning of P(n, r) and C(n, r). Simple applications.

UNIT 5: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:

Binomial theorem for a positive integral index, general term and middle term and simple applications.

UNIT 6: SEQUENCE AND SERIES:

Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers, Relation between A.M and G.M.

UNIT 7: LIMIT, CONTINUITY AND DIFFERENTIABILITY:

Real–valued functions, algebra of functions; polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two, Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions,

Maxima and minima of functions of one variable.

UNIT 8: INTEGRAL CALCULAS:

Integral as an anti-derivative, Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Evaluation of simple integrals of the type

UNIT 9: DIFFRENTIAL EQUATIONS :

Ordinary differential equations, their order and degree, the solution of differential equation by the method of separation of variables, solution of a homogeneous and linear differential equation of the type 𝑑

𝑑 + � � � = �(�).

UNIT 10: CO-ORDINATE GEOMETRY :

Cartesian system of rectangular coordinates in a plane, distance formula, sections formula, locus and its equation, the slope of a line, parallel and perpendicular lines, intercepts of a line on the co-ordinate axis. Straight line: Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, the distance of a point form a line, co-ordinate of the centroid, orthocentre and circumcentre of a triangle. Circle, conic sections: A standard form of equations of a circle, the general form of the equation of a circle, its radius and centre, equation of a circle when the endpoints of a diameter are given, points of intersection of a line and a circle with the centre at the origin and sections of conics, equations of conic sections (parabola, ellipse and hyperbola) in standard forms.

UNIT 11: THREE DIMENSIONAL GEOMETRY :

Coordinates of a point in space, the distance between two points, sectionformula, direction ratios and direction cosines and the angle between two intersecting lines. Equation of a line; Skew lines, the shortest distance between them and its equation.

UNIT 12: VECTOR ALGEBRA :

Vectors and scalars, the addition of vectors, components of a vector in two dimensions and three-dimensional spaces, scalar and vector products.

UNIT 13: STATISTICS AND PROBABILITY :

Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data, calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variable.

UNIT 14: TRIGONOMETRY :

Trigonometrical identities and trigonometrical functions, inverse trigonometrical functions their properties.

Weekly Test, Monthly Test

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1. Real Numbers

1.1 Introduction

1.2 The Fundamental Theorem of Arithmetic

1.3 Revisiting Irrational Numbers

1.4 Summary

2. Polynomials

2.1 Introduction

2.2 Geometrical Meaning of the Zeroes of a Polynomial

2.3 Relationship between Zeroes and Coefficients of a Polynomial

2.4 Summary

3. Pair of Linear Equations in Two Variables

3.1 Introduction

3.2 Graphical Method of Solution of a Pair of Linear Equations

3.3 Algebraic Methods of Solving a Pair of Linear Equations

3.3.1 Substitution Method

3.3.2 Elimination Method

3.4 Summary

4. Quadratic Equations

4.1 Introduction

4.2 Quadratic Equations

4.3 Solution of a Quadratic Equation by Factorisation

4.4 Nature of Roots

4.5 Summary

5. Arithmetic Progressions

5.1 Introduction

5.2 Arithmetic Progressions

5.3 nth Term of an AP

5.4 Sum of First n Terms of an AP

5.5 Summary

6. Triangles

6.1 Introduction

6.2 Similar Figures

6.3 Similarity of Triangles

6.4 Criteria for Similarity of Triangles

6.5 Summary

7. Coordinate Geometry

7.1 Introduction

7.2 Distance Formula

7.3 Section Formula

7.4 Summary

8. Introduction to Trigonometry

8.1 Introduction

8.2 Trigonometric Ratios

8.3 Trigonometric Ratios of Some Specific Angles

8.4 Trigonometric Identities

8.5 Summary

9. Some Applications of Trigonometry

9.1 Heights and Distances

9.2 Summary

10. Circles

10.1 Introduction

10.2 Tangent to a Circle

10.3 Number of Tangents from a Point on a Circle

10.4 Summary

11. Areas Related to Circles

11.1 Areas of Sector and Segment of a Circle

11.2 Summary

12. Surface Areas and Volumes

12.1 Introduction

12.2 Surface Area of a Combination of Solids

12.3 Volume of a Combination of Solids

12.4 Summary

13. Statistics

13.1 Introduction

13.2 Mean of Grouped Data

13.3 Mode of Grouped Data

13.4 Median of Grouped Data

13.5 Summary

14. Probability

14.1 Probability — A Theoretical Approach

14.2 Summary

Weekly test, Assignments

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The NDA Maths Foundation Online Course by Aditya Khaneda is a structured, goal-oriented preparation program designed for students aiming to crack the NDA (National Defence Academy) examination with a strong score in Mathematics. This course is built to take students from zero level to advanced level, ensuring complete syllabus coverage, deep concept clarity, and extensive exam-oriented practice.

Mathematics plays a decisive role in the NDA written exam, and achieving a 300–400+ score requires not just formula memorisation, but a solid understanding of concepts, speed, accuracy, and familiarity with NDA-style questions. This course focuses on all these aspects through systematic teaching, regular practice, and continuous assessment.

The batch is ideal for school students (Classes 6–10), NDA foundation aspirants, and serious NDA candidates who want disciplined preparation with a clear roadmap and consistent mentoring.

📘 What Students Will Learn (Complete NDA Maths Syllabus)

✔ Algebra

Basic algebraic operations
Polynomials, factorisation & identities
Quadratic equations
Sequences & series
Logarithms
PYQs with concept-wise explanation
Short tricks for fast problem-solving

✔ Trigonometry

Trigonometric ratios & identities
Trigonometric equations
Heights & distances
Graph-based understanding
NDA-focused question practice

✔ Coordinate Geometry

Straight lines
Distance & section formula
Circle basics
Analytic geometry concepts
Application-based questions

✔ Calculus (Foundational Level)

Limits (basic understanding)
Differentiation (formulas & applications)
Integration (basic techniques & applications)

This section is taught carefully to ensure clarity for first-time learners.

✔ Vector & 3D Geometry

Vector algebra
Dot & cross product
Direction ratios & cosines
Lines & planes in 3D
Visualization-based problem solving

✔ Matrices & Determinants

Matrix operations
Determinants
Adjoint & inverse
System of linear equations
NDA-standard questions

✔ Probability & Statistics

Probability basics
Events & outcomes
Mean, median & mode
Statistical analysis for NDA
Practical problem-solving approach

✔ Mensuration & Geometry

2D & 3D mensuration
Surface area & volume
Geometry theorems & applications
Formula-based and concept-based questions

🎯 Teaching Method

Aditya Khaneda follows a concept-first, exam-oriented teaching strategy, ensuring students gain both understanding and speed:

Live interactive online classes
Step-by-step explanation from basics to advanced level
NDA-style question practice after every topic
Previous Year Question (PYQ) detailed solutions
Daily practice sheets & homework
Weekly tests & full-length mock tests
Shortcut tricks for faster calculations
Dedicated doubt-solving sessions
Continuous performance analysis & feedback

The course is structured to build confidence gradually and steadily.

👨‍🏫 Why This Tutor – Aditya Khaneda

Students choose Aditya Khaneda for his:

Strong command over NDA Maths syllabus
Ability to teach complex topics in simple language
Logical and disciplined teaching approach
Focus on concept clarity and exam strategy
Regular motivation and guidance for defence aspirants

His aim is not just to complete the syllabus, but to make students exam-ready, confident, and accurate.

🎓 Who Should Enroll

NDA aspirants (current & future attempts)
Students preparing for NDA foundation
Class 6–10 students strengthening Maths basics
Learners targeting high scores in NDA Maths
Students who want structured preparation from zero level
Aspirants looking for disciplined online coaching

✨ Benefits / Outcomes

By the end of this course, students will:

Complete the full NDA Maths syllabus with clarity
Improve calculation speed and accuracy
Gain confidence in solving NDA-level problems
Perform strongly in PYQs and mock tests
Develop strong analytical and logical thinking
Move closer to achieving a 300–400+ score in NDA Maths

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Aditya Khaneda is an experienced Mathematics and Physics tutor with 5 years of teaching experience, offering both online and offline classes. He specializes in school-level Mathematics and Physics, IIT Foundation Maths, and NDA Mathematics, helping students build strong fundamentals and analytical skills through a structured and exam-oriented approach.

Qualifications Summary

Bachelor of Technology / Bachelor of Engineering (B.Tech / B.E.)

His engineering background supports a logical, problem-solving-based teaching style that helps students understand concepts clearly and apply them effectively.

Experience Overview

With 5 years of experience, Aditya Khaneda has taught students from Grades 6 to 10, Class 11, and foundation-level competitive exam aspirants. He has guided learners in Mathematics, Statistics, Probability, and Physics, focusing on clarity, accuracy, and exam preparedness.

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The JEE Foundation Mathematics Program, taught by Saranya O, is designed for school students who want to build a strong conceptual base for future engineering entrance exams such as JEE Main, JEE Advanced, BITSAT, and other competitive mathematics assessments.
The course provides systematic coverage of essential mathematical concepts including Algebra, Trigonometry, Coordinate Geometry, Calculus, Vectors, 3D Geometry, Probability, and Statistics—topics that form the backbone of higher-level mathematics.
With a focus on clarity, step-by-step problem-solving, and conceptual depth, Saranya ensures that students gain the confidence and skills required to tackle advanced mathematical thinking in the coming years.
What Students Will Learn
The course includes complete foundational coverage of mathematics topics frequently used in JEE preparation.
1. Algebra – Core Foundation Skills
- Real numbers & inequalities
- Polynomials & algebraic identities
- Quadratic equations
- Sequences & series
- Logarithms
- Functions & basic transformations
- Fundamental logical reasoning
Outcome:
✔ Strong algebraic manipulation skills
✔ Ability to handle complex expressions & identities
2. Trigonometry – Essential JEE Building Block
- Trigonometric ratios & identities
- Heights & distances
- Trigonometric equations
- Properties of triangles
- Inverse trigonometry basics
Outcome:
✔ Clear understanding of identities and transformations
✔ Enhanced accuracy in trigonometric calculations
3. Coordinate Geometry – Visualization & Analytical Thinking
- Straight lines
- Distance, section & midpoint formulae
- Circles
- Conic sections (fundamentals)
- Graph interpretation
Outcome:
✔ Improved geometric visualization
✔ Ability to convert geometry into algebraic solutions
4. Calculus (Foundation Level)
- Concept of limits
- Introduction to derivatives
- Basic differentiation rules
- Rate of change
- Simple application problems
Outcome:
✔ Prepared for advanced calculus in Class 11–12
✔ Understanding of the idea of change & continuity
5. Vectors & 3D Geometry
- Scalars vs vectors
- Vector operations: addition, dot product, cross product
- Direction ratios & cosines
- 3D geometry basics (lines & planes)
Outcome:
✔ Strengthened visualization for 3D mathematical structures
✔ Early preparation for high-scoring JEE topics
6. Probability & Statistics
- Fundamental counting principle
- Permutations & combinations (basics)
- Introduction to probability
- Mean, median, mode
- Basic data interpretation
Outcome:
✔ Logical thinking and problem-solving
✔ Conceptual strength for future competitive exams
Teaching Method
Saranya’s approach focuses on clarity, structured learning, and active practice:
- Concept-first, problem-after teaching style
- Step-by-step breakdown of difficult topics
- Regular practice worksheets
- Weekly assignments to reinforce learning
- Doubt-solving sessions in every class
- Interactive online sessions
- Training in exam-style problem-solving
- Gradual progression to more complex questions
Her teaching style ensures students develop both conceptual understanding and practical problem-solving ability, making the transition to JEE-level difficulty much smoother.
Why This Tutor
- Skilled in A & AS Level Mathematics and strong in foundational concepts
- Experienced in guiding students toward competitive-level mathematics
- Strong clarity in explaining tough concepts in simple form
- Encourages logical reasoning and independent thinking
- Patient, supportive, and student-friendly
Benefits / Outcomes
- Strong mathematical foundation from early classes
- Improved logical reasoning & analytical skills
- Confidence in tackling school and competitive exam problems
- Smooth transition into Class 11–12 JEE-level rigor
- Better performance in school exams, Olympiads & aptitude tests
This program is ideal for students who want to start preparing early and build the confidence needed for future JEE success.

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Saranya O is a skilled online Mathematics tutor with 6 years of teaching experience across CBSE, IIT-level Mathematics, JEE Foundation, and A & AS Level Mathematics. With strong academic qualifications and a structured teaching approach, she helps students build confidence in Mathematics through clear explanations, regular practice, and exam-oriented preparation. Her online classes are suitable for students across India seeking consistent and concept-driven Maths guidance.

Qualifications Summary

M.Phil
M.Sc.
B.Tech / B.E.
Polytechnic Diploma
Diploma

Her diverse academic background enables her to explain mathematical concepts logically and adapt explanations to different learning levels.

Experience Overview

Saranya O brings 6 years of experience teaching Mathematics to school students and competitive exam aspirants. She has guided learners from Class 8 to Class 12, supported JEE Foundation and IIT Maths preparation, and taught A & AS Level Mathematics, focusing on conceptual clarity and problem-solving accuracy.

Subjects Taught

Mathematics
CBSE Mathematics
Class 8 Mathematics
Class 9 Mathematics
Class 10 Mathematics
Class 10 CBSE Mathematics
Class 11 Mathematics
Class 12 Mathematics
IIT Maths
JEE Foundation Mathematics
Vector Algebra and Integral Calculus
Functions, Statistics, and Trigonometry (FST)
Statistics and Probability (CBSE Mathematics)
A & AS Level Mathematics

(All topics are taught as per respective board and exam syllabi.)

Teaching Languages

English
Tamil
Telugu

Teaching Approach

Saranya follows a student-friendly, structured, and exam-focused teaching method:

Concept-by-concept explanation with real-time examples
Stepwise problem-solving techniques
Focus on CBSE, IIT, and A & AS Level exam patterns
Regular practice, revision, and doubt-clearing sessions
Personalized attention in both batch and one-to-one online classes

Her approach helps students strengthen fundamentals and improve performance in both school and competitive exams.

Mode-Based Details (Online Learning)

Mode: Online
Batch Type: Individual and batch classes
Reach: Students across India

Online sessions offer flexibility and structured learning for students at different academic levels.

Address & Locality

Online Tutor – Available for students across India

Why Students Should Learn from Saranya O

6 years of Mathematics teaching experience
Strong academic and technical qualifications
Expertise across CBSE, IIT, JEE Foundation, and A & AS Level Maths
Multilingual teaching in English, Tamil, and Telugu
Clear, structured, and exam-oriented explanations
Supportive and student-focused online learning environment

Saranya O is a reliable choice for students aiming to build strong Mathematics fundamentals and exam confidence through guided online learning.

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Build a strong foundation in Mathematics and excel in both Board Exams (CBSE/NCERT) and Competitive Examinations with the guidance of Uttam Ram, a dedicated and result-oriented Mathematics tutor from Kullu, Himachal Pradesh. With years of teaching experience and a proven track record where over 90% of students have achieved excellent results, Uttam focuses on strengthening core concepts, improving accuracy, and developing smart problem-solving strategies.

This course is structured to support students from Class 6 to Class 12, covering the complete NCERT and CBSE curriculum. Whether you are preparing for school finals, board exams, olympiads, or skill-based math competitions, the classes are tailored according to your academic goals and learning pace.

Uttam’s approach emphasizes concept clarity, step-by-step explanations, and foundation building, ensuring that students never feel lost or confused at any stage of learning. His teaching philosophy is simple:
Build basics, develop confidence, and create problem-solvers who succeed in any exam.

What This Course Covers

Class 6–8 Mathematics

Number System & Whole Numbers
Fractions, Decimals & Percentages
Geometry & Mensuration
Ratio & Proportion
Algebra Basics
Practical Geometry
Data Handling & Graphs

Class 9 Mathematics

Number Systems
Polynomials
Linear Equations
Coordinate Geometry
Geometry: Triangles, Circles
Surface Area & Volume
Statistics & Probability
Introduction to Trigonometry

Class 10 Mathematics

Real Numbers
Polynomials
Quadratic Equations
Trigonometry (Full Syllabus)
Coordinate Geometry
Arithmetic Progressions
Circles & Constructions
Surface Area & Volume
Statistics & Probability

Class 11 Mathematics

Sets, Relations & Functions
Trigonometric Functions
Straight Lines & Conic Sections
Quadratic Expressions
Sequences & Series
Limits & Derivatives
Permutation & Combination
Probability

Class 12 Mathematics

Relations & Functions
Inverse Trigonometric Functions
Matrices & Determinants
Continuity & Differentiability
Application of Derivatives
Integrals & Applications
Differential Equations
3D Geometry
Probability

Competitive & Olympiad Preparation

Maths Olympiad Training
Speed-building techniques
Shortcuts & mental math strategies
Problem-solving for competitive exams
Test series for exam readiness

Teaching Mode (Both Online & Offline)

Students can choose between Live Online Classes or Offline Coaching in Kullu, Himachal Pradesh.

Why Learn Mathematics from Uttam Ram?

Expert in CBSE & NCERT syllabus (Class 6–12)
90%+ success rate among students
Focus on strong basics & long-term understanding
Concept-based and exam-oriented teaching
Personalized guidance according to student level
Doubt-clearing sessions after every class
Regular tests & practice worksheets

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📘 What Students Will Learn (Complete NDA Maths Syllabus)

✔ Algebra

✔ Trigonometry

✔ Coordinate Geometry

✔ Calculus (Foundational Level)

✔ Vector & 3D Geometry

✔ Matrices & Determinants

✔ Probability & Statistics

✔ Mensuration & Geometry

🎯 Teaching Method

👨‍🏫 Why This Tutor – Aditya Khaneda

🎓 Who Should Enroll

✨ Benefits / Outcomes

Qualifications Summary

Experience Overview

What Students Will Learn

1. Algebra – Core Foundation Skills

2. Trigonometry – Essential JEE Building Block

3. Coordinate Geometry – Visualization & Analytical Thinking

4. Calculus (Foundation Level)

5. Vectors & 3D Geometry

6. Probability & Statistics

Teaching Method

Why This Tutor

Benefits / Outcomes

Qualifications Summary

Experience Overview

Subjects Taught

Teaching Languages

Teaching Approach

Mode-Based Details (Online Learning)

Address & Locality

Why Students Should Learn from Saranya O

What This Course Covers

Class 6–8 Mathematics

Class 9 Mathematics

Class 10 Mathematics

Class 11 Mathematics

Class 12 Mathematics

Competitive & Olympiad Preparation

Teaching Mode (Both Online & Offline)

Why Learn Mathematics from Uttam Ram?

Expert statistics and probability Tutors in Vijayanagaram

No Statistics and probability Tutors Found in Vijayanagaram