This course is designed to build a strong foundation in Trigonometry and Calculus from the absolute basics. It is suitable for students who want to start from zero and understand the core concepts clearly before moving to advanced problem-solving.

Course Duration

Total Duration: 2 Months
Subjects Covered:

• Trigonometry

• Calculus

What Student Will Learn

Month 1: Trigonometry Foundation

Week 1: Basics of Mathematics Needed for Trigonometry

• Introduction to basic algebra revision

• Understanding numbers, fractions, and decimals

• Basic equations and simplification

• Powers, roots, and square roots

• Understanding ratios and proportions

• Coordinate basics

• Introduction to angles

• Types of angles

• Degree and radian basics

• Positive and negative angles

Week 2: Introduction to Trigonometry

• What is trigonometry

• Why trigonometry is used

• Real-life applications of trigonometry

• Right triangle basics

• Sides of a triangle

• Hypotenuse, base, perpendicular

• Introduction to trigonometric ratios

• Sine, cosine, tangent

• Cosecant, secant, cotangent

• Understanding formulas using triangles

• Basic value finding

Week 3: Trigonometric Ratios and Standard Values

• Trigonometric table basics

• Standard angles

• Values of sin, cos, tan

• Values of cosec, sec, cot

• Complementary angles

• Relationship between trigonometric ratios

• Important identities

• Practice on basic value-based questions

• Solving simple trigonometric expressions

Week 4: Trigonometric Identities and Basic Applications

• Fundamental identities

• Proving simple identities

• Height and distance basics

• Application of trigonometry in triangles

• Word problems on heights and distances

• Angle of elevation

• Angle of depression

• Basic problem-solving practice

• Revision of full trigonometry basics

• Weekly test and doubt-solving session

Month 2: Calculus Foundation

Week 5: Pre-Calculus Basics

• What is calculus

• Why calculus is important

• Understanding functions

• Types of functions

• Graph basics

• Linear functions

• Quadratic functions

• Polynomial basics

• Concept of slope

• Concept of rate of change

• Introduction to limits idea

Week 6: Introduction to Limits and Continuity

• Basic idea of limits

• Understanding function behavior

• Left-hand limit and right-hand limit

• Simple limit evaluation

• Limit laws basics

• Introduction to continuity

• Continuous and discontinuous functions

• Basic examples of continuity

• Practice questions on limits and continuity

Week 7: Introduction to Derivatives

• Meaning of derivative

• Derivative as rate of change

• Derivative as slope of tangent

• Basic derivative formula idea

• Derivatives of simple functions

• Derivative of constants

• Derivative of x

• Derivative of x², x³

• Derivative of polynomial functions

• Introduction to derivative rules

• Basic applications of derivatives

Week 8: Introduction to Integration

• What is integration

• Integration as reverse of differentiation

• Basic integration formulas

• Integration of constants

• Integration of powers

• Simple polynomial integration

• Introduction to indefinite integration

• Introduction to area concept

• Relation between derivative and integration

• Final revision of calculus basics

• Final assessment and practice session

Structured Topic-Wise Content

Part 1: Trigonometry

• Basics of angles

• Degree and radian

• Right triangle basics

• Trigonometric ratios

• Standard trigonometric values

• Trigonometric identities

• Complementary angle relations

• Basic trigonometric equations

• Heights and distances

• Simple real-life applications

Part 2: Calculus

• Introduction to functions

• Graph basics

• Slope and rate of change

• Limits

• Continuity

• Derivatives

• Basic differentiation rules

• Applications of derivatives

• Integration basics

• Basic integration formulas

Teaching Approach

• Start from very basic definitions

• Explain each concept with simple examples

• Solve easy problems first

• Move from theory to practice gradually

• Weekly revision

• Weekly test for concept clarity

• Focus on formula understanding, not only memorization

• Doubt-solving in every class

• Practice sheets after each topic

Suggested Class Flow

For each class:

• Concept explanation

• Formula discussion

• Simple examples

• Practice questions

• Homework

• Quick revision of previous topic

Learning Outcomes

By the end of this 2-month course, students will be able to:

• Understand the basics of trigonometry

• Solve standard trigonometric value questions

• Apply identities in simple problems

• Solve height and distance questions

• Understand the meaning of calculus

• Solve basic limits questions

• Understand derivatives from the foundation level

• Perform basic differentiation

• Understand integration as the reverse process of derivatives

• Build confidence in 10th to 12th standard mathematics basics