Lesson-1.1: Introduction to Algebra: Understanding Indices and Surds - Arif Sir's Science Hub

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Course Content

Chapter-1: Algebra & Functions

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Lesson-1.1: Introduction to Algebra: Understanding Indices and Surds

Lesson-1.2: Understanding Quadratics: Solving Equations and Graphing Functions

Lesson-1.3: Exploring Factorization: Techniques for Factoring Quadratics

Lesson-1.4: Solving Simultaneous Equations: Strategies and Applications

Lesson-1.5: Mastering Inequalities: Techniques for Solving Linear Inequalities

Lesson-1.6: Review and Practice: Strengthening Skills and Understanding

Lesson-1.7: Rationalizing Denominators: Methods and Uses

Lesson-1.8: Recap and Practice: Consolidating Knowledge and Skills

Lesson-1.9: Exploring Polynomials: Structure, Operations, and Applications

Lesson-1.10: Understanding Graphs and Functions: Transformations and Uses

Chapter-2. Coordinate geometry in the (x, y) plane

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Lesson-2.1: Introduction to Coordinate Geometry

Lesson-2.2: Understanding Slope: Calculating and Interpreting the Slope of a Line

Lesson-2.3: Equations of Lines: Exploring Different Forms of Linear Equations

Lesson-2.4: Finding Midpoints: Using the Midpoint Formula to Locate the Middle Point Between Two Points

Lesson-2.5: Parallel and Perpendicular Lines: Identifying and Graphing Lines with Specific Slopes

Lesson-2.6: Computing Distances: Utilizing the Distance Formula to Determine Lengths and Distances

Lesson-2.7: Plotting Circles: Understanding the Equation of a Circle and Graphing Circles on the Coordinate Plane

Lesson-2.8: Equations of Circles: Deriving Equations of Circles Based on Different Criteria

Lesson-2.9: Exploring Conic Sections: Understanding Ellipses and Hyperbolas

Lesson-2.10: Focus on Parabolas: Investigating the Characteristics and Equations of Parabolas

Lesson-2.11: Intersections of Lines and Curves: Solving Systems of Equations Graphically

Lesson-2.12: Tangents and Normals: Determining Equations of Tangent and Normal Lines to Curves

Lesson-2.13: Graphing Quadratic Functions: Understanding the Relationship Between Quadratic Functions and Parabolas

Lesson-2.14: Review and Practice: Consolidating Concepts and Skills in Coordinate Geometry

Lesson-2.15: Advanced Applications of Coordinate Geometry: Real-Life Problem-Solving Strategies

Chapter-3: Trigonometry

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Lesson-3.1: Understanding Trigonometric Ratios: Sine, Cosine, and Tangent

Lesson-3.2: Graphing Sine and Cosine Functions: Basic Characteristics and Periodicity

Lesson-3.3: Transformations of Sine and Cosine Functions: Amplitude, Period, Phase Shift, and Vertical Shift

Lesson-3.4: Graphing the Tangent Function: Characteristics and Behavior

Lesson-3.5: Transformations of the Tangent Function: Effects on Graphs

Lesson-3.6: Introduction to Reciprocal Trigonometric Functions: Cosecant, Secant, and Cotangent

Lesson-3.7: Graphing Reciprocal Trigonometric Functions: Characteristics and Behavior

Lesson-3.8: Transformations of Reciprocal Trigonometric Functions: Amplitude, Period, Phase Shift, and Vertical Shift

Lesson-3.9: Combined Graphs of Trigonometric Functions: Analyzing Interactions between Functions

Lesson-3.10: Inverse Trigonometric Functions: Graphs and Properties

Lesson-3.11: Transformations of Inverse Trigonometric Functions: Effects on Graphs

Lesson-3.12: Trigonometric Identities and Equations: Solving Equations and Simplifying Expressions

Lesson-3.13: Graphing Composite Trigonometric Functions: Analyzing Complex Functions

Lesson-3.14: Periodic Behavior and Applications: Modeling Periodic Phenomena

Lesson-3.15: Review and Practice: Consolidating Concepts and Problem-Solving Strategies

Lesson-3.16: Polar Coordinates: Introduction and Conversion from Rectangular Coordinates

Lesson-3.17: Graphing Polar Equations: Polar Functions and Their Graphs

Lesson-3.18: Conic Sections in Polar Coordinates: Understanding Ellipses, Hyperbolas, and Parabolas

Lesson-3.19: Advanced Graphing Techniques: Graphing Polar Equations with Transformations

Lesson-3.20: Advanced Applications of Trigonometry: Real-World Problem-Solving

Lesson-3.21: Trigonometric Identities: Verifying and Proving Trigonometric Equations

Lesson-3.22: Sum and Difference Formulas: Derivation and Application in Problem-Solving

Lesson-3.23: Double and Half Angle Formulas: Derivation and Application in Trigonometric Equations

Lesson-3.24: Trigonometric Equations and Inequalities: Solving Complex Equations and Inequalities

Lesson-3.25: Review and Practice: Analytical Trigonometry Problems and Applications

Lesson-3.26: Trigonometric Series: Introduction to Fourier Series and Their Applications

Lesson-3.27: Complex Numbers and Trigonometry: Understanding the Relationship

Lesson-3.28: Vectors and Trigonometry: Applications in Physics and Engineering

Lesson-3.29: Non-Euclidean Geometry and Trigonometry: Introduction to Hyperbolic Trigonometry

Lesson-3.30: Special Topics in Trigonometry: Exploration of Advanced Concepts and Research Areas

Chapter-4: Differentiation

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Lesson-4.1 : Introduction to Differentiation: Understanding the Derivative

Lesson-4.2: Limits and Continuity: The Foundation of Differentiation

Lesson-4.3: Definition of the Derivative: Computing Derivatives from First Principles

Lesson-4.4: Basic Differentiation Rules: Power Rule, Product Rule, and Quotient Rule

Lesson-4.5: Chain Rule: Computing Derivatives of Composite Functions

Lesson-4.6: Implicit Differentiation: Finding Derivatives of Implicitly Defined Functions

Lesson-4.7: Logarithmic Differentiation: Applying Logarithmic Differentiation to Complex Functions

Lesson-4.8: Differentiation of Exponential Functions: Derivatives of Exponential Functions and Their Applications

Lesson-4.9: Differentiation of Trigonometric Functions: Derivatives of Sine, Cosine, and Tangent Functions

Lesson-4.10: Differentiation of Inverse Trigonometric Functions: Derivatives of Arcsine, Arccosine, and Arctangent Functions

Lesson-4.11: Related Rates: Solving Related Rates Problems Using Differentiation

Lesson-4.12: Optimization Problems: Maximizing or Minimizing Functions Using Derivatives

Lesson-4.13: Curve Sketching: Analyzing Functions Using First and Second Derivatives

Lesson-4.14: Linear Approximation and Differentials: Estimating Function Values Using Derivatives

Lesson-4.15: Newton’s Method: Approximating Roots of Equations Using Derivatives

Lesson-4.16: Higher-Order Derivatives: Computing Second, Third, and Higher Derivatives

Lesson-4.17: Implicit Differentiation in Higher Dimensions: Differentiating Implicit Functions in Multivariable Calculus

Lesson-4.18: Parametric Differentiation: Finding Derivatives of Parametrically Defined Curves

Lesson-4.19: Taylor and Maclaurin Series: Representing Functions as Infinite Series Using Derivatives

Lesson-4.20: Advanced Applications of Differentiation: Exploring Additional Applications and Research Topics

Chapter-5: Integration

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Lesson-5.1: Introduction to Integration: Understanding the Definite and Indefinite Integrals

Lesson-5.2: Antiderivatives: Finding Functions from Their Derivatives

Lesson-5.3: Basic Integration Rules: Power Rule, Constant Rule, and Sum Rule

Lesson-5.4: Integration by Substitution: Applying the Chain Rule in Reverse

Lesson-5.5: Integration by Parts: Applying the Product Rule in Reverse

Lesson-5.6: Trigonometric Integrals: Integrating Trigonometric Functions and Their Powers

Lesson-5.7: Integration of Exponential and Logarithmic Functions: Integrating Exponential and Logarithmic Functions

Lesson-5.8: Integration of Rational Functions: Partial Fractions and Long Division

Lesson-5.9: Integration of Irrational Functions: Integration Involving Square Roots and Rationalizing Substitutions

Lesson-5.10: Area under Curves: Finding Areas Using Definite Integrals

Lesson-5.11: Volume of Revolution: Finding Volumes Using Disk and Washer Methods

Lesson-5.12: Arc Length and Surface Area: Calculating Arc Lengths and Surface Areas Using Integrals

Lesson-5.13: Improper Integrals: Evaluating Integrals with Infinite Limits or Discontinuities

Lesson-5.14: Integration in Polar Coordinates: Integrating Functions in Polar Form

Lesson-5.15: Advanced Applications of Integration: Exploring Additional Applications and Research Topics

Edexcel A Level Maths Pure 1 Revision Notes

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