mathematics: analysis and approaches sl

This subject covers units such as trigonometry, geometry, algebra, differential calculus, integral calculus and, statistics and probability

Algebra covers chapters such as Sequences and Series, Exponential and Logarithmic Functions, Algebra and Function Basics and, Functions, Equations and Inequalities

Algebra

Trigonometry contains chapter Trigonometric Functions and Equations

Trigonometry

Geometry contains chapter Geometry and Trigonometry

Geometry

Statistics and Probability covers chapters such as Probability, Statistics and, Probability Distributions

Statistics and Probability

Differential Calculus covers chapters such as Differential Calculus 1 and Differential Calculus 2

Differential Calculus

Integral Calculus contains chapter Integral Calculus

Integral Calculus

Mathematics : Analysis and Approaches Standard Level Course Companion

Trigonometric Ratios of Complementary Angles

Mean Deviation, Its Merits, and Demerits

Measures of Dispersion

Mean Deviation of Ungrouped Data

Variance - Properties, Merits and Demerits

Standard Deviation - Properties, Merits and Demerits

Variance and SD for Grouped Frequency Distribution

Mean Deviation of Grouped Data

Trigonometric Ratios for the Angle of 30 Degrees

Mean of Grouped Data: Example

Exponents & Logarithms

Examples of Area of Triangles

Examples of Properties of Triangles

Napier's Analogy

Cosine Rule

Sine Rule

Properties of Triangles

Examples on Logarithms

Working Rules for Logarithms

n- Geometric Means Between Two Numbers

Inverse Function: Theorem

Inverse Function

One-one and Onto of Composition of Functions

Composite Functions: Illustration

Composition of Functions: Theorem

Composition of Functions

Types of Functions

Angle Between Two Lines

Finding N Arithmetic Means Between Two Numbers

Arithmetic Mean

Modulus Function

The Reciprocal Function

Range of a Function: Illustration

Domain, Co-Domain and Range of a Function

Concept of a Function

Venn Diagrams

Perfect Square Method to Solve Quadratic Equation

Exponents and Surds

Surface Area and Volume of Right Triangular Prism

Exponents and Powers

Interpretation of a Bar Graph

Illustration on Binomial Distribution

Binomial Distribution Problem

Example on Binomial Distribution

Bernoulli Trials and Binomial Distribution

Probability Distribution of a Random Variable

Random Variable and Probability Distribution

Introduction to Random Variable

Illustration on Conditional Probability

Problem on Conditional Probability

Area Enclosed by a Curve and a Line: Illustration

Area Under Curve: Illustration

Integration by Parts: Illustration

Integration by Parts

Integrals With Trigonometric Substitutions

Indefinite Integrals: Illustration

Properties of Indefinite Integrals

Concept of Integration

Properties of Odd Function in Definite Integral

Properties of Even Function in Definite Integral

Properties of Definite Integral - 4

Properties of Definite Integral - 3

Properties of Definite Integral - 2

Properties of Definite Integral

Definite Integral as the Limit of Sum: Proof

Definite Integration as the Limit of a Sum

Increasing Functions

Equation of a Tangent: Illustration

Slope of Tangent at a Point

Global Maxima and Minima

Second Derivative Test for Maxima and Minima

Critical Points and First Derivative Test

Higher Order Derivative

Derivative of Composite Functions - Chain Rule

IlLustration on Probability of Events

Axiomatic Definition of Probability

Mutually Exclusive Events

Differentiation of Algebraic Functions - Example

Product and Quotient Rule of Differentiation

Addition and Subtraction Rule of Differentiation

Some More Standard Derivatives

Some Standard Derivatives: Proof

Some Standard Derivatives

Physical Interpretation of Derivative

First Principle of Differentiation

Definition of Derivative

Theorem on Limits

Left-hand and Right-hand Limit

Basics of Limits

Definition of the Limit

Distance Formula in 3D: Illustration

Distance Formula in 3D

Coordinate Axes and Coordinate Planes in 3D

Slope Intercept Form of a Straight Line

Equation of a Line in Point-slope & Two Point Form

The Slope of a Straight Line

Sum of First n Natural Numbers

Introduction to Geometric Mean

Sum of n Terms of a GP When nᵗʰ Term is Given

This chapter covers topics, such as, Basics of Probability, Venn Diagrams and Operations with Events, Conditional Probability & Geometrical Application of Probability etc.

Probability

This chapter covers topics, such as, Binomial Theorem, Arithmetic Progression, Series, Geometric Progression, Basics of Sequence and Series & Applications of Arithmetic and Geometric Progressions etc.

Sequences and Series

This chapter covers topics, such as, Logarithmic Functions, Exponential Functions & Basics of Exponents etc.

Exponential and Logarithmic Functions

This chapter covers topics, such as, Differentiation Rules, Optimisation & Derivatives of Exponential and Logarithmic Functions etc.

Differential Calculus 2

This chapter covers topics, such as, Heights and Distances, Surface Area and Volume of 3-Dimensional Solids, Circum-radius and In-radius of a Regular Polygon & Solution of Triangles etc.

Geometry and Trigonometry

This chapter covers topics, such as, Measures of Central Tendency, Graphical Tools, Measures of Variability, Grouped Data, Sampling, Linear Regression, Box Plot, Shape of the Distribution & Ranking etc.

Statistics

This chapter covers topics, such as, Graphs of Trigonometric Functions, Trigonometric Equations and Identities, Angles, Circles, Arcs and Sectors & Introduction to Trigonometric Functions etc.

Trigonometric Functions and Equations

This chapter covers topics, such as, Binomial Distribution, Random Variables & Normal Distribution etc.

Probability Distributions

This chapter covers topics, such as, Quadratic Functions, Rational Function & Solution of Equations and Inequalities etc.

Functions, Equations and Inequalities

This chapter covers topics, such as, Derivative of a Function, Limits of Functions, Maxima and Minima, Monotonicity & Tangents and Normals etc.

Differential Calculus 1

This chapter covers topics, such as, Modelling Linear Motion, Methods of Integration, Area and the Definite Integral, Areas & Antiderivatives and the Indefinite Integral etc.

This chapter covers topics, such as, Equations and Formulae, Inequalities, Basics of Functions, Types of Functions, Composite Functions, Inverse Functions & Transformations of Functions etc.

Algebra and Function Basics

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