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CBSE 10 Mathematics
Explore and master the fundamentals of CBSE 10 Mathematics
You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.Chapter 1
REAL NUMBERS
This chapter explores real numbers, focusing on the Fundamental Theorem of Arithmetic and its implications. It establishes that every composite number can be uniquely factored into prime numbers and discusses various applications of this theorem, including the proof of the irrationality of certain numbers. The chapter concludes with exercises and activities designed to reinforce understanding of these concepts.
Chapter 2
POLYNOMIALS
Polynomials are essential mathematical expressions characterized by their degrees. This chapter explores the definitions, types, and geometric interpretations of polynomials, particularly focusing on their zeroes and the relationship between zeroes and coefficients. It also discusses the division algorithm for polynomials and highlights key concepts through various examples.
Chapter 3
PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Exploration of pair of linear equations in two variables offers insights into graphical and algebraic methods for finding solutions. Key concepts include identifying consistent, inconsistent, and dependent systems of equations while analyzing their graphical representations. Various mathematical representations and methods to approach these equations are emphasized throughout the chapter.
Chapter 4
QUADRATIC EQUATIONS
The chapter delves into quadratic equations, exploring their forms, roots, and various methods of solving them. It illustrates real-life applications of quadratic equations, enriches the understanding of their properties, and highlights the significance of the discriminant in determining the nature of roots. A series of exercises and activities help in consolidating the concepts explained.
Chapter 5
ARITHMETIC PROGRESSIONS
This chapter introduces arithmetic progressions (AP), providing insights into their structure and properties. Key concepts include the definition of AP, its common difference, and how to derive the nth term and the sum of the first n terms. Practical examples and exercises illustrate the application of these concepts in various real-life scenarios.
Chapter 6
Triangles
The chapter discusses similarity in triangles, establishing fundamental criteria for determining when two figures are similar, particularly focusing on triangles. It highlights the importance of corresponding angles and side ratios while also applying these concepts in various practical scenarios, such as indirect measurements. Additionally, the chapter introduces several theorems and activities to facilitate understanding of these concepts.
Chapter 7
COORDINATE GEOMETRY
This chapter explores the fundamentals of coordinate geometry, focusing primarily on the distance between points and the section formula for dividing line segments. It emphasizes the relationship between algebra and geometry through various examples and concepts, such as forming triangles and determining collinearity among points. The introduction of key formulas and the exploration of real-life applications exemplify the significance of coordinate geometry in numerous fields.
Chapter 8
INTRODUCTION TO TRIGONOMETRY
Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. The chapter introduces trigonometric ratios and identities, discussing the significance of sine, cosine, tangent, and their reciprocals. Additionally, it explores the values of trigonometric functions for specific angles and various trigonometric identities.
Chapter 9
Some Applications of Trigonometry
Trigonometry plays a vital role in determining heights and distances in various real-life applications. The chapter introduces concepts like line of sight, angles of elevation, and angles of depression, providing a foundation for solving practical problems using trigonometric ratios. Through several examples and exercises, the chapter illustrates how these concepts can be applied effectively to calculate unknown heights and distances.
Chapter 10
CIRCLES
This chapter explores the properties and characteristics of tangents to circles, defining tangents as lines that touch the circle at a single point. It establishes that the tangent is perpendicular to the radius at the point of contact and examines the conditions under which tangents can be drawn from points both inside and outside the circle. Various activities and examples illustrate these concepts and highlight the equal lengths of tangents from an external point.
Chapter 11
AREAS RELATED TO CIRCLES
The chapter covers the concepts of sectors and segments of a circle, including the formulas needed to calculate their areas and the lengths of arcs. It provides detailed explanations of how to derive the area of a sector based on its angle and radius, and also discusses the relationship between the areas of segments and their corresponding triangles. Various examples reinforce the application of these concepts in solving problems relevant to circles.
Chapter 12
Surface Areas and Volumes
The chapter provides insights on surface areas and volumes of various solids, particularly combinations of basic shapes such as cubes, cylinders, cones, and hemispheres. It emphasizes methods to calculate the surface areas and volumes efficiently by breaking compounds into simpler components. Several real-life applications of these geometric principles are demonstrated through examples and exercises.
Chapter 13
Statistics
This chapter covers the extension of measures of central tendency, including mean, median, and mode, from ungrouped to grouped data. It introduces methods for calculating mean, including direct, assumed mean, and step-deviation methods, alongside strategies for finding mode and median in grouped data. The chapter concludes with various exercises and activities that reinforce these statistical concepts.
Chapter 14
PROBABILITY
The chapter introduces the concept of probability, focusing on theoretical probability and empirical probability. It explains the importance of equally likely outcomes and provides various examples to illustrate how to calculate the probability of different events, including impossible and certain events. The chapter culminates in exercises that test the understanding of probability through real-world scenarios.