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Class 10 Mathematics: Concepts and Examples
Chapter 1 Real Numbers
This chapter explores the number system, focusing on real numbers, rational and irrational numbers, and their properties. Students also learn about Euclid’s division lemma, the Fundamental Theorem of Arithmetic, and how to represent real numbers on the number line.
Chapter 2 Polynomials
Students learn about polynomials, their degree, types, and operations like addition, subtraction, and multiplication. The chapter also covers the factorization of polynomials, roots of a polynomial, and the Remainder and Factor Theorems.
Chapter 3 Pair of Linear Equations in Two Variables
This chapter introduces systems of linear equations in two variables. Students learn how to solve these systems using various methods such as substitution, elimination, and graphical methods.
Chapter 4 Quadratic Equations
The chapter focuses on solving quadratic equations, which are equations of the form ax2 + bx + c = 0. Students learn methods like factorization, completing the square, and using the quadratic formula.
Chapter 5 Arithmetic Progressions
Students learn about sequences of numbers in which the difference between consecutive terms is constant. The chapter covers the general term of an arithmetic progression (AP), the sum of the first nnn terms, and the applications of AP in solving real-life problems.
Chapter 6 Triangles
This chapter revisits the properties of triangles and explores important theorems related to triangle similarity, congruence, and properties of special types of triangles (like right-angled triangles). Theorems such as Pythagoras' Theorem are also introduced.
Chapter 7 Coordinate Geometry
Students explore the Cartesian coordinate system further, learning how to find the distance between two points and the midpoint of a line segment. The chapter also covers the equation of a line in different forms, including the slope-intercept form.
Chapter 8 Introduction to Trigonometry
This chapter introduces students to trigonometric ratios like sine, cosine, and tangent, and their applications. It covers right-angled triangles, where these ratios are defined, and students also learn to solve basic trigonometric problems.
Chapter 9 Some Applications of Trigonometry
Students learn to apply trigonometric ratios to solve problems related to heights and distances, such as finding the height of a tower or the distance between two points.
Chapter 10 Circles
The chapter covers the properties of circles, including tangents, secants, and chords. Students also learn the angle subtended by a chord at the center and the cyclic properties of certain quadrilaterals.
Chapter 11 Constructions
Students learn geometric constructions involving circles, triangles, and other polygons. This includes constructing tangents to a circle, constructing a triangle given certain conditions, and the construction of special angles.
Chapter 12 Areas Related to Circles
This chapter focuses on the calculation of the area and perimeter of circles, sectors, and segments. It includes real-life applications involving areas related to circular shapes.
Chapter 13 Surface Areas and Volumes
Students learn to calculate the surface area and volume of various 3D objects such as cubes, cuboids, spheres, cones, and cylinders. The chapter includes formulas for each shape and their real-world applications.
Chapter 14 Statistics
This chapter deals with the collection, organization, and representation of data. Students learn about measures of central tendency (mean, median, mode) and how to interpret and analyze data using bar graphs, histograms, and cumulative frequency distributions.
Chapter 15 Probability
The probability chapter introduces the fundamental concepts of probability, such as favorable outcomes and total outcomes. Students learn to calculate the probability of an event and its applications in different scenarios.