CBSE Class 10 Maths Notes
CBSE Class 10 Mathematics Concepts, based on the latest syllabus for Class 10 Boards helps to understand all the concepts of class 10 maths chapter-wise. Notes provided by GeeksforGeeks comprise of all the formulae, theorems, concepts, proofs descriptions, definitions, graphs, that a student needs to practice and score good marks in their board examinations.
Chapter 1: Real Numbers
The chapter Real numbers include both irrational and rational numbers with all natural numbers, whole numbers, integers, etc and discuss their characteristics.
- Euclid’s Division Algorithm
- Fundamental Theorem of Arithmetic
- HCF and LCM
- Decimal Expansion of Rational Numbers
Chapter 2: Polynomials
Polynomials are algebraic expressions that consist of coefficients and variables or indeterminate. An arithmetic operation such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable can be performed on polynomials.
- Geometrical meaning of the Zeroes of polynomial
- Relationship between Zeroes and coefficients of a polynomial
- Division Algorithm for polynomials
- Division Algorithm Problems and Solutions
Chapter 3: Pair of Linear Equations in Two Variables
An equation of the form ax+by+c, where a, b and c are real numbers and a, b are not equal to zero, is termed as the linear equation in two variables. However, in a pair of linear equations in two variables, there exist two such equations whose solution is a point on the line denoting the equation.
- Pair of Linear Equations in Two Variables
- Number of Solutions to a System of Equations Algebraically
- Graphical methods of Solving a Pair of Linear Equations
- Algebraic methods of Solving a Pair of Linear Equations
- Equation Reducible to a Pair of linear equations in two variables
Chapter 4: Quadratic Equations
The degree 2 polynomial equations in one variable are called the Quadratic equations. The general form of a quadratic equation is ax2 + bx + c where a, b, c, ∈ R and a ≠ 0, where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of the complete equation.
- Quadratic Equations
- Solution of a Quadratic equation by different methods
- Roots of a Quadratic Equation
Chapter 5: Arithmetic Progressions
The arithmetic progression is explained as the sequence of numbers where the difference between any two subsequent numbers is a constant.
Chapter 6: Triangles
Geometrically, a triangle is defined as a three-sided polygon consist of three edges and three vertices. The most important and applied property of a triangle is its Angle sum property which means the sum of the internal angles of a triangle is equal to 180 degrees only.
- Construction of Similar Triangles
- Similar Triangles
- Pythagoras Theorem and its Converse
- Thales’s Theorem
- Criteria for Similarity of Triangles
Chapter 7: Coordinate Geometry
Coordinate Geometry is defined as the link between geometry and algebra using graphs along with the curves and lines. In this way, it provides geometric aspects in Algebra and leads to solve geometric problems.
Chapter 8: Introduction to Trigonometry
Trigonometry can be defined as calculations including in triangles to study its lengths, heights and angles. Trigonometry and its functions have an enormous number of uses in our daily life.
- Introduction to Trigonometric Ratios of a Triangle
- Trigonometric Ratios of Some Specific Angles
- Reciprocal of Trigonometric Ratios
- Trigonometric Identities
- Applications of Trigonometry
Chapter 9: Some Applications of Trigonometry
Trigonometry has a lot of practical applications in our real-life. This part of geometry discusses the line of sight, angle of deviation, angle of elevation, and angle of depression. Using trigonometry and trigonometric ratios the height of a building, or a mountain, from a viewpoint and the elevation angle can be determined easily.
Chapter 10: Circles
A circle is a geometrical shape that is defined as the locus of points that move in a plane so that its distance from a fixed point is always constant. This fixed point is the Centre of the circle while the fixed distance from it is called the radius of the circle.
- Tangent to a circle
- Tangent at any point of a circle is perpendicular to the radius through the point of contact
- Number of Tangents from a point on a circle
- Lengths of tangents drawn from an external point to a circle are equal
Chapter 11: Constructions
Construction helps to understand the approach to construct different types of triangles for different given conditions using a ruler and compass of required measurements.
Chapter 12: Areas Related to Circles
Area related to circles are the amount of space covered by a circle, which is defined in different ways. Some areas related to a circle are, area of the circle itself, Area of the sector, area of the segment, area of the triangle or parallelogram, etc located in a circle.
- Perimeter of circular figures, Areas of sector and segment of a circle & Areas of combination of plane figures
Chapter 13: Surface Areas and Volumes
Surface area and volume are the measures calculated for a three-dimensional geometrical shape like a cube, cuboid, sphere, etc. The surface area of any given object is the area occupied by the surface of the object while volume is the amount of space available in an object.
Chapter 14: Statistics
Statistics is the study of the representation, collection, interpretation, analysis, presentation, and organization of data. In other words, it is a mathematical way to collect, summarize data. The representation of data differently along with the frequency distribution.
- Step deviation Method for Finding the Mean with Examples
- Mean, Median, and Mode of a grouped data
- Cumulative Frequency Curve
Chapter 15: Probability
The Probability in this class includes basic probability theory, which is also used in the probability distribution, to learn the possibility of outcomes for a random experiment and to find the probability of a single event to occur, when the total number of possible outcomes.