uild Strong Mathematical Foundations for Class 10

Class 10 Mathematics is an important stage in a student’s academic journey because it strengthens analytical thinking and prepares learners for higher secondary studies. Topics such as algebra, geometry, trigonometry, statistics, and coordinate geometry require clear conceptual understanding along with consistent practice.

This online course is designed for students studying Class 8, Class 9, and Class 10 CBSE Mathematics. The focus is on understanding concepts thoroughly, improving problem-solving ability, and developing confidence for school examinations.

Unit 1: Number Systems

Chapter 1: Real Numbers

• The Fundamental Theorem of Arithmetic: Statements and verification through examples.

• Prime Factorisation: Finding HCF and LCM of composite numbers.

• Irrationality Proofs: Formal proofs of irrationality for \(\sqrt{2}\), \(\sqrt{3}\), and \(\sqrt{5}\).

Unit 2: Algebra

Chapter 2: Polynomials

• Geometrical Meaning of Zeros: Visualising zeros by looking at graphs of polynomials.

• Zeros and Coefficients: Relationship between the zeros and coefficients of a quadratic polynomial.

Chapter 3: Pair of Linear Equations in Two Variables

• Graphical Representation: Consistency and inconsistency of a pair of linear equations.

Algebraic Solution Methods:

• Substitution Method

• Elimination Method

• Applications: Solving simple real-world word problems based on equations.

Chapter 4: Quadratic Equations

• Standard Form: Understanding ax² + bx + c = 0 (where a ≠ 0).

• Methods of Solution: Finding roots of quadratic equations by factorisation and by using the Quadratic Formula.

• Nature of Roots: Using the discriminant (D = b² - 4ac) to determine real, equal, or imaginary roots.

• Word Problems: Solving situational problems based on quadratic equations related to day-to-day activities.

Chapter 5: Arithmetic Progressions (AP)

• Introduction: Motivation for studying Arithmetic Progressions and identifying patterns.

• The \(n^{\text{th}}\) Term: Derivation and application of the formula for the general term (\(a_{n}\)).

• Sum of n Terms: Finding the sum of the first n terms of an AP (\(S_{n}\)) and its application in solving daily life problems.

Unit 3: Coordinate Geometry

Chapter 6: Coordinate Geometry

• Concepts of Coordinate Geometry: Review of plotting lines and understanding graphs.

• Distance Formula: Derivation and application to find the distance between two points.

• Section Formula: Finding coordinates of a point that divides a line segment internally in a given ratio m:n.

Unit 4: Geometry

Chapter 7: Triangles

• Definitions & Examples: Understanding similar figures vs. congruent figures.

• Similarity Criteria: Axioms and proofs for AAA, SAS, and SSS similarity.

• Basic Proportionality Theorem (Thales Theorem): Proof and application.

Chapter 8: Circles

• Tangent to a Circle: Definition and identification of the tangent at a point of contact.

• Theorems & Proofs:

  • Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

  • Prove that the lengths of tangents drawn from an external point to a circle are equal.

Unit 5: Trigonometry

Chapter 9: Introduction to Trigonometry

• Trigonometric Ratios: Defining \(\sin, \cos, \tan, \cot, \sec, \csc\) for acute angles of a right-angled triangle.

• Values of Ratios: Specific values for 0°, 30°, 45°, 60°, and 90°.

• Trigonometric Identity: Proof and application of the fundamental identity: \(\sin^2\theta + \cos^2\theta = 1\).

Chapter 10: Heights and Distances

• Angles of Elevation and Depression: Definitions and identifying line of sight.

• Applications: Solving simple problems involving heights and distances using no more than two right triangles (restricted to angles 30°, 45°, 60°).

Unit 6: Mensuration

Chapter 11: Areas Related to Circles

• Circle Segments & Sectors: Calculating the area of a sector and segment of a circle.

• Combined Plane Figures: Finding the area of shapes combined with triangles, rectangles, and circles (angles of sectors restricted to 60°, 90°, and 120°).

Chapter 12: Surface Areas and Volumes

• Surface Area of Combined Solids: Finding total surface area of combinations of any two: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

• Volume of Combined Solids: Calculating the space occupied by these combined solid figures.

Unit 7: Statistics & Probability

Chapter 13: Statistics

• Grouped Data Analysis: Calculating the Mean, Median, and Mode of grouped data sets.

• Bimodal Situations: Handling data and understanding the relationship between the three measures of central tendency (Empirical formula).

Chapter 14: Probability

• Classical Probability: Theoretical definition and calculation of simple events.

• Real-World Scenarios: Finding outcomes related to tossing coins, throwing dice, and drawing cards from a deck.

FAQs

1. What topics are covered in the Class 10 Mathematics course?

The course covers the complete CBSE Class 10 syllabus, including Number Systems, Algebra, Coordinate Geometry, Geometry, Trigonometry, Mensuration, Statistics, and Probability.

2. Is this course useful for board examination preparation?

Yes. The course focuses on conceptual clarity, regular practice, important question types, and exam-oriented preparation to help students perform confidently in CBSE board examinations.

3. Are the online classes available in Hindi and English?

Yes. The Mathematics classes are conducted in both Hindi and English, allowing students to learn in the language they are most comfortable with.