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Class 11th CBSE ICSE Maths

Class 11th CBSE ICSE Maths

Pure Mathematcis is a highly reputed institute for the preparation for class 11th Math exams in Chandigarh and Pnachkula It has given outstanding results in all courses. Chandigarh and Panchkula. pure Mathematics is one of the leading institutes located in Chandigarh and Panchkula which provides the best education & training of Math Coaching and provide Latest study material to its students and helps them to improve their overall performance in academics and also provide expert guidance to the students for enhancing the personality.

Pure Mathematcis is eminent institute for Math Coaching for class 7th 8th 9th 10th 11th 12th. We have 15 years teaching experienced in mathematics subject.This course is designed to provide a comprehensive understanding of Class 9th Mathematics as per the CBSE and ICSE syllabi. It covers fundamental concepts, problem-solving techniques, and applications of mathematics in real-life scenarios. The course is structured to build a strong foundation for higher classes and competitive exams.

Syllabus of Mathematics

Course Structure

The course is divided into 15 units, covering all the topics prescribed by CBSE and ICSE boards. Each unit includes theoretical explanations, solved examples, practice problems, and quizzes.

Unit 1: Number Systems

  1. Introduction to Real Numbers

    • Natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

    • Representation of real numbers on the number line.

  2. Operations on Real Numbers

    • Addition, subtraction, multiplication, and division of real numbers.

    • Rationalization of denominators.

  3. Laws of Exponents for Real Numbers

    • Positive, negative, and zero exponents.

    • Simplification of expressions using exponents.

Unit 2: Polynomials

  1. Introduction to Polynomials

    • Definition, types (monomial, binomial, trinomial), and degree of polynomials.

  2. Operations on Polynomials

    • Addition, subtraction, multiplication, and division.

  3. Factorization of Polynomials

    • Factor theorem, remainder theorem, and algebraic identities.

  4. Zeroes of a Polynomial

    • Finding zeroes and their relationship with coefficients.

Unit 3: Coordinate Geometry

  1. Cartesian System

    • Axes, quadrants, and coordinates.

  2. Plotting Points on a Plane

    • Locating points and understanding their coordinates.

  3. Distance Formula

    • Derivation and application.

Unit 4: Linear Equations in Two Variables

  1. Introduction to Linear Equations

    • Definition and standard form.

  2. Graphical Representation

    • Plotting linear equations on a graph.

  3. Solution of Linear Equations

    • Finding solutions algebraically and graphically.

Unit 5: Lines and Angles

  1. Basic Terms and Definitions

    • Line, line segment, ray, collinear points, and angles.

  2. Types of Angles

    • Acute, obtuse, right, straight, reflex, and complementary angles.

  3. Pairs of Angles

    • Adjacent angles, linear pairs, vertically opposite angles.

  4. Parallel Lines and Transversals

    • Corresponding angles, alternate angles, and co-interior angles.

Unit 6: Triangles

  1. Congruence of Triangles

    • SSS, SAS, ASA, RHS congruence rules.

  2. Properties of Triangles

    • Angle sum property, exterior angle property.

  3. Inequalities in Triangles

    • Relationship between sides and angles.

Unit 7: Quadrilaterals

  1. Properties of Quadrilaterals

    • Types of quadrilaterals: parallelogram, rectangle, rhombus, square, trapezium.

  2. Mid-Point Theorem

    • Statement, proof, and applications.

Unit 8: Circles

  1. Basic Terms

    • Radius, diameter, chord, arc, segment, sector.

  2. Properties of Circles

    • Angle subtended by chords, perpendicular from the center to a chord.

  3. Cyclic Quadrilaterals

    • Properties and theorems.

Unit 9: Heron's Formula

  1. Area of Triangles

    • Using base and height.

  2. Heron's Formula

    • Derivation and application to find the area of triangles.

Unit 10: Surface Areas and Volumes

  1. Surface Area

    • Cuboid, cube, cylinder, cone, and sphere.

  2. Volume

    • Formulas and applications.

Unit 11: Statistics

  1. Collection of Data

    • Primary and secondary data.

  2. Presentation of Data

    • Frequency distribution table, bar graph, histogram.

  3. Measures of Central Tendency

    • Mean, median, and mode.

Unit 12: Probability

  1. Introduction to Probability

    • Experiments, outcomes, events.

  2. Calculation of Probability

    • Basic problems and applications.

Unit 13: Constructions (Geometry)

  1. Basic Constructions

    • Angle bisector, perpendicular bisector.

  2. Construction of Triangles

    • Given base, angles, and sides.

Unit 14: Mensuration (ICSE Specific)

  1. Area and Perimeter

    • Rectangle, square, triangle, circle.

  2. Volume and Surface Area

    • Cuboid, cube, cylinder.

Unit 15: Trigonometry (ICSE Specific)

  1. Introduction to Trigonometry

    • Trigonometric ratios: sine, cosine, tangent.

  2. Applications of Trigonometry

    • Simple problems on heights and distances.

Teaching Methodology

  1. Interactive Lectures

    • Use of visual aids, animations, and real-life examples.

  2. Problem-Solving Sessions

    • Step-by-step solutions to problems.

  3. Practice Worksheets

    • Regular assignments and quizzes.

  4. Doubt Clearing Sessions

    • Weekly doubt-solving sessions.

Assessment and Evaluation

  1. Periodic Tests

    • Conducted after every unit.

  2. Mid-Term and Final Exams

    • Comprehensive exams covering the entire syllabus.

  3. Project Work

    • Practical applications of mathematical concepts.

Recommended Textbooks

  1. CBSE

    • NCERT Mathematics Textbook for Class 9.

  2. ICSE

    • Concise Mathematics by Selina Publishers.

Additional Resources

  1. Online Platforms

    • Khan Academy, BYJU’S, and Toppr.

  2. Reference Books

    • RD Sharma, RS Aggarwal.

Course Duration

  • Total Duration: 10 months (aligned with the academic year).

  • Weekly Schedule: 4 hours per week (2 lectures + 2 practice sessions).

Learning Outcomes

By the end of this course, students will:

  1. Have a strong understanding of fundamental mathematical concepts.

  2. Be able to solve complex problems with ease.

  3. Develop analytical and logical thinking skills.

  4. Be well-prepared for Class 10th board exams and competitive exams.

This course is designed to make learning mathematics enjoyable and effective for Class 9th students. Let’s embark on this exciting journey of numbers and logic! 🚀

write course on Class 10th (CBSE & ICSE) Maths

Course Outline: Class 10th Mathematics (CBSE & ICSE)

Course Overview

This course is designed to provide a comprehensive understanding of Class 10th Mathematics as per the CBSE and ICSE syllabi. It focuses on building a strong foundation in mathematical concepts, problem-solving skills, and real-life applications. The course is structured to prepare students for board exams and competitive exams.

Course Structure

The course is divided into 15 units, covering all the topics prescribed by CBSE and ICSE boards. Each unit includes theoretical explanations, solved examples, practice problems, and quizzes.

Unit 1: Real Numbers

  1. Euclid’s Division Lemma

    • Statement, proof, and applications.

  2. Fundamental Theorem of Arithmetic

    • Prime factorization and its uniqueness.

  3. Irrational Numbers

    • Proofs of irrationality (e.g., √2, √3).

  4. Rational Numbers and Their Decimal Expansions

    • Terminating and non-terminating decimals.

Unit 2: Polynomials

  1. Zeroes of a Polynomial

    • Relationship between zeroes and coefficients.

  2. Division Algorithm for Polynomials

    • Statement and application.

  3. Factorization of Polynomials

    • Using algebraic identities and factor theorem.

Unit 3: Pair of Linear Equations in Two Variables

  1. Graphical Method

    • Solving linear equations graphically.

  2. Algebraic Methods

    • Substitution, elimination, and cross-multiplication methods.

  3. Applications of Linear Equations

    • Word problems based on real-life scenarios.

Unit 4: Quadratic Equations

  1. Introduction to Quadratic Equations

    • Standard form and solutions.

  2. Methods of Solving Quadratic Equations

    • Factorization, completing the square, and quadratic formula.

  3. Nature of Roots

    • Discriminant and its significance.

Unit 5: Arithmetic Progressions (AP)

  1. Introduction to AP

    • Definition, terms, and common difference.

  2. nth Term of an AP

    • Formula and applications.

  3. Sum of First n Terms of an AP

    • Formula and problem-solving.

Unit 6: Triangles

  1. Similarity of Triangles

    • Criteria for similarity (AA, SAS, SSS).

  2. Basic Proportionality Theorem (Thales Theorem)

    • Statement, proof, and applications.

  3. Pythagoras Theorem

    • Statement, proof, and applications.

Unit 7: Coordinate Geometry

  1. Distance Formula

    • Derivation and applications.

  2. Section Formula

    • Internal and external division.

  3. Area of a Triangle

    • Using coordinates.

Unit 8: Trigonometry

  1. Trigonometric Ratios

    • Sine, cosine, tangent, and their reciprocals.

  2. Trigonometric Identities

    • Fundamental identities and their proofs.

  3. Heights and Distances

    • Applications in real-life problems.

Unit 9: Applications of Trigonometry (ICSE Specific)

  1. Angle of Elevation and Depression

    • Problems based on heights and distances.

  2. Real-Life Applications

    • Solving practical problems using trigonometry.

Unit 10: Circles

  1. Tangent to a Circle

    • Properties and theorems related to tangents.

  2. Number of Tangents from a Point to a Circle

    • Direct and transverse tangents.

Unit 11: Constructions

  1. Division of a Line Segment

    • Using basic proportionality theorem.

  2. Construction of Tangents to a Circle

    • From an external point.

Unit 12: Areas Related to Circles

  1. Perimeter and Area of a Circle

    • Formulas and applications.

  2. Areas of Sector and Segment

    • Calculations and problem-solving.

Unit 13: Surface Areas and Volumes

  1. Surface Area

    • Cuboid, cube, cylinder, cone, and sphere.

  2. Volume

    • Formulas and applications.

  3. Conversion of Solids

    • Problems based on melting and recasting.

Unit 14: Statistics

  1. Mean, Median, and Mode

    • Grouped and ungrouped data.

  2. Cumulative Frequency Distribution

    • Graphical representation (ogive curves).

Unit 15: Probability

  1. Introduction to Probability

    • Experiments, outcomes, and events.

  2. Theoretical Probability

    • Calculation and applications.

Teaching Methodology

  1. Interactive Lectures

    • Use of visual aids, animations, and real-life examples.

  2. Problem-Solving Sessions

    • Step-by-step solutions to problems.

  3. Practice Worksheets

    • Regular assignments and quizzes.

  4. Doubt Clearing Sessions

    • Weekly doubt-solving sessions.

Assessment and Evaluation

  1. Periodic Tests

    • Conducted after every unit.

  2. Mid-Term and Final Exams

    • Comprehensive exams covering the entire syllabus.

  3. Project Work

    • Practical applications of mathematical concepts.

Recommended Textbooks

  1. CBSE

    • NCERT Mathematics Textbook for Class 10.

  2. ICSE

    • Concise Mathematics by Selina Publishers.

Additional Resources

  1. Online Platforms

    • Khan Academy, BYJU’S, and Toppr.

  2. Reference Books

    • RD Sharma, RS Aggarwal.

Course Duration

  • Total Duration: 10 months (aligned with the academic year).

  • Weekly Schedule: 4 hours per week (2 lectures + 2 practice sessions).

Learning Outcomes

By the end of this course, students will:

  1. Have a strong understanding of fundamental mathematical concepts.

  2. Be able to solve complex problems with ease.

  3. Develop analytical and logical thinking skills.

  4. Be well-prepared for Class 10th board exams and competitive exams.

This course is designed to make learning mathematics enjoyable and effective for Class 10th students. Let’s embark on this exciting journey of numbers and logic! 🚀

write course on Class 11th (CBSE & ICSE) Maths

Course Outline: Class 11th Mathematics (CBSE & ICSE)

Course Overview

This course is designed to provide a comprehensive understanding of Class 11th Mathematics as per the CBSE and ICSE syllabi. It focuses on building a strong foundation in advanced mathematical concepts, problem-solving skills, and applications in real-life scenarios. The course is structured to prepare students for competitive exams like JEE, NEET, and other entrance tests.

Course Structure

The course is divided into 16 units, covering all the topics prescribed by CBSE and ICSE boards. Each unit includes theoretical explanations, solved examples, practice problems, and quizzes.

Unit 1: Sets

  1. Introduction to Sets

    • Definition, types, and representation of sets.

  2. Operations on Sets

    • Union, intersection, difference, and complement.

  3. Venn Diagrams

    • Applications in solving problems.

Unit 2: Relations and Functions

  1. Cartesian Product of Sets

    • Definition and properties.

  2. Relations

    • Types of relations: reflexive, symmetric, transitive, and equivalence relations.

  3. Functions

    • Definition, types, and graphs of functions.

Unit 3: Trigonometric Functions

  1. Angles and Their Measurement

    • Degree and radian measures.

  2. Trigonometric Functions

    • Sine, cosine, tangent, and their graphs.

  3. Trigonometric Identities

    • Fundamental identities and their proofs.

  4. Heights and Distances

    • Applications in real-life problems.

Unit 4: Principle of Mathematical Induction

  1. Introduction to Induction

    • Basic principles and applications.

  2. Proofs by Induction

    • Solving problems using mathematical induction.

Unit 5: Complex Numbers and Quadratic Equations

  1. Introduction to Complex Numbers

    • Definition, algebra, and conjugate of complex numbers.

  2. Argand Plane and Polar Representation

    • Graphical representation and polar form.

  3. Quadratic Equations

    • Solving quadratic equations with complex roots.

Unit 6: Linear Inequalities

  1. Algebraic Solutions of Linear Inequalities

    • Graphical representation and solution sets.

  2. System of Linear Inequalities

    • Solving systems of inequalities.

Unit 7: Permutations and Combinations

  1. Fundamental Principle of Counting

    • Basic counting techniques.

  2. Permutations

    • Arrangement of objects.

  3. Combinations

    • Selection of objects.

Unit 8: Binomial Theorem

  1. Introduction to Binomial Theorem

    • Statement and proof.

  2. General and Middle Terms

    • Finding specific terms in binomial expansion.

Unit 9: Sequences and Series

  1. Arithmetic Progression (AP)

    • nth term and sum of first n terms.

  2. Geometric Progression (GP)

    • nth term and sum of first n terms.

  3. Arithmetic Mean and Geometric Mean

    • Definitions and applications.

Unit 10: Straight Lines

  1. Slope of a Line

    • Definition and calculation.

  2. Equations of Lines

    • Various forms: slope-intercept, point-slope, two-point form.

  3. Distance of a Point from a Line

    • Formula and applications.

Unit 11: Conic Sections

  1. Introduction to Conic Sections

    • Circle, parabola, ellipse, and hyperbola.

  2. Standard Equations and Properties

    • Derivation and graphical representation.

Unit 12: Introduction to Three-Dimensional Geometry

  1. Coordinate Axes and Planes

    • 3D coordinate system.

  2. Distance Formula

    • Derivation and applications.

  3. Section Formula

    • Internal and external division.

Unit 13: Limits and Derivatives

  1. Introduction to Limits

    • Definition and properties.

  2. Derivatives

    • Definition, rules, and applications.

Unit 14: Mathematical Reasoning

  1. Statements and Logical Operations

    • Negation, conjunction, disjunction, implication.

  2. Validating Statements

    • Techniques for validation.

Unit 15: Statistics

  1. Measures of Dispersion

    • Range, mean deviation, variance, and standard deviation.

  2. Analysis of Frequency Distributions

    • Graphical representation and interpretation.

Unit 16: Probability

  1. Introduction to Probability

    • Experiments, outcomes, and events.

  2. Conditional Probability

    • Definition and applications.

  3. Bayes' Theorem

    • Statement and applications.

Teaching Methodology

  1. Interactive Lectures

    • Use of visual aids, animations, and real-life examples.

  2. Problem-Solving Sessions

    • Step-by-step solutions to problems.

  3. Practice Worksheets

    • Regular assignments and quizzes.

  4. Doubt Clearing Sessions

    • Weekly doubt-solving sessions.

Assessment and Evaluation

  1. Periodic Tests

    • Conducted after every unit.

  2. Mid-Term and Final Exams

    • Comprehensive exams covering the entire syllabus.

  3. Project Work

    • Practical applications of mathematical concepts.

Recommended Textbooks

  1. CBSE

    • NCERT Mathematics Textbook for Class 11.

  2. ICSE

    • Concise Mathematics by Selina Publishers.

  • Total Duration: 10 months (aligned with the academic year).

  • Weekly Schedule: 4 hours per week (2 lectures + 2 practice sessions).

Learning Outcomes

By the end of this course, students will:

  1. Have a strong understanding of fundamental mathematical concepts.

  2. Be able to solve complex problems with ease.

  3. Develop analytical and logical thinking skills.

  4. Be well-prepared for Class 12th board exams and competitive exams.



Category: Class 11th Math

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