# Business Mathematics - Class XI Resources

The following list of online resources are provided as a sample of curated resources. New resources shall be added as we come across interesting and relevant online materials.

#### 1. Determinants

Description: This web link contains a pdf file on the “introduction” and “brief history” of the determinants.

Core Concepts: “Introduction and “History” of the Determinants.

Description: This web link contains a webpage on the importance of learning determinants, as well as the utility and scope of this chapter.

Core Concepts: “Utility” and “scope” of the Determinants.

Description: This web link contains a video lesson on the concepts on determinants, its type and examples.

Core Concepts: Concepts of determinants of a Matrix.

Description: This web link includes a video lesson on calculating 2x2 determinants, detailing the procedures, steps, and methods involved.

Core Concepts: Finding the determinant of order 2.

Description: This web link contains a video lesson on calculating determinants of order 3, detailing the procedures, steps, and methods involved.

Core Concepts: Finding the determinant of order 3.

Description: This web link contains a video lesson on finding the minor and cofactor of a determinant.

Core Concepts: Minor and cofactor of determinants .

Description: This web link contains a video lesson on solving a system of equations in two and three variables using Crammer’s rule.

Core Concepts: Solving a system of equations using Cramer’s rule.

Description: This web link contains a video lesson on the concepts on what is consistency, checking through the graphical methods.

Core Concepts: Understanding the consistency of a system graphically.

Description: This web link includes a PDF file containing a flowchart for checking a system for consistency.

Core Concepts: Checking a system for consistency.

Description: This web link contains a video lesson on calculating minor and cofactor of determinants.

Core Concepts: Understanding the minor and cofactor of determinants.

#### 2. Logarithm

Description: This web link contains a web page on the introduction of logarithm.

Core Concepts: Introduction on logarithm.

Description: This web link contains the utility and scope of logarithm.

Core Concepts: Utility and scope of  logarithm.

Description: This web link directs to a webpage containing the laws of exponents.

Core Concepts: Laws of exponents.

Description: These weblinks contain videos on the concept of logarithm.

Core Concepts: Definition logarithm.

Description: This weblink contains a video lesson on the laws and properties of logarithm.

Core Concepts: Laws and properties of log.

Description: This web link contains a web page containing some questions on logarithm.

Core Concepts: Practice question on logarithm.

Description: This web link contains a video lesson on the application of the laws of logarithm.

Core Concepts: Application of the laws of logarithm.

#### 3. Binomial Theorem

Description: This web link contains a web page on brief introduction and the history of binomial theorem.

Core Concepts: Introduction and history of binomial theorem.

Description: This web link contains a web page on the utility and scope of binomial theorems.

Core Concepts: Utility and scope on binomial theorem.

Description: These web links contain video lessons about the basic concept of binomial theorem.

Core Concepts: Introduction and concept of binomial theorem.

Description: This web link contains a video lesson on the properties of binomial theorem and their importance in solving binomial theorem .

Core Concepts: Properties of binomial theorem.

Description: This web link contains quiz questions on binomial theorems.

Core Concepts: Quiz on binomial theorem.

#### 4. Banking

Description: This web link contains a webpage on the introduction of Banking.

Core Concepts: Introduction of banking.

#### 5. Sequence and Series

Description: This web link contains a presentation on the history and introduction of sequence and series.

Core Concepts: History and introduction of sequence and series.

Description: This web link contains a video lesson on the differences between A.P. and G.P.

Core Concepts: Arithmetic Differences between A.P. and G.P.

Description: This web link contains a video lesson on the derivation of the nth term of A.P.

Core Concepts: Arithmetic Progression and its general term.

Description: This web link contains a webpage consisting of questions on the general term of an Arithmetic Progression.

Core Concepts: Questions related to the general term of an A.P.

Description: The web link contains a video lesson on derivation of sum of n terms of an A.P.

Core Concepts: Sum of n terms of an A.P.

Description: This web link contains a video lesson on the concept of geometric sequence.

Core Concepts: Concept of geometric sequence.

Description: This web link contains a video lesson about the general term of a geometric progression.

Core Concepts: General Term of Geometric Progression.

Description: This web link contains a video on first n terms of Geometric Series.

Core Concepts: Partial sum of Geometric Series.

Description: This web link contains a video lesson on the sum of infinite Geometric Series.

Core Concepts: Sum of infinite Geometric Series.

Description: This web link contains a video lesson on the derivation of the sum of n natural numbers.

Core Concepts: Sum of n natural numbers.

Description: This web link contains a video lesson on the sum of squares of natural numbers.

Core Concepts: Sum of the squares of natural numbers.

Description: This web link contains a web page on the sum of the cubes of natural numbers.

Core Concepts: Sum of the cubes of natural numbers.

#### 6. Remainder and Factor Theorem

Description: This web link contains a web page about the introduction to the remainder and factor theorem.

Core Concepts: Introduction to the remainder and factor theorem.

Description: This web link contains a video lesson on the application of remainder and factor theorem.

Core Concepts: Application of remainder and factor theorem.

Description: This web link contains a worksheet on remainder and factor theorem.

Core Concepts: Worksheet on remainder and factor theorem.

Description: This web link contains a research paper on the history and introduction of quadratic equations.

Core Concepts: Introduction and History of quadratic equations.

Description: These web links contain videos on the utility and scope of quadratic equations in real life.

Core Concepts: Utility and scope of quadratic equation.

Core Concepts: Worksheet in quadratic equation.

Description: This web link contains a video on solving quadratic equations using formula methods.

Core Concepts: Solving quadratic equations by formula method.

Description: This web link contains a video on the discriminant and the nature of roots of quadratic equations.

Core Concepts: Discriminant and nature of roots.

Description: This web link contains a video lesson on solving quadratic inequalities algebraically.

Core Concepts: Solving quadratic inequalities algebraically.

Description: This web link contains a video on graphing the quadratic inequality, its methods and strategies.

Core Concepts: Graphing inequality.

#### 8. Partial Fractions

Description: This web link contains a web page containing an introduction to Partial Fractions.

Core Concepts: Introduction to partial fraction.

Description: This web link contains a webpage on the applications of partial fractions in real life.

Core Concepts: Utility and scope  on partial fraction.

Description: This web link features a video lesson on decomposing rational fractions with non-repeating linear factors in their denominators into partial fractions.

Core Concepts: Resolving rational fractions of denominators containing non-repeated linear factors.

Description: The concepts regarding repeated linear factors, its solution and procedures are explained.

Core Concepts: Resolving rational fraction containing repeated linear factors.

Description: This web link contains a video lesson on partial fractions of rational fractions with quadratic factors.

Core Concepts: Resolving rational fraction containing repeated linear factors.

Description: This web link contains a video lesson on partial fractions of improper rational fractions.

Core Concepts: Resolving improper fractions into partial fractions.

Description: This web link contains a web page containing some questions on partial fractions for practice.

Core Concepts: Practice questions on partial fractions.

#### 9. Limits

Description: This web link contains a web page on the introduction of Limits.

Core Concepts: Introduction of Limits.

Description: This web link contains a video lesson on the utility and scope of limits.

Core Concepts: Utility and Scope of Limits.

Description: This web link contains a video lesson on the concept of limits.

Core Concepts: Concept of Limits.

Description: This web link contains a video lesson on the right and left hand limits.

Core Concepts: Right and left hand limits.

Description: This web link offers a video lesson on determining the existence of limits at a specific point.

Core Concepts: Determining the existence of limits at a specific point..

Description: This web link contains a web page on the theorems of limits.

Core Concepts: Limit Theorems.

Description: This web link provides a video lesson on evaluating the limit of a function using direct substitution.

Core Concepts: Evaluating the limit of a function using direct substitution.

Description: This web link provides a video lesson on evaluating the limit of a function using factorization.

Core Concepts: Evaluating the limit of a function using direct substitution.

Description: This web link provides a video lesson on evaluating the limit of a function using rationalisation.

Core Concepts: Evaluating the limit of a function using rationalisation.

Description: This web link provides a video lesson on evaluating the limit of a function using expansion.

Core Concepts: Evaluating the limit of a function using expansion.

Description: This web link provides a video lesson on evaluating the limit of a function at infinity.

Core Concepts: Evaluating the limit of a function at infinity.

Description: This web link contains a live worksheet on limits.

Core Concepts: Limit worksheet.

Description: These web links contain video lessons on the concept of continuity and discontinuity of functions.

Core Concepts: Continuity and discontinuity of a function.

Description: This web link contains a video lesson on testing for continuity of a function.

Core Concepts: Testing for continuity of a function.

Description: This web link contains a video lesson on finding the limit of removable discontinuity.

Core Concepts: Removable discontinuity.

Description: This web link provides a video lesson explaining the continuity functions over an interval.

Core Concepts: Continuity of functions over an interval.

Description: This web link provides a web page containing some questions on the continuity of functions.

Core Concepts: Questions on continuity of functions.

#### 10. Differentiation

Description: These web links provide video lessons on the History of Calculus.

Core Concepts: History and Introduction of Calculus.

Description: This web link provides a video lesson on the concept of differentiation.

Core Concepts: Concept of differentiation.

Description: This web link provides a video on the differentiation of a function by Definition.

Core Concepts: Differentiating a function by definition/ first principle.

Description: This web link contains a video lesson on differentiating a function using the product rule.

Core Concepts: Differentiation of product of two functions.

Description: This web link contains a video lesson on differentiating a function using the quotient rule.

Core Concepts: Differentiation of quotients of two functions.

#### 11. Integration

Description: This web link contains a pdf file containing the history of integration.

Core Concepts: History of Integral Calculus.

Description: This web link contains a video lesson on the concept of integration.

Core Concepts: Understanding integration as a reverse process of differentiation.

Description: This web link contains a video lesson on the notation of integral.

Core Concepts: Notation and the meaning of integral sign.

Description: This web link contains a video lesson on the arbitrary constant of integrals.

Core Concepts: Arbitrary constant of integral.

Description: These web links contain pdf files containing some questions on integration.

Core Concepts: Practice questions on integration.

Description: These web links contain video lessons on integration by substitution.

Core Concepts: Integration by substitution.

#### 12.  Points and their coordinates in 2-D

Description: This web link contains a web page on the history of coordinate geometry.

Core Concepts: History and Introduction of coordinate geometry.

Description: This web link contains a web page containing some utilities and scopes of coordinate geometry.

Core Concepts: Utility and Scope of Coordinate Geometry.

Description: This web link contains a video lesson explaining the cartesian coordinate system.

Core Concepts: Cartesian coordinate system.

Description: This web link contains a video lesson on the distance formula.

Core Concepts: Distance between two points in 2-D plane.

Description: This web link contains a video lesson on the application of distance formula.

Core Concepts: Application of distance formula.

Description: This web link features a video lesson on the section formula for 2-D coordinates.

Core Concepts: Section formula.

Description: These web links lead to web pages that contain questions on the application of the section formula.

Core Concepts: Application of section formula.

Description: This web link contains a video lesson on the derivation of section formula for external division.

Core Concepts: Section formula for external division.

Description: This web link leads to a web page featuring interactive quiz questions on the 2-D coordinate system.

Core Concepts: Quiz on 2-D coordinate system.

#### 13.  The Straight Line

Description: This web link contains a video lesson on slope and y-intercept form of a straight line.

Core Concepts: Slope and y-intercept form of straight line.

Description: This web link contains a video lesson on the point slope form of a straight line.

Core Concepts: Point slope form of a straight line.

Description: This web link contains a video lesson on the two-point form of a straight line.

Core Concepts: Two-point form of a straight line.

Description: These web links contain videos on the applications of straight lines in commerce and economics.

Core Concepts: Application of straight lines in commerce and economics.

#### 14. The Circle and Its Theorem

Description: This web link provides a video on the definition of circle.

Core Concepts: Definition of circle.

Description: This web link contains a video on the concepts of a circle.

Core Concepts: Concept of circle.

Description: This web link contains a video on the derivation of the equation of a circle.

Core Concepts: The equation of a circle.

Description: This web link contains a video on the equation of a circle in centre-radius form.

Core Concepts: The equation of a circle in centre-radius form.

Description: This web link contains a video on the equation of a circle in its diameter form.

Core Concepts: The equation of a circle in its diameter form.

Description: This web link contains a video on determining the centre and radius of a circle from a given equation.

Core Concepts: Determining centre and radius of a circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: a straight line drawn from the centre of a circle to bisect a chord is perpendicular to the chord.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: A straight line, drawn from the centre of a circle perpendicular to a chord, bisects the chord.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: One and only one circle can be drawn through three points not lying in the same straight line.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: Equal chords of a circle are equidistant from the centre; Chords of a circle that are equidistant from the centre are equal.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The angle subtended at the centre by an arc of a circle is double the angle which these subtends at any remaining part of the circumference.

Core Concepts: Theorems on Arcs and Angles.

Link: Geogebra diagram of Theorem 6

Description:The web link contains an interactive GeoGebra diagram on the chords of a circle: In a circle the angle in a semicircle is a right angle.

Core Concepts: Theorems on Arcs and Angles.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: Angles in the same segment of a circle are equal.

Core Concepts: Theorems on Arcs and Angles.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The opposite angles of a cyclic quadrilateral are supplementary.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: If a side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The tangent at any point of a circle and the radius through this point are perpendicular to each other.

Core Concepts: Theorem on Tangent Lines and Circles.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: If two circles touch each other, the point of contact lies on the straight line joining the centres of two circles.

Core Concepts: Theorem on Tangent Lines and Circles.

#### 15.  Measures of Central Tendency

Description: This web link leads to a web page introducing the concept of central tendencies.

Core Concepts: Introduction of central tendencies.

Description: This web link leads to a web page discussing the utility and scope of central tendencies.

Core Concepts: Utility and scope of central tendencies.

Description: These web links contain the videos on the meaning of central tendencies.

Core Concepts: Concept of central tendencies.

Description: This web link leads to a video on finding the mean using the shortcut method.

Core Concepts: Finding mean of a data by shortcut method.

Description: This web link contains a video on how to find the mean using the step-deviation method.

Core Concepts: Finding mean of a data by step-deviation method.

Description: This web link contains a video on finding the central tendencies of simple distribution data.

Core Concepts: Central tendencies of simple distribution.

Description: This web link contains a video on finding the central tendencies of discrete data.

Core Concepts: Central tendencies of discrete data.

Description: This web link contains a video on finding the central tendencies of a grouped data.

Core Concepts: Central tendencies of grouped data.

Description: This web link contains a video on finding the mode of a grouped data.

Core Concepts: Finding the mode of a grouped data.

#### 16.  Dispersion

Description: This web link contains a video on measuring the dispersion of data using standard deviation.

Core Concepts: Measuring the dispersion of data using standard deviation.

Description: This web link contains a video on finding the combined mean.

Core Concepts: Finding combined mean.

#### 17.  Probability

Description: This web link leads to a web page detailing the history of probability.

Core Concepts: Introduction and history of probability.

Description: This web link contains a web page detailing the utility and scope of probability.

Core Concepts: Utility and scope of probability.

Description: This web link contains a video on the introduction of probability.

Core Concepts: Probability concepts.

Description: These web links contain the videos on set theory concepts.

Core Concepts: Set theory.

Description: This web link provides a video on the probability of complementary events.

Core Concepts: Probability of complementary events.

Description: This web link contains a video on the odds vs probability.

Core Concepts: Odds and Probability

Description: This web link contains a web page with interactive questions on probability.

Core Concepts: Interactive Probability questions

Description: These web links contain videos on the “addition rule” of probability.

Core Concepts: Addition rule of probability.

Description: This web link leads to a web page with some probability questions.

Core Concepts: Application of addition rule in probability.