# Business Mathematics - Class XII 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. Matrices

Description: This web link contains a video on the history of matrices.

Core Concepts: History of matrices

Description: This web link leads to a web page detailing the utilities and scope of matrices.

Core Concepts: Utility and scope of matrices

Description: This web link contains a pdf file with some questions on addition and subtraction of matrices.

Core Concepts: Addition and subtraction of matrices

Description: This web link contains a pdf file with some questions on multiplication of matrices.

Core Concepts: Multiplication of matrices.

Description: This web link contains a video lesson on the properties of matrix multiplication.

Core Concepts: Properties of matrix multiplication.

Description: This web link contains a video on the transpose of a matrix.

Core Concepts: Transpose of a matrix.

Description: This web link contains a video on the adjoint of a matrix.

Core Concepts: Adjoint of a  matrix.

Description: This video contains finding the inverse of 2x2 matrix.

Core Concepts: Inverse of 2x2 Matrices.

Description: This video contains finding an inverse of a 3x3 matrix.

Core Concepts: Inverse of 3x3 Matrices.

Description: This web link contains a worksheet on finding inverse matrices.

Core Concepts: Inverse of matrices.

Description: This video contains a solving system of equations using the matrix method.

Core Concepts: Solving system of equations using matrix method (Martin’s rule).

Description: This video contains  graphing equations of 3-D planes using Geogebra.

Core Concepts: Graphing equations of 3-D plane.

#### 2. Annuities

Description: This web link contains a webpage on the history and introduction of annuity.

Core Concepts: History and Introduction of annuities.

Description: This web link contains a video lesson explaining the concept of annuity.

Core Concepts: Concept of Annuity.

Description: This web link contains a video lesson explaining the types of annuities.

Core Concepts: Types of Annuity.

Description: This web link contains a video lesson explaining the differences between future value and present value of annuity.

Core Concepts: Future and Present value.

Description: This web link contains a video lesson explaining the derivation of the formula for the future value of annuity.

Core Concepts: Future value of annuity.

Description: This web link contains video lessons explaining the examples of future value of annuity.

Core Concepts: Future value of annuity.

Description: These web links contain three online banking calculators for recurring deposits and loans.

Core Concepts: Future and Present value

Description: These web links contain video lessons explaining the derivation of the formula for the present value of annuity.

Core Concepts: Present value of annuity.

Description: These web links contain video lessons on the examples of application of present value.

Core Concepts: Present value of annuity.

Description: This web link contains a video lesson explaining the annuity perpetuity.

Core Concepts: Annuity Perpetuity.

#### 3. Discount

Description: These web links contain a webpage and a video lesson on the history of discounts and bills of exchange.

Core Concepts: Introduction to Discount.

Description: This web link contains a pdf file of chapter 26 of BHSEC Book I.

Core Concepts: Discount.

Description: This web link contains a pdf file with questions on discounts that students have learned in class X.

Core Concepts: Practice questions on trade discounts.

Description: This web link contains a video on the concept of bills of exchange.

Core Concepts: Bills of exchange.

Description: This web link contains a webpage explaining the differences between the true discount and bankers discount.

Core Concepts: True discount and bankers discount.

Description: This web link contains a video lesson on the examples of Bills of exchange problems.

Core Concepts: Examples of Bills of exchange.

#### 4. Permutations and Combinations

Description: This web link contains a web page with notes on the introduction of permutation and combinations and its history.

Core Concepts: Introduction of permutation and combination.

Description: This web link contains a webpage that provides information on the utility and scope of learning permutations and combinations.

Core Concepts: Utility and scope of permutation and combination.

Description: Explains fundamental principle counting.

Core Concepts: Fundamental principle of counting.

Description: This web link contains a video lesson on calculating permutation.

Core Concepts: Calculating permutation in general case.

Description: This web link contains a video lesson about the permutation of repeated items.

Core Concepts: Permutation of repetition cases.

Description: These web links contain video lessons on permutation of letters of a word.

Core Concepts: Permutation of letters.

Description: This web link contains a video lesson sharing the knowledge about on circular permutation.

Core Concepts: Circular permutation.

Description: This web link contains a video on the comparison of permutation and combination.

Core Concepts: Comparing permutation and combination.

Description: This web link contains a video on the combination examples.

Core Concepts: Combination.

#### 5. Differentiation

Description: These web links contain videos on the history and introduction of calculus and differentiation.

Core Concepts: Introduction to Calculus and differentiation.

Description: This web link contains a web page that provides information on the utility and scope of differentiation.

Core Concepts: Utility and scope of differentiation.

Description: This web link contains video lesson on differentiation concepts.

Core Concepts: Concepts of differentiation.

Description: This web link contains video lesson on differentiation of quotient of two functions.

Core Concepts: Differentiation  of quotient of two function.

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

Core Concepts: Differentiation using chain rule.

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

Core Concepts: Differentiation of quotient of two function.

Description: This web link contains a video on differentiating a product of two functions.

Core Concepts: Differentiation using product rule.

Description: These web links contain video lessons on differentiation of implicit functions.

Core Concepts: Differentiation of implicit functions.

Description: This web link contains a video lesson differentiation of parametric functions.

Core Concepts: Differentiation of parametric function.

Description: This web link contains a video lesson on the differentiation of a function concerning another function.

Core Concepts: Differentiation of function concerning other function.

Description: These web links contain video lessons on successive differentiation of the algebraic functions.

Core Concepts: Successive differentiation.

#### 6. Maxima and Minima

Description: This web page contains the Introduction of Maxima and Minima.

Core Concepts: Introduction to Maxima and Minima.

Description: This link to the PDF explains the application of maxima and minima in economics optimization theory.

Core Concepts: Utility and scope.

Description: This web link to the video explains three types of turning points (maxima, Minima and Inflexion).

Core Concepts: Stationary points.

Description: These web links to the videos contain explanations of the algorithm of how to determine turning points and maximum minimum values.

Core Concepts: Problem-solving of maxima and Minima

Description: This web link to the video examines on existence of inflexion point (s) or not.

Core Concepts: Inflexion point.

Description: This web link to the video explains the applications of maxima and minima in commerce and economics.

Core Concepts: Applications.

#### 7. Integration

Description: These web links contain videos on the history and introduction of integration.

Core Concepts: History and introduction of integration.

Description: This web link contains a video explaining the differences between differentiation and integration.

Core Concepts: Differences between differentiation and integration.

Description: This web link contains a video on basic integration rules.

Core Concepts: Integration rules.

Description: These web links contain two videos on the integration using the substitution method.

Core Concepts: Integration using the substitution method.

Description: This web link contains presentation slides on integration by partial fractions.

Core Concepts: Integration by partial fractions.

Description: This web link contains a worksheet of some questions on integration.

Core Concepts: Integration worksheet.

Description: The link contains a web page which provides information on the application of calculus in economics and commerce.

Core Concepts: Application of calculus in economics and commerce.

#### 8. The Conic Section

Description: This web link contains the introduction of the conic section.

Core Concepts: Introduction of conics.

Description: This web page and video contain applications of conic sections in our daily lives.

Core Concepts: Utility and scope.

Description: This video explains the meaning of the conic section.

Core Concepts: Conic section concept.

Description: This web link contains a conic section Geogebra worksheet.

Core Concepts: Conic section Geogebra worksheet.

Description: This video contains a derivation of the equation of the right-hand parabola with an example.

Core Concepts: Parabola

Description: This web link contains the parabola Geogebra worksheet.

Core Concepts: Parabola

Description: The video contains the derivation of equations of left-hand parabola and vertical parabola.

Core Concepts: Parabola

Description: These videos explain how to find the equation of a parabola when its parts are given and vice versa.

Core Concepts: Parabola

Description: These videos contain examples of parabolas in solving real-life applications.

Core Concepts: Parabola

Description: This video contains the derivation of the equation of ellipse.

Core Concepts: Ellipse

Description: This web link contains a Geogebra worksheet to explain ellipses visually.

Core Concepts: Ellipse

Description: This video contains an explanation of  the parts of the ellipse.

Core Concepts: Ellipse

Description: These videos contain an explanation of finding the equation of an ellipse when its parts are given and vice versa.

Core Concepts: Ellipse

Description: These videos contain examples of ellipse in solving real-life applications.

Core Concepts: Ellipse

Description: This link contains Geogebra explaining the hyperbola visually.

Core Concepts: Hyperbola

Description: This web link to the video contains the derivation of the equation of the hyperbola.

Core Concepts: Hyperbola

Description: This web link to the video explains the parts of the hyperbola.

Core Concepts: Hyperbola and its parts

Description: This web link to the video contains examples of the hyperbola in solving real-life applications.

Core Concepts: Hyperbola and its application

Description: This web link contains Geogebra worksheets on types of conic sections.

Core Concepts: Worksheets on hyperbola, Ellipse and Parabola.

#### 9. Points and their Coordinates in 3-Dimensions

Description: Web link contains a history of Points and their Coordinates in 3-Dimensions.

Core Concepts: History of Points and their Coordinates in 3-Dimensions.

Description: This link contains applications and examples of Geometry in daily life.

Core Concepts: Utility and scope.

Description: This video contains an introduction to 3-D geometry.

Core Concepts: Introduction of 3-D geometry.

Description: This video includes the derivation  of the distance formula.

Core Concepts: Derivation of distance formula.

Description: These videos contain section formulas.

Core Concepts: Section formula.

Description: These videos contain direction cosines and ratios.

Core Concepts: Direction cosines and direction ratios.

Description: This video contains conditions of parallelism and perpendicularity of lines.

Core Concepts: Parallelism and perpendicularity of lines.

#### 10. Correlation

Description: This web link contains an introduction and history of correlation.

Core Concepts: Introduction of correlation.

Description: This web link contains the application of correlation.

Core Concepts: Utility and scope.

Description: This web link contains the interpretation of value of correlation coefficient.

Core Concepts: Degree of correlation.

Description: This video contains an explanation of  finding Karl Pearson’s correlation coefficient.

Core Concepts: Karl Pearson’s correlation.

Description: This video contains finding Spearman’s rank correlation coefficient.

Core Concepts: Spearman’s rank correlation coefficient.

Description: This video contains finding Spearman’s rank correlation coefficient of tied ranks.

Core Concepts: Spearman’s rank correlation coefficient of tied ranks.

#### 11.  Regression

Description: These web links contain an introduction to regression.

Core Concepts: Introduction of regression.

Description: These web links contain concepts and applications of regression.

Core Concepts: Utility and scope.

Description: This video contains the formation of regression line y on x.

Core Concepts: Regression line y on x.

#### 12. Probability

Description: This web link contains an introduction of probability.

Core Concepts: Introduction of probability.

Description: This web link includes application of probability.

Core Concepts: Utility and scope.

Description: This video contains an explanation  of addition rule with examples.

Description: This video contains explanation  of the multiplication rule with examples.

Core Concepts: Multiplication rule.

Description: This web link contains problem solving using both addition and multiplication rule.

Core Concepts: Addition and multiplication rule.

Description: This video contains calculating probability through the concepts of permutation and combination.

Core Concepts: Probability using permutation and combination.

Description: These videos contains examples on calculating probability using permutation.

Core Concepts: Probability using permutation.

Description: These videos and web link contain  methods, utility and scope of conditional probability.

Core Concepts: Conditional probability.