# 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. Multiplication of Matrices

Description: The web link contains a worksheets and multiplication of matrices

Core Concepts: 12P-A1 Matrix

Core Concepts: 12P-A1 Matrix

Description: A video contains properties of matrix addition

Core Concepts: 12P-A1 Matrix

#### 4. Properties of Multiplication

Description: A video contains properties of multiplication

Core Concepts: 12P-A1 Matrix

#### 5. Matrix Transpose

Description: A video contains transpose of a matrix

Core Concepts: 12P-A1 Matrix

#### 6. Adjoint of Matrix 2x2

Description: A video contains how to find the adjoint of matrix 2x2 and matrix 3x3

Core Concepts: 12P-A1 Matrix

Description: A video contains how to find the inverse of matrix 2x2

Core Concepts: 12P-A1 Matrix

Description: The web link contains a worksheet on the inverse of matrix 2x2

Core Concepts: 12P-A1 Matrix

Description: The web link contains a worksheet on the adjoint of matrix 2x2

Core Concepts: 12P-A1 Matrix

#### 8. Inverse of Matrix

Description: A video contains how to find the inverse of matrix 3x3

Core Concepts: 12P-A1 Matrix

Description: The web link contains a worksheet on the inverse of matrix 3x3

Core Concepts: 12P-A1 Matrix

#### 9. Annuity

Description: The web link contains a video explaining the meaning of future value and how the formula for future value is generated.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining Future Value for immediate annuity with two examples.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining Future value of annuity due with an example.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video showing an example on how to find the installment needed to be deposited to have a certain future value.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining the relation between future value and present value and derives the formula for present value.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining the meaning of perpetual annuity and its formula to find present value of a perpetual annuity with an example.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining two examples of finding present value for immediate annuity using different methods.

Core Concepts: 12B-A2 Annuity

Description: The web link contains a video explaining the present value of an annuity due with two examples.

Core Concepts: 12B-A2 Annuity

Description: The web link (slide 1 to 10) contains a PowerPoint presentation defining different terms and different types of annuities.
Core Concepts: 12B-A2 Annuity

Description: The web links contain online RD calculators of different banks.

Core Concepts: 12B-A2 Annuity

Description: The web link contains an online EMI calculator of loans for different banks.

Core Concepts: 12B-A2 Annuity

#### 10. Discount

Description: The web link contains a worksheet for students on discount.

Core Concepts: 12B-A3 Discount

Description: The web link contains notes on meaning of trade discount, present value, true discount, banker’s discount , banker’s gain.

Core Concepts: 12B-A3 Discount

Description: The web links contain notes on calculating trade discount, present value, true discount, banker’s discount and banker’s gain.

Core Concepts: 12B-A3 Discount

Description: The web links contain practice questions for Discount and trade discount.

Core Concepts: 12B-A3 Discount

#### 11.  Counting Rule

Description: The web link contains the video explaining the fundamental principle of counting.

Core Concepts: 12B-A3 Permutation and combination

#### 12. Permutation

Description: The link contains video explanations of different methods to calculate permutation of n things taken r at a time.

Core Concepts: 12B-A3 Permutation and combination

Description: The weblink contains a video explaining an example of formation of numbers when repetition is not allowed and when repetition is allowed.

Core Concepts: 12B-A3 Permutation and combination

Description: The weblink contains a video explaining an example of arrangement of people on chairs.

Core Concepts: 12B-A3 Permutation and combination

Description: The weblink contains a video explaining an example of forming anagram (permutation of alike things).

Core Concepts: 12B-A3 Permutation and combination.

Description: The weblink contains a video explaining circular permutations with examples.

Core Concepts: 12B-A3 Permutation and combination

#### 13. Combination

Description: The weblink contains videos explaining different methods to calculate combinations.

Core Concepts: 12B-A3 Permutation and combination.

Description: The web links contain a video explaining an example of selection of a group of boys and girls.

Core Concepts: 12B-A3 Permutation and combination

#### 14. Combination and Permutation

Description: The web links contain worksheet on combination and permutation.

Core Concepts: 12B-A3 Permutation and combination

#### 15. General Understanding on Derivative

Description: The link contains video general understanding of what is derivative.

Core Concepts: 12B-B1 Differentiation

#### 16. Algebraic Differentiation

Description: The weblink contains video on derivatives using difference quotient.

Core Concepts: 12B-B1 Differentiation

Description: The web link contains videos on derivatives using chain rule.

Core Concepts: 12B-B1 Differentiation

Description: The weblink contains video on derivatives of constant.

Core Concepts: 12B-B1 Differentiation

Description: The weblink contains video on derivative using quotient rule.

Core Concepts: 12B-B1 Differentiation

Description: The weblink contains video on derivative using product rule.

Core Concepts: 12B-B1 Differentiation

#### 17. Implicit Derivative

Description: The link contains a video on the derivative of implicit function.

Core Concepts: 12B-B1 Differentiation

#### 18. Parametric Derivative

Description: The link contains derivatives of the parametric of functions.

Core Concepts: 12B-B1 Differentiation

#### 19. Differentiation of Function with Another Function

Description: The weblink contains a video lesson, the procedures and steps involved differentiating function with respect to other functions.

Core Concepts: 12B-B1 Differentiation

#### 20. Successive Differentiation

Description: The weblink contains video on successive differentiation

Core Concepts: 12B-B1 Differentiation

#### 21. Condition for Maxima and Minima

Description: The link contains the notes second condition for maxima and minima.

Core Concepts: 12B-B1 Differentiation

#### 22. Introduction of Point of Inflexion

Description: The link contain the video on introduction of point of inflexion.

Core Concepts: 12B-B1 Differentiation

#### 23. The Point of Inflexion

Description: The weblink contains point of inflexion video graphically.

Core Concepts: 12B-B1 Differentiation

Description: The weblink contains worksheet on the point of inflexion.

Core Concepts: 12B-B1 Differentiation

Description: The link contains practice question points of inflexion.

Core Concepts: 12B-B1 Differentiation

#### 24. Maxima and Minima

Description: Link contains an application of derivatives in algebraic problems.

Core Concepts: 12B-B1 Differentiation

#### 25. Application Derivatives

Description: The contains the application of derivatives.

Core Concepts: 12B-B1 Differentiation

#### 26. Integration

Description: link contains a video on basic integral rules for algebraic and trigonometric functions.

Core Concepts: 12B-B2 Integration

Description: link contains a video on substitution method for simple algebraic and trigonometric functions.

Core Concepts: 12B-B2 Integration

#### 27. Integration

Description: The weblink contains a power point presentation on partial fraction decompositions.

Core Concepts: 12B-B2 Integration

Description: The weblink contains video explaining an example of integration using partial fractions (non-repeated linear factor).

Core Concepts: 12B-B2 Integration

#### 28. Applications of Calculus

Description: The document explains the application of calculus in Commerce and Economics.

Core Concepts: 12B-B3 Application of calculus in Commerce and Economics

Description: Explains about functions and break-even analysis with the examples.

Core Concepts: 12B-B3 Application of calculus in Commerce and Economics

Description: Defines about revenue function, cost function and profit function with solved problem.

Core Concepts: 12B-B3 Application of calculus in Commerce and Economics

Description: Discusses about marginal and break even analysis with the examples.

Core Concepts: 12B-B3 Application of calculus in Commerce and Economics

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

Description: The web link contains a video explaining a point in 3D-coordinate system.

Core Concepts: 12B-CD1 Points and their coordinates in 3-dimensions.

Description: The web link contains a video explaining the distance formula in 3D space.

Core Concepts: 12B-CD1 Points and their coordinates in 3-dimensions.

Description: The web link contains notes on Section formula with solved examples and practice questions and quiz.

Core Concepts: 12B-CD1 Points and their coordinates in 3-dimensions.

Description: The weblink contains the concept of Direction cosines and direction ratios.

Core Concepts: 12B-CD1 Points and their coordinates in 3-dimensions.

Description: The web link contains a video on the introduction of direction cosines and direction ratios.

Core Concepts: 12B-CD1 Points and their coordinates in 3-dimensions.

#### 30. Conic Section

Description: The web link contains a GeoGebra worksheet on different conic sections formed when plane cutting the double-napped cone is inclined at different angles.

Core Concepts: 12B-CD2 Conic section

Description: The web link contains a video explaining conics on a circular cone.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a GeoGebra worksheet where one can manipulate the focus and directrix and to check the points on parabola; to help students visualize a parabola as locus of points equidistant from a fixed point, focus and fixed line, directrix.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video introducing parabolas.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video on finding focus, directrix, eccentricity, latus rectum and axes of standard form of right-handed parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video on finding focus, directrix, eccentricity, latus rectum and axes of standard form of downward parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains the summary table of standard form of parabola, solved problems and quiz to check students’ understanding.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video solving example on finding focus, directrix, eccentricity, latus rectum and axes for a given standard form of parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video solving example on finding focus, directrix, eccentricity, latus rectum and axes for a given standard form of parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains calculator for equation of parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video solving an example when a general equation of parabola is given.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a GeoGebra worksheet to allow students to visualize how ellipse changes when the components change and vice versa.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video introducing ellipse and its components:

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains video introducing hyperbola and explains its components:

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a chart with summary of the properties of different conics.

Core Concepts: 12B-CD2 Conic sections

Description: The web links contain videos solving example questions on finding the equation of parabola in standard form when condition(s) are given.

Core Concepts: 12B-CD2 Conic sections

Description: The web links consist of video lessons introducing and solving questions on Ellipse in standard form.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contain online calculator for the equation of ellipse.

Core Concepts: 12B-CD2 Conic sections

Description: The web links consist of video lessons introducing and solving questions on Hyperbola in standard form.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains online calculator for equation of hyperbola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a GeoGebra worksheet on parabola.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a GeoGebra worksheet on ellipse.

Core Concepts: 12B-CD2 Conic sections

Description: The web link contains a GeoGebra worksheet on hyperbola.

Core Concepts: 12B-CD2 Conic sections

#### 31. Correlation

Description: The web link contains a video explaining the correlation between two variables with the use of scatter plot.

Core Concepts: 12B-E1 Correlations

Description: The web link contains a video on use of covariance formula to find Karl Pearson’s coefficient of correlation.

Core Concepts: 12B-E1 Correlations

Description: The web link contains a video solving an example using the formula of Spearman’s rank correlation coefficient.

Core Concepts: 12B-E1 Correlations

Description: The web link contains an article to compare between Pearson’s and Spearman’s correlation coefficient.

Core Concepts: 12B-E1 Correlations

#### 32. Regression

Description: The web link contains a video explaining a regression of y on X.

Core Concepts: 12B-E2 Correlations

#### 33. Probability: Pre Assessment Permutation and Combination

Description: The weblink contains video on concept of permutation and combination .

Core Concepts: 12B-E3 Probability

#### 34. Probability (Permutation and Combination)

Description: The weblink contains lesson on the concepts of calculating probability using permutation and combination.

Core Concepts: 12B-E3 Probability

#### 35. Probability (Permutation)

Description: The weblink contains notes on calculating probability using permutation.

Core Concepts: 12B-E3 Probability

#### 36. Probability (combination)

Description: The weblink contains notes on calculating probability using combination.

Core Concepts: 12B-E3 Probability

#### 37. Probability (Addition Rule of Probabilities)

Description: The weblink which contains a lesson on building the concepts on the addition rule of probabilities.

Core Concepts: 12B-E3 Probability

#### 38. Probability (Dependent and Independent)

Description: The weblink which contains the concepts with examples on finding probability dependent and independent events .

Core Concepts: 12B-E3 Probability

#### 39. Probability (Multiplication Theorem)

Description: The weblink which contains video lessons on understanding the concepts on multiplication theorem on probability.

Core Concepts: 12B-E3 Probability

#### 40. Probability (Conditional)

Description: The weblink which contains a video lesson on conditional probability.

Core Concepts: 12B-E3 Probability

#### 42. Probability (Multiplication Theorem on Dependent Probability)

Description: The weblink contains video lessons on multiplication theorem on dependent probability.

Core Concepts: 12B-E3 Probability

#### 43. Probability (Combination and Permutation)

Description: The weblink contains video finding probability using combination and permutation.

Core Concepts: 12B-E3 Probability