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.

Links: 

2. Addition of Matrices

Description: The web link contains a worksheets and addition of matrices.

Core Concepts: 12P-A1 Matrix.

Links:

3. Properties of Addition

Description: A video contains properties of matrix addition.

Core Concepts: 12P-A1 Matrix.

Link: Video on properties of matrix addition

4. Properties of Multiplication

Description: A video contains properties of multiplication.

Core Concepts: 12P-A1 Matrix.

Link: Video on properties of multiplication

5. Matrix Transpose

Description: A video contains transpose of a matrix.

Core Concepts: 12P-A1 Matrix.

Link: Video on transpose of a 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.

Links:

7. Adjoint of Matrix

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

Core Concepts: 12P-A1 Matrix.

Link: Video on how to find the inverse of matrix 2x2

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

Core Concepts: 12P-A1 Matrix.

Link: Webpage on the inverse of matrix 2x2

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

Core Concepts: 12P-A1 Matrix.

Link: Webpage on the adjoint of matrix 2x2

8. Inverse of Matrix

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

Core Concepts: 12P-A1 Matrix.

Link: Video on how to find the inverse of matrix 3x3

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

Core Concepts: 12P-A1 Matrix.

Link: Webpage on the inverse of matrix 3x3

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.

Link: Video on how the formula for future value is generated

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

Core Concepts: 12B-A2 Annuity.

Link: Video on future value for immediate annuity with examples

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

Core Concepts: 12B-A2 Annuity.

Link: Video on future value of annuity due with an examples

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.

Link: Video on how to find the installment needed to be deposited to have a certain future value

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.

Link: Video on relation between future and present value derives the formula for present value

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.

Link: Video on present value of a perpetual annuity with an example

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.

Link: Video on present value of a perpetual annuity with an example

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

Core Concepts: 12B-A2 Annuity.

Link: Video on present value of an annuity due with two examples

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.

Link: PPT on defining different terms and different types of annuities

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

Core Concepts: 12B-A2 Annuity.

Links:

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

Core Concepts: 12B-A2 Annuity.

Links:

10. Discount

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

Core Concepts: 12B-A3 Discount.

Link: Webpage on 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.

Link: Webpage on 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.

Links: 

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

Core Concepts: 12B-A3 Discount.

Links: 

11.  Counting Rule

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

Core Concepts: 12B-A3 Permutation and combination. 

Link: Video on fundamental principle of counting

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. 

Link: Video on methods to calculate permutation

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. 

Link: Video on formation of number

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

Core Concepts: 12B-A3 Permutation and combination.

Link: Video on arrangement of people on chairs

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

Core Concepts: 12B-A3 Permutation and combination. 

Link: Video on forming of anagram

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

Core Concepts: 12B-A3 Permutation and combination. 

Link: Video on circular permutations with examples

13. Combination

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

Core Concepts: 12B-A3 Permutation and combination. 

Link: Video on different method to calculate combinations

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. 

Link: Video on selection of a  group of boys and girls

14. Combination and Permutation

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

Core Concepts: 12B-A3 Permutation and combination 

Link: PDF on combination and permutation

15. General Understanding on Derivative

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

Core Concepts: 12B-B1 Differentiation.

Link: Video on what is derivative

16. Algebraic Differentiation

Description: The weblink contains video on derivatives using difference quotient 

Core Concepts: 12B-B1 Differentiation.

Link: Video on derivatives using different quotient

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

Core Concepts: 12B-B1 Differentiation.

Link: Video on derivatives using chain rule 

Description: The weblink contains video on derivatives of constant.

Core Concepts: 12B-B1 Differentiation.

LinkVideo on derivatives of constant 

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

Core Concepts: 12B-B1 Differentiation.

LinkVideo on derivatives using quotient rule  

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

Core Concepts: 12B-B1 Differentiation.

LinkVideo on derivative using product rule

17. Implicit Derivative

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

Core Concepts: 12B-B1 Differentiation.

Link: Video  on  Implicit Differentiation

18. Parametric Derivative

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

Core Concepts: 12B-B1 Differentiation.

Link: Video on parametric of functions

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.

Link: Video on function with respect to other functions

20. Successive Differentiation

Description: The weblink contains video on successive differentiation 

Core Concepts: 12B-B1 Differentiation.

Links:

21. Condition for Maxima and Minima

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

Core Concepts: 12B-B1 Differentiation.

Link: Webpage on second condition for maxima and minima

22. Introduction of Point of Inflexion

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

Core Concepts: 12B-B1 Differentiation. 

Link: Video on introduction of point of inflexion

23. The Point of Inflexion

Description: The weblink contains point of inflexion video graphically.

Core Concepts: 12B-B1 Differentiation.

Link: Video on graphically

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

Core Concepts: 12B-B1 Differentiation.

Link: Webpage on point of inflexion

Description: The link contains practice question points of inflexion.

Core Concepts: 12B-B1 Differentiation

Link: Webpage on practice question points of inflexion

24. Maxima and Minima

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

Core Concepts: 12B-B1 Differentiation.

Links:

25. Application Derivatives

Description: The contains the application of derivatives.

Core Concepts: 12B-B1 Differentiation. 

Link: Video on application of derivatives

26. Integration

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

Core Concepts: 12B-B2 Integration.

Link: Video on basic integral rules for algebraic and trigonometric functions

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

Core Concepts: 12B-B2 Integration.

Link: Video on substitution method for simple algebraic and trigonometric functions

27. Integration

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

Core Concepts: 12B-B2 Integration.

Link: PPT on partial fraction decompositions

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

Core Concepts: 12B-B2 Integration.

Link: Video on explaining an example of integration using partial fractions

28. Applications of Calculus

Description: pdf. file Application of calculus in Commerce and Economics .

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

Link: PDF on 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. 

Link: Video on function and break-even analysis with examples

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

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

Link: Video on revenue, cost and profit function with solved problem

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

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

Link: Video on marginal and break even analysis with examples

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. 

Link: Video on explaining a point in 3D-coordinate system

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.

Link: Video on explaining the distance formula in 3D space

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.

Link: Webpage on section formula with solved examples and practice questions and quiz

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

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

Link: Webpage on direction cosines and direction ratios

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.

Link: Video on introduction of direction cosines and direction ratios

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.

Link: Webpage on different conic section formed

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

Core Concepts: 12B-CD2 Conic sections.

Link: Video on explaining conics on a circular cone

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.

Link: Webpage on geogebra worksheet

Description: The web link contains video introducing parabolas.

Core Concepts: 12B-CD2 Conic sections.

Link: Video on introducing parabolas

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.

Link: Video on finding focus, directrix, eccentricity, latus rectum and axes 

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.

Link: Video on finding focus, directrix, eccentricity, latus rectum and axe

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.

Link: Webpage on standard form of parabola

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.

Link: Video on solving example on finding focus, directrix, eccentricity, latus rectum and axes

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.

Link: Video on solving example on finding focus, directrix, eccentricity, latus rectum and axes

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on calculator for equation of parabola

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

Core Concepts: 12B-CD2 Conic sections.

Link: Video on solving an example when a general equation of parabola is given

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.

Link: Webpage on geogebra worksheet

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

Core Concepts: 12B-CD2 Conic sections.

Link: Video on introducing ellipse and its components

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

Core Concepts: 12B-CD2 Conic sections.

Link: Video on introducing hyperbola and explain its components

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on chart with summary of the properties of different conics

 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.

Links:

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

Core Concepts: 12B-CD2 Conic sections.

Links:

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on online calculator for the equation of ellipse

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

Core Concepts: 12B-CD2 Conic sections.

Links:

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on online calculator for equation of hyperbola

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on geogebra worksheet on parabola

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on geogebra worksheet on ellipse

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

Core Concepts: 12B-CD2 Conic sections.

Link: Webpage on geogebra worksheet on hyperbola

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.

Link: Video on explaining the correlation between two variable with the use of scatter plot

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.

Link: Video on use of covariance to find karl pearson's coeffiecient of correlation

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

Core Concepts: 12B-E1 Correlations.

Link: Video on solving an example using the formula of spearman's rank correlation coefficient

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

Core Concepts: 12B-E1 Correlations.

Link: PDF on compare between pearson's and spearman's correlation coefficient

32. Regression

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

Core Concepts: 12B-E2 Correlations.

Link: Video on explaining a regression of Y on X

33. Probability: Pre Assessment Permutation and Combination

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

Core Concepts: 12B-E3 Probability.

Link: Video on concept of permutation and combination

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.

Link: Video on concept of calculating probability using permutation and combination

35. Probability (Permutation)

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

Core Concepts: 12B-E3 Probability.

Links:

36. Probability (combination)

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

Core Concepts: 12B-E3 Probability.

Links:

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.

Link: Video on concept on the addition rule of probabilities

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 .

Link: Video on finding probabilities dependent and independent events

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.

Link: Video on understanding the concepts on multiplication theorem on probability

40. Probability (Conditional)

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

Core Concepts: 12B-E3 Probability.

Link: Video on conditional probability

41. Probability (Notes on Conditional)

Description: The weblink contains notes and video lessons on conditional probability.
Core Concepts: 12B-E3 probability
Link: Webpage on conditional 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.

Link: Video on multiplication theorem o dependent probability

43. Probability (Combination and Permutation)

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

Core Concepts: 12B-E3 Probability.

Link: Webpage on finding probability using combination and permutation