# Pure 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 worksheet on multiplication of matrices.

Core Concepts: 12P-A1 Multiplication of matrices.

Core Concepts: 11P-A1 Addition of matrices.

Description: A video contains addition of matrices

Core Concepts: 12P-A1 Addition of matrices.

#### 4. Multiplication of Matrices

Description: A video contains multiplication of matrices.

Core Concepts: 12P-A1 Multiplication of matrices.

#### 5. Multiplication of Matrices

Description: A video contains multiplication of matrices.

Core Concepts: 12P-A1 Multiplication of Matrices.

Description: A video contains properties of matrix addition.

Core Concepts: 12P-A1 Properties of addition.

#### 7. Properties of Multiplication

Description: A video contains properties of multiplication.

Core Concepts: 12P-A1 Properties of multiplication.

#### 8. Matrix Transpose

Description: A video contains transpose of a matrix.

Core Concepts: A video contains transpose of a matrix.

#### 9. Adjoint of Matrix 2x2

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

Core Concepts: 12P-A1 Adjoint of matrix 2x2.

#### 10. Inverse of Matrices

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

Core Concepts: 12P-A1 Inverse of matrix 2x2.

#### 11. Inverse of Matrices

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

Core Concepts: 12P-A1 Inverse of matrix 2x2.

#### 12. Adjoint of Matrix 2x2

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

Core Concepts: 11P-A1 Adjoint of matrix 2x2.

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

Core Concepts: 11P-A1 Adjoint of matrix 3x3.

#### 14. Inverse of Matrices

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

Core Concepts: 12P-A1 Inverse of matrix 3x3.

#### 15. Inverse of Matrices

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

Core Concepts: 12P-A1 Inverse of matrix 3x3.

#### 15. Imaginary Number

Description: These weblink video contains an introduction of concepts of I.

Core Concepts: 12P-A1 Complex number.

#### 16. The Trigonometric or Polar form of a Complex Number

Description: The link video contains concepts of polar of complex number.

Core Concepts: 12P-A1 Complex number.

#### 17. Locus Problem

Description: The video contains locus problem.

Core Concepts: 12P-A1 Complex number.

#### 18. Cubic Roots and its Unity

Description: These link contains concepts of understanding cubic roots and its unity.

Core Concepts: 12P-A1 Complex number.

#### 19. Application of Complex Number

Description: The link contains notes on application of complex number.

Core Concepts: 12P-A1 Complex number.

#### 20. Counting Rule

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

Core Concepts: 12P-A2 Permutation and combination.

#### 21. Permutation

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

Core Concepts: 12P-A2 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.

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

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

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

#### 22. Combination

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

Core Concepts: 12P-A2 Permutation and combination.

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

#### 23. Combination and Permutation

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

Core Concepts: 12P-A2 Permutation and combination.

#### 24. General Understanding on Derivative

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

Core Concepts: 12P-B1 Differentiation.

#### 25. Concepts On Derivatives

Description: The link contains the video lesson on different concepts on derivatives.

Core Concepts: 12P-B1 Differentiation.

#### 26. Algebraic Differentiation

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

Core Concepts: 12P-B1 Differentiation.

Description: The weblink contains video on derivatives of constant.

Core Concepts: 12P-B1 Differentiation.

Description: The weblink contains video on derivative using product rule

Core Concepts: 12P-B1 Differentiation.

#### 27. Logarithmic Differentiation

Core Concepts: 12P-B1 Differentiation.

Description: The weblink contains examples of logarithmic differentiation.

Core Concepts: 12P-B1 Differentiation.

#### 28. Exponential Function

Description:  The weblink contains understand the concepts use the PowerPoint presentation on differentiating exponential functions.

Core Concepts: 12P-B1 Differentiation.

#### 29. The Derivative of Inverse Trigonometric Functions

Description:  The video shows how to find the derivatives of the inverses of trigonometric functions by using implicit differentiation

Core Concepts: 12P-B1 Differentiation.

#### 30. The Derivative of Inverse Trigonometric Functions

Description:  The weblink contains video alternative proving the fact or identity.

Core Concepts: 12P-B1 Differentiation.

#### 31. Derivative of Implicit Function

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

Core Concepts: 12P-B1 Differentiation.

#### 32. Parametric Derivative

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

Core Concepts: 12P-B1 Differentiation.

#### 33. 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: 12P-B1 Differentiation.

#### 34. Successive Differentiation

Description:  The weblink contains video on successive differentiation.

Core Concepts: 12P-B1 Differentiation.

#### 35. Condition for Maxima and Minima

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

Core Concepts: 12P-B1 Differentiation.

#### 36. Introduction of Point of Inflexion

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

Core Concepts: 12P-B1 Differentiation.

#### 37. Point of Inflexion

Description:  The weblink contains point of inflexion video graphically.

Core Concepts: 12P-B1 Differentiation.

#### 38. The point of Inflexion

Description:  The weblink contains worksheet on the point of inflexion

Core Concepts: 12P-B1 Differentiation.

#### 39. Turning Point

Description:  The link contains the video checking point of inflexion.

Core Concepts: 12P-B1 Differentiation.

#### 40. Point of Inflexion

Description:  The link contains practice question points of inflexion.

Core Concepts: 12P-B1 Differentiation.

#### 41. Critical Point

Description:  The link contains practice questions from finding critical point.

Core Concepts: 12P-B1 Differentiation.

#### 42. Maxima and Minima

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

Core Concepts: 12P-B1 Differentiation.

#### 43. Application of Derivatives

Description:  The weblink contains an application derivatives

Core Concepts: 12P-B1 Differentiation.

44. Maxima and Minima in Geometrical Figure

Description:  Link contains an application of derivatives of the geometrical figure.

Core Concepts: 12P-B1 Differentiation.

#### 45. Mensuration

Description:  Link contains a video on the application of derivative, the formulation of maxima and minima.

Core Concepts: 12P-B1 Differentiation.

Description:  Link contains an application of derivative in solving mensuration problem.

Core Concepts: 12P-B1 Differentiation.

#### 46. Application of Derivatives

Core Concepts: 12P-B1 Differentiation.

#### 47. Integration

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

Core Concepts: 12P-B2 Integration.

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

Core Concepts: 12P-B2 Integration.

#### 48. Integration by Substitution

Description: The weblink contains a video explaining integration by method of substitution with examples.

Core Concepts: 12P-B2 Integration.

#### 49. Integration by Parts

Description: The weblink contains a description explaining integration by method by parts.

Core Concepts: 12P-B2 Integration.

#### 50. Integration by Partial Fraction

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

Core Concepts: 12P-B2 Integration.

#### 51. Integration by Partial fraction

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

Core Concepts: 12P-B2 Integration.

#### 52. Definite Integration

Description: The weblink contains notes on definite integration and its properties.

Core Concepts: 12P-B2 Integration.

#### 53. Definite Integral as Limit Sum

Description: The weblink contains a video and explanation of proof of definite integral as the limit of sum.

Core Concepts: 12P-B2 Integration.

#### 54. Definite Integration Application for Finding Area under Curve

Description: The web link contains a video lesson explaining the area under the curve as the limit of sum.

Core Concepts: 12P-B2 Integration.

Description: The weblink contains a video explaining the formula for area under the curve as a definite integral.

Core Concepts: 12P-B2 Integration.

Description: The weblink contains video lessons explaining methods of finding an area bounded by a curve and x-axis.

Core Concepts: 12P-B2 Integration.

Description: The link explains the finding of the area of a region under the x-axis..

Core Concepts: 12P-B2 Integration.

Description: The weblink contains a video explaining how to find the area between the curve and x-axis when regions are both above and below the x-axis.

Core Concepts: 12P-B2 Integration.

#### 55. Application of Definite Integral for Finding Area under Curve

Description: The weblink contains a video explaining how to find the area between the curve and the y-axis.

Core Concepts: 12P-B2 Integration.

Description: The weblink contains a video explaining examples on finding areas defined by two curves.

Core Concepts: 12P-B2 Integration.

Description: The web link contains a GeoGebra worksheet which shows formation of a cone from revolving a line.

Core Concepts: 12P-B2 Integration.

Description: The web link contains a GeoGebra worksheet which shows formation of a vase from revolving a curve.

Core Concepts: 12P-B2 Integration.

Description: The weblink explains the volume of solid of revolution with the help of examples of solid formed by revolving.

Core Concepts: 12P-B2 Integration.

#### 56. Differential Calculus

Description: The weblink contains video lessons on the definition of Differential Equation.

Core Concepts: 12P-B3 Differential Equation.

#### 57. Differential Equation (Order and Degree)

Description: The weblink which contains the concepts on order and degree of differential equation.

Core Concepts: 12P-B3 Differential equation.

#### 58. Differential Equation (Linear and Non-linear)

Description: The weblink contains power-point which define what is linear and nonlinear differential type.

Core Concepts: 12P-B3 Differential equation.

#### 59. Differential Equation (General and Particular Solution)

Description: The weblink contains video on the general and particular solution of the differential education

Core Concepts: 12P-B3 Differential equation.

#### 60. Differential Equation (Variable Separable)

Description: The weblink contains online calculator to calculate.

Core Concepts: 12P-B3 Differential equation.

#### 61. Differential Equation (Homogeneous Equation)

Description: The weblink contains notes on homogeneous equation.

Core Concepts: 12P-B3 Differential equation.

Core Concepts: 12P-B3 Differential equation.

Description: The weblink contains a calculator to check the working solution of the given examples of differential equations.

Core Concepts: 12P-B3 Differential equation.

Description: The weblink contains video for understanding for understanding the concept of equation reducible to a homogenous form.

Core Concepts: 12P-B3 Differential equation.

#### 62. Differential Equation (Solving a Homogeneous Equation)

Description: The weblink contains video lessons giving examples related to the topics.

Core Concepts: 12P-B3 Differential equation.

#### 63. Differential Equation (Linear Equation)

Description: The weblink which contains a video lesson on solving the linear equation of different types of function.

Core Concepts: 12P-B3 Differential equation.

#### 64. Inverse Trigonometric Function (Domain and Range)

Description: The weblink contains a ppt. which discusses the domain and range of the inverse trigonometric functions.

Core Concepts: 12P-C1 Inverse trigonometric function.

#### 65. Inverse Trigonometric Function (Domain and Range)

Description: The weblink contains a ppt. which discusses the domain and range of the inverse trigonometric functions.

Core Concepts: 12P-C1 Inverse trigonometric function.

#### 66. Inverse Trigonometric Function (Principal Value)

Description: The weblink contains a ppt. which discusses the graphs and principal value of inverse trigonometric functions.

Core Concepts: 12P-C1 Inverse trigonometric function.

#### 67. Inverse Trigonometric Function (Definition)

Description: The link contains a video which explains the definition of inverse trigonometric functions and the graphs of inverse t-functions.

Core Concepts: 12P-C1 Inverse trigonometric function.

#### 68. Inverse Trigonometric Function (Properties of Trig Function)

Description: The weblink contains examples on use of different properties of inverse trigonometric functions in questions.

Core Concepts: 12P-C1 Inverse trigonometric function.

#### 69. Inverse Trig Function (Quiz Question)

Description: The weblink contains sample quiz questions related to trig functions

Core Concepts: 12P-C1 Inverse trigonometric function.

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

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

Core Concepts: 12P-D1 Points and their coordinates in 3-dimensions.

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

Core Concepts: 12P-D1 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: 12P-D1 Points and their Coordinates in 3-Dimensions.

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

Core Concepts: 12P-D1 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: 12P-D1 Points and their Coordinates in 3-Dimensions.

#### 71. Pair of Straight Line

Description: The web link contains a video summarizing on the concepts of straight lines

Core Concepts: 12P-D2 Pair of straight lines.

Description: The web link contains a GeoGebra working sheet.

Core Concepts: 12P-D2 Pair of straight lines.

Description: The web link contains a video explaining the angle between the lines and the equation of bisector of angles for the homogeneous equation of a pair of straight lines.

Core Concepts: 12P-D2 Pair of straight lines.

Description: The web link contains a video on the condition for pairs of straight lines with a solved example.

Core Concepts: 12P-D2 Pair of straight lines.

Description: The web link contains notes explaining how to separate the pair of straight line into individual equations with solved examples.

Core Concepts: 12P-D2 Pair of straight lines.

Description: The web link contains different questions and their solutions from pair of straight line.

Core Concepts: 12P-D2 Pair of straight lines.

#### 72. Conic Sections

Description: The web link contains a GeoGebra worksheet on conic sections whereby one can manipulate the graph and conics by changing the angle.

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 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: 12P-D3 Conic sections.

Description: The web link contains video introducing parabolas.

Core Concepts: 12P-D3 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: 12P-D3 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: 12P-D3 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: 12P-D3 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: 12P-D3 Conic sections.

Description: The web link contains calculator for equation of parabola

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 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: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

Description: The web link contains a playlist of videos on Parabola and solving of related problems.

Core Concepts: 12P-D3 Conic sections.

Description: The web link contains a playlist of videos on Ellipse and solving of related problems.

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

Description: The web link contains lessons on hyperbola and related solved problems.

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

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

Core Concepts: 12P-D3 Conic sections.

Description: The web link contains problems and solutions from conic sections.

Core Concepts: 12P-D3 Conic sections.

#### 73. Plane Introduction

Description: The link contains the video lesson on what is a plane in 3-D?

Core Concepts: 12P-D4 plane.

Description: The weblink contains a notes derivation of the general equation of a plane and one point form of the equation of the plane.

Core Concepts: 12P-D4 plane.

Description: The weblink contains video lessons on concept and derivation of general equation of a plane.

Core Concepts: 12P-D4 plane.

#### 74. Plane (Equation of Plane)

Description: The weblink contains video on equation of plane.

Core Concepts: 12P-D4 plane.

#### 75. Plane (Normal Form of Equation of Plane)

Description: The weblink contains video lesson on the concepts of normal form of the equation of a plane

Core Concepts: 12P-D4 plane.

#### 76. Plane (Condition of Equation of Plane)

Description: The weblink contains video lessons on finding the equation of a plane with a different condition.

Core Concepts: 12P-D4 plane.

#### 77. Plane (Intercepts Form of Equation of Plane)

Description: The weblink contains video lessons on the intercept form of the equation of a plane with a different condition.

Core Concepts: 12P-D4 plane.

#### 78. Plane (Angle between Plane)

Description: The weblink contains video for finding the angle between two planes.

Core Concepts: 12P-D4 plane.

#### 79. Plane (Angle between Plane)

Description: The weblink contains video for finding the angle between two planes.

Core Concepts: 12P-D4 plane.

Description: The weblink contains the supplement in understanding the concepts of the angle between two planes.

Core Concepts: 12P-D4 plane.

#### 80. Plane (Calculator)

Description: The web link contains a calculator to calculate questions.

Core Concepts: 12P-D4 plane.

#### 80. Plane (Angle between Line and Plane)

Description: The weblink contains video to understand the concepts and explore angle between plane and line.

Core Concepts: 12P-D4 plane.

#### 81. Plane (Online Calculator)

Description: The weblink contains online calculator.

Core Concepts: 12P-D4 plane.

#### 82. Plane (Plane under given Condition)

Description: The weblink contains video lesson on finding equation of plane under given condition.

Core Concepts: 12P-D4 plane.

#### 83. Correlation

Description: The web link contains simulator to explain the direction and degree of correlation between two variables and its scatter plot.

Core Concepts: 12-E1 Correlations.

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

Core Concepts: 12-E1 Correlations.

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

Core Concepts: 12-E1 Correlations.

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

Core Concepts: 12-E1 Correlations.

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

Core Concepts: 12-E1 Correlations.

#### 84. Regression

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

Core Concepts: 12P-E2 Regression.

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

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

Core Concepts: 12P-E3 probability.

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

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

Core Concepts: 12P-E3 probability.

#### 87. Probability (Permutation)

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

Core Concepts: 12P-E3 probability.

#### 88. Probability (Combination)

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

Core Concepts: 12P-E4 probability.

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

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

Core Concepts: 12P-E4 probability.

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

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

Core Concepts: 12P-E4 probability.

#### 91. Probability (Multiplication Theorem)

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

Core Concepts: 12P-E4 probability.

#### 92. Probability (Conditional)

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

Core Concepts: 12P-E4 probability.

#### 93. Probability (Notes on Conditional)

Description: The weblink contains notes and video lessons on conditional probability.

Core Concepts: 12P-E4 probability.

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

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

Core Concepts: 12P-E4 probability.

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

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

Core Concepts: 12P-E4 probability. 