# 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. Matrices

Description: This video contains the history of matrices.

Core Concepts: History of matrices.

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

Core Concepts: Utility and Scope of Matrix.

Description: This web link contains a worksheet on  addition and subtraction of matrices.

Core Concepts: Addition and subtraction of matrices.

Description: This web link contains a worksheet on matrix multiplications.

Core Concepts: Multiplication of matrices.

Description: This video contains the properties of matrix multiplication.

Core Concepts: Properties of matrix multiplication.

Description: This video contains finding transpose of a matrix.

Core Concepts: Transpose of matrices.

Description: This video contains finding adjoints of matrices.

Core Concepts: Adjoint of Matrices.

Description: This video contains finding the inverse of a 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 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.

Description: This web link contains sample word problems.

Core Concepts: Sample question on  matrices.

#### 2. Complex Number

Description: This webpage contains an introduction and history of complex numbers.

Core Concepts: Introduction on complex number.

Description: These web pages contain explanations of  the utility and scope of learning complex numbers in various fields.

Core Concepts: Utility and scope on complex number.

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Description: This video contains  modulus of complex numbers.

Core Concepts: Modulus of complex number.

Description: This video contains properties of complex numbers..

Core Concepts: Properties of modulus of complex numbers.

Description: This video contains arguments of complex numbers.

Core Concepts: Argument of complex number.

Description: This video contains an explanation of conversion of complex numbers from cartesian to polar form.

Core Concepts: Polar form of complex number.

Description: This web link contains sample questions on polar form.

Core Concepts: Sample question on polar form.

Description: This web page contains the locus of complex numbers.

Core Concepts: Locus of  complex number.

Description: This video contains square roots of complex numbers.

Core Concepts: Square roots  of  complex number.

Description: This web page contains the cube root of unity.

Core Concepts: Cube roots of unity.

Description: This web link contains MCQ on the polar form of complex numbers.

Core Concepts: Multiple choice questions on polar form.

Description: This web link contains solved examples of the locus of complex numbers.

Core Concepts: Solved examples on locus of complex number.

#### 3. Combination and Permutation

Description: These web links contain history and introduction of combination and permutation.

Core Concepts: Introduction of permutation and combination.

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Description: This web link contains real life applications of permutation and combination.

Core Concepts: Utility and scope of permutation and combination.

Description: This video contains the fundamental principle of counting.

Core Concepts: Fundamental principle of  counting.

#### 4. Permutation

Description: This video contains forming numbers using digits with and without repetition of digits.

Core Concepts: Formation of numbers.

Description: This video contains arranging people.

Core Concepts: Arranging people.

Description: This video contains forming words using letters..

Core Concepts: Forming words.

Description: This video contains a circular permutation.

Core Concepts: Circular permutation.

#### 5. Combination

Description: This video contains combinations.

Core Concepts: Combination.

Link: Video on combination

Description: This video contains problem solving using combinations.

Core Concepts: Problem solving using combination.

#### 6. Derivatives

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

Core Concepts: Introduction and history of derivative.

Description: This web link contains the application of derivatives.

Core Concepts: Utility and scope learning derivative.

Description: This video contains derivatives of algebraic and trigonometric functions using chain rule.

Core Concepts: Chain rule.

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Description: This web link contains derivatives of composite functions.

Core Concepts: Derivative of composite function.

Description: These videos contain derivatives of exponential,  inverse trigonometric functions and logarithmic differentiation.

Core Concepts: Derivative of exponential,  inverse trigonometric functions and logarithmic differentiation.

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Description: This video contains differentiation by using a transformation method.

Core Concepts: Differentiation by transformation method.

Description: This video contains derivatives of implicit function.

Core Concepts: Derivative of implicit  type of functions.

Description: This video contains derivatives of parametric function.

Core Concepts: Derivative of parametric function.

Description: This video contains higher order derivatives of function.

Core Concepts: Higher order derivatives functions.

Description: This video contains maxima, minima and point of inflection.

Core Concepts: Maxima, minima and point of inflection.

Description: This video contains identifying minima, maxima and point of inflection.

Core Concepts: Identifying maxima, minima and point of inflection.

Description: These web links contain a worksheet on differentiation of exponential and logarithmic function.

Core Concepts: Sample questions on differentiation.

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#### 7. Integration

Description: This video contains history of integration.

Core Concepts: History of integration.

Description: These videos contain real life applications of integration.

Core Concepts: Utility and scope of integration.

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Description: This video contains integration of trigonometric functions.

Core Concepts: Integration of trigonometric functions.

Description: This video contains problem solving on integration using the substitution method.

Core Concepts: Integration by substitution method.

Description: This video contains integration of exponential functions using the substitution method.

Core Concepts: Integration of exponential function using substitution method.

Description: This video contains problem solving on integration of  trig function using the integration by parts.

Core Concepts: Integration by parts.

Description: This PPT and video contain integration using partial fraction.

Core Concepts: Integration by partial fraction methods.

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#### 8. Definite Integral

Description: This web link contains concepts on definite integrals.

Core Concepts: Concepts on definite integral.

Description: This video contains evaluating integration as a limit of sum.

Core Concepts: Definite integral as limit of sum.

Description: This video contains a geometrical interpretation of definite integral.

Core Concepts: Geometrical interpretation of definite integral.

Description: This video contains properties of definite integral.

Core Concepts: Properties of definite integral.

Description: This video contains area bounded between curve and axes.

Core Concepts: Area under the curve.

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Description: This video explains finding the area between two curves.

Core Concepts: Area between two curves.

Description: This web link contains practice questions on areas bounded by curves.

Core Concepts: Practice questions on area bounded by curves.

Description: This web link contains sketching curves using GeoGebra.

Core Concepts: Sketching curves using GeoGebra.

Description: This web link contains an animation of the solid of revolution using GeoGebra.

Core Concepts: Volume of solid of revolution by using GeoGebra.

Description: These videos contain finding the volume of revolution of a region between curve and axes.

Core Concepts: Volume of revolution of region between curve and axes.

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Description: This video contains finding the volume of solid of revolution of the region between two curves.

Core Concepts: Volume of solid of revolution of region between two curves.

Description: This web link contains the formation of cones by a revolving line.

Core Concepts: Revolving line using GeoGebra.

Description: This web link contains solved examples on volume of the solid of revolution.

Core Concepts: Solved examples on volume of solid of revolution.

#### 9. Differential Equation

Description: This pdf file contains the history of differential equations.

Core Concepts: History of differential equation.

Description: These videos contain definition and examples of order and degree of DE.

Core Concepts: Order and degree of differential equation.

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Description: This video contains difference  between linear and non-linear DE.

Core Concepts: Difference between linear and non-linear DE.

Description: These videos contain solving DE using variable separable methods.

Core Concepts: Solving DE using variable separable method.

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Description: This video and web link contains solving homogeneous DE.

Core Concepts: Homogeneous differential equation.

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Description: This video contains solving first order linear DE using the integrating factor method.

Core Concepts: Solving first order linear DE using integrating factor method.

#### 10. Inverse Trigonometric Functions

Description: This web link contains an introduction of the inverse trigonometric function.

Core Concepts: Introduction of inverse trigonometric function.

Description: This web link contains applications of inverse trigonometric function.

Core Concepts: Utility and scope  on inverse trigonometric function.

Description: This video contains the definition, domain, range and  principal value of inverse trigonometric function.

Core Concepts: Definition, domain and range of inverse trigonometric functions.

Description: This web link contains the principal value of the inverse trigonometric function.

Core Concepts: Principal value of inverse trigonometric function.

Description: This web link contains properties of inverse trigonometric function.

Core Concepts: Properties of inverse trigonometric function.

Description: This web link contains solved sample questions.

Core Concepts: Solved sample questions.

Description: This web link contains a quiz on inverse trigonometric functions.

Core Concepts: Quiz

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

Description: This web link contains 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 of 3-D geometry.

Core Concepts: Introduction of 3-D geometry.

Description: This video contains a derivation  of the distance formula.

Core Concepts: Derivation of distance formula.

Description: These videos contain explanations of  section formulas.

Core Concepts: Section formula.

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Description: These videos contain direction cosines and ratios.

Core Concepts: Direction cosines and direction ratios.

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

Core Concepts: Parallelism and perpendicularity of lines.

#### 12. Pair of Straight Lines

Description: This web link contains the history of straight lines.

Core Concepts: History of straight lines.

Description: This web link contains an introduction of a pair of straight lines.

Core Concepts: Introduction of paris of straight lines.

Description: This video and web link contains an application of a pair of straight lines.

Core Concepts: Utility and scope of pairs of straight lines.

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Description: This video contains basic concepts of straight lines.

Core Concepts: Concepts of the straight lines.

Description: This  web link contains a GeoGebra sheet of a pair of straight lines.

Core Concepts: Graphing calculator of general equation.

Description: This video contains angles between lines..

Core Concepts: Angles between lines.

Description: This video contains conditions and examples for  general second degree form to represent pair of  straight lines.

Core Concepts: Conditions for general second degree form to represent pair of  straight lines.

Description: This video contains equation of bisector of the angles for the general equation of the pair of straight lines.

Core Concepts: Equation of bisector.

Description: This video contains the splitting of a pair of straight lines.

Core Concepts: Pairs of of  straight lines from second degree.

Description: This web link contains problems and solutions of a pair of straight lines.

Core Concepts: Questions and solutions on pairs of straight lines.

#### 13. Conic Section

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

Core Concepts: Introduction of conic section.

Description: This web link and video contains applications of the conic section.

Core Concepts: Utility and scope.

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Description: This web link contains a worksheet on the conic section.

Core Concepts: Conic section exercise.

Description: This video contains the concept on the conic section and its type with examples.

Core Concepts: Concept on the conic section.

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

Core Concepts: GeoGebra worksheet on parabola.

Description: This video contains parts of parabola.

Core Concepts: Parts of  parabola.

Description: This video contains a problem on the application of parabola and focus.

Core Concepts: Parabola and focus application.

Description: This video contains the derivation of the equation of standard parabola.

Core Concepts: Equation of standard parabola.

Description: This web link contains an online parabola calculator.

Core Concepts: Parabola online calculator.

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

Core Concepts: Properties of ellipse.

Description: This web link contains a GeoGebra worksheet of  hyperbola.

Core Concepts: Properties of hyperbola.

Description: This video includes parts of an ellipse.

Core Concepts: Parts of ellipse.

Description: This video includes concepts on hyperbola.

Core Concepts: Concepts on hyperbola.

Description: This web link contains concepts on all types of conic sections.

Core Concepts: Concepts on conic sections.

Description: This video contains an application of an ellipse in an elliptical pool table.

Core Concepts: Ellipse application.

Description: This web link contains notes on application of conic section.

Core Concepts: Application of conics.

Description: This video contains identifying types of conic from the second degree general equation.

Core Concepts: Second degree general equation.

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

Core Concepts: Parabola.

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

Core Concepts: Ellipse.

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

Core Concepts: Hyperbola.

Description: This video contains solving real world problems using parabola.

Core Concepts: Solving problems using parabola.

#### 14. Plane

Description: This web link contains an introduction on planes.

Core Concepts: Introduction.

Description: This web link contains real life applications of planes.

Core Concepts: Utility and Scope.

Description: This video contains the definition of plane.

Core Concepts: Definition of plane.

Description: This video contains finding the angle between two planes.

Core Concepts: Angle between two planes.

Description: This video contains finding the angle between line and plane.

Core Concepts: Angle between line and plane.

Description: This video contains  finding the distance of a point from a plane.

Core Concepts: Distance of point from a plane.

Description: This video contains finding the distance between two parallel planes.

Core Concepts: Distance between two parallel planes.

Description: This video contains reducing the general equation to normal form.

Core Concepts: Reducing the general equation to normal form.

Description: This video contains the definition and equation of the intercept form of the plane.

Core Concepts: Intercepts the form of a plane.

#### 15. 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 value of correlation coefficient.

Core Concepts: Degree of correlation.

Description: This video contains 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.

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#### 15. Regression

Description: These web links contain an introduction of regression.

Core Concepts: Introduction of regression.

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

Core Concepts: Utility and scope.

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

Core Concepts: Regression line y on x.

#### 16. Probability

Description: This video contains an introduction of probability.

Core Concepts: Introduction of probability.

Description: This web link contains an application of probability.

Core Concepts: Utility and scope.

Description: This video contains the concept of addition rule with examples.

Core Concepts: Addition rule.

Description: This video contains the concept of 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.

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

Core Concepts: Probability using permutation.

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

Core Concepts: Conditional probability.

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Description: This web link contains  notes on conditional probability with solved examples.

Core Concepts: Conditional probability.

Description: This web link contains a theorem of multiplication of dependent probability with solved examples.

Core Concepts: Dependent  probability.

Description: This web link contains  practice questions on multiplication probability.

Core Concepts: Multiplication  probability.