# Pure Mathematics - Class XI 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. Determinants

Description: This web link contains a research paper on Short History on Determinant of a Matrix by Babarinsa Olayiwola.

Core Concepts: Short History of Determinant of a Matrix.

Description: This web link contains the importance of learning determinants, the utility and scope of learning determinants.

Core Concepts: Scope of  Determinants.

Description: The web link contains a video explaining the symbol of the determinant of a matrix, applications of the determinant of a matrix and only square matrices have a determinant.

Core Concepts: Concepts on  Determinants.

Description: This web link to the video contains calculating determinants of order 2 explaining the solving procedures, its steps and methods.

Core Concepts: Determinants of Order 2.

Description: This web link to the video of the determinant of a 3x3 matrix, how to find the determinant of a matrix and steps to find the determinant of a 3x3 matrix.

Core Concepts: Determinants of Order 3.

Description: This web link to the video explains finding minor and cofactor determinants, the difference between minor and cofactor.

Core Concepts: Minor and cofactor of determinants .

Description: These web links explain how to solve a system of equations in two variables using Cramer's rule.

Core Concepts: Solving a system of equations using Cramer’s rule for two variables.

Description: This web link explains how to solve a system of equations in three variables using Cramer's rule.

Core Concepts: Solving a system of equations using Cramer’s rule for three variables.

Description: This link is the sharing of the flow chart on the condition of consistency, its procedures and steps.

Core Concepts: Conditions of consistency.

Description: This web link to the video shares the application of determinants in the area of polygons.

Core Concepts: Finding the area of a triangle.

#### 2. Logarithms

Description: This web link to the video explains how they invented logarithms.

Core Concepts: Introduction on logarithm.

Description: This web link to the web page contains the applications of Logarithms.

Core Concepts: Applications of Logarithms.

Description: This web link to the web page contains a quiz on powers and exponents exploration on exponents laws and their relation with the logarithm.

Core Concepts: Logarithm and exponents laws.

Description: This web link to videos contains the definition of a logarithm and how to convert between exponential notation and logarithmic notation.

Core Concepts: Logarithm - Definition and conversion.

Description: This web link to the web page contains the differences between logarithms and natural logarithms with examples.

Core Concepts: Difference between Logarithms and Natural logarithms.

Description: This web link to the video contains logarithms - changing of base.

Core Concepts: Logarithms - Change of base.

Description: This web link to the video contains properties of logarithms: Power rule, Quotient rule and the product with examples.

Core Concepts: Difference between Logarithms and Natural logarithms.

Description: These web links to the videos contain the proof of the properties of logarithms and its importance in calculating the logarithm functions.

Core Concepts: Properties of logarithms.

Description: This web link to the video contains the use of logarithms in a real-life situation.

Core Concepts: Application of  logarithms.

Description: This web link to the video contains an exponential decay word problem as an example of the use of logarithms in real-life situations.

Core Concepts: Application of  logarithms - exponential decay.

#### 3. Complex Numbers

Description: This web link to the web page contains an Introduction and a brief history of complex numbers.

Core Concepts: Introduction to complex numbers.

Description: These web links to the videos contain the Backstory of complex numbers.

Core Concepts: Introduction to complex numbers.

Description: This web link to the web page contains complex numbers and their applications.

Core Concepts: Complex numbers and their application.

Description: This web link to the video contains the introduction to imaginary numbers, explaining how they differ from real numbers and why there was a need to discover them.

Core Concepts: Introduction to imaginary numbers.

Description: This web link to the video contains the operating powers of imaginary numbers.

Core Concepts: Operating powers of i (imaginary number).

Description: This web link to the web page contains the concept of complex numbers with examples and procedures for solving real and complex numbers.

Core Concepts: Concept of complex numbers.

Description: This web link to the web page contains the concept of complex numbers with general definitions and operations.

Core Concepts: Real and complex numbers.

Description: This web link to the video contains the conjugate of complex numbers and its operation.

Core Concepts: Conjugate of complex numbers.

Description: his web link to the web page contains the summary sheet of understanding the complex numbers with worksheets.

Core Concepts: Worksheets on complex numbers.

Description: This web link to the web page represents the complex numbers in an argand plane including how to find coordinates from complex numbers and how to plot coordinates in a complex plane.

Core Concepts: Complex numbers in the argand plane.

Description: This web link to the video contains the operation of complex numbers.

Core Concepts: Operation of complex numbers.

Description: This web link to the video contains solving equations of complex numbers.

Core Concepts: Solving equations of complex numbers.

#### 4. Binomial Theorem

Description: This web link to the web page contains a brief introduction and history of the binomial theorem.

Core Concepts: Introduction to the binomial theorem.

Description: This web link to the web page contains a how binomial theorem can be applied in real-life.

Core Concepts: Scope on binomial theorem.

Description: These web links to the videos contain the binomial theorem, its definition, the examples and procedures for the solution.

Core Concepts: Introduction to the binomial theorem.

Description: This web link to the video contains Pascal triangle concepts to enhance the concepts on the binomial theorem .

Core Concepts: Pascal's triangle and binomial theorem .

Description: This web link to the video contains the properties of the binomial theorem and how the properties are important in solving the binomial theorem.

Core Concepts: Properties on binomial theorem.

Description: This web link to the video contains a general term of binomial expansion.

Core Concepts: The general term of binomial expansion.

Description: This web link to the video contains an independent term for binomial expansion.

Core Concepts: Independence term of binomial expansion.

Description: This web link to the video contains findings of the middle term with examples.

Core Concepts: The middle term of binomial expansion.

Description: This web link to the video contains finding a coefficient of a particular power of x with the steps and procedures given from the link.

Core Concepts: Finding the coefficient of a particular power of x.

Description: This web link to the web page contains quiz questions on binomial theorem.

Core Concepts: Quiz questions on binomial theorem.

Description: This web link to the video contains the use of binomial theorem in a real-life situation.

Core Concepts: Application of the binomial theorem.

#### 5. Sequences and Series

Description: This web link links to a presentation on a brief introduction to sequences and series.

Core Concepts: Introduction to sequences and series.

Description: This web link to the video contains the difference between sequences and series.

Core Concepts: Difference between Sequence and Series.

Description: This web link to the video contains derivations of Arithmetic Sequence formulas.

Core Concepts: Derivations of arithmetic Progression Formula.

Description: This web link to the Web page which contains arithmetic progression questions with solutions.

Core Concepts: Arithmetic Progression formula.

Description: This link to the Web page contains Arithmetic Progression Practice Problems with solutions and explanations.

Core Concepts: Arithmetic Progression problem examples.

Description: This web link to the video contains the sum of the first n terms of an Arithmetic Sequence.

Core Concepts: Arithmetic Progression formula - the sum of the nth term.

Description: This web link to the video contains an explanation of the geometric sequence.

Core Concepts: Geometric Progression.

Description: This web link to the video contains finding the n term of Geometric Sequence.

Core Concepts: Finding the nth term of GP.

Description: This web link to the video contains Geometric Series, Sum of the first n terms with proof.

Core Concepts: Proof of sum of first n term of GP.

Description: This web link to the video contains the sum of the first n terms of a geometric sequence.

Core Concepts: The sum of the first n terms of GP.

Description: The web link to the video contains the sum of infinite Geometric Series.

Core Concepts: The sum of infinite GP.

Description: This web link to the video contains an explanation of the concept of summation notation.

Core Concepts: Summation notation.

Description: This web link to the video on the sum of the first n natural numbers.

Core Concepts: The sum of n term of natural numbers.

Description: This web link to the video contains the sum of the first n squares or square numbers.

Core Concepts: Squares of natural numbers.

Description: This web link to the web page contains the sum of the Cubes of first n natural Numbers.

Core Concepts: Cube of natural numbers.

#### 6. Remainder and Factor Theorem

Description: This web link to the web page contains a brief introduction to the remainder and factor theorem.

Core Concepts: Introduction to remainder and factor theorem.

Description: This web link to the web page on utility and scope of remainder and factor theorem.

Core Concepts: Utility and scope  on remainder and factor theorem.

Description: This web link to the video contains the relation between the remainder and factor theorem with the example and solution.

Core Concepts: Remainder and factor theorem.

Description: This web link to the web page contains the remainder theorem practise questions with solution.

Core Concepts: Remainder theorem Practice questions.

Description: This web link to the web page contains the application of factors in real-life.

Core Concepts: Application of factors in real-life.

Description: This web link contains a PDF worksheet on remainder and factor theorem.

Core Concepts: Worksheet for remainder and factor theorem.

Description: This web link to the web page contains a research paper on the brief history and introduction of the quadratic equations.

Core Concepts: Introduction to a quadratic equation.

Description: This web link to the video contains a brief history and introduction to the quadratic equations.

Core Concepts: History of quadratic equation.

Description: This web link to the video contains the application of quadratic equation.

Core Concepts: Application of quadratic equation.

Description: This web link to the video contains everyday use of quadratic equations.

Core Concepts: Every day use of quadratic equation.

Description: This web link to the video contains how quadratic equations are used in real-life.

Core Concepts: Utility and scope of quadratic equation.

Description: This web link to the web page has the worksheet on quadratic function.

Core Concepts: Worksheet on quadratic equation.

Description: This web link to the video contains solving quadratic equations using the formula.

Core Concepts: Solving quadratic equations using formula.

Description: This web link to the video contains the nature of roots and the discriminant.

Core Concepts: Nature of roots.

Description: This web link to the web page provides the worksheet  on solving the nature of roots.

Core Concepts: Worksheet on the nature of roots.

Description: This web link to the video contains graphing the quadratic inequality, its methods and strategies.

Core Concepts: Graphing inequality graph.

Description: This web link to the web page provides the worksheet related to quadratic inequalities.

Description: This web link to web page contains the application of partial fractions in real-life.

Core Concepts: Utility and scope  on partial fraction.

Description: This web link to the video contains an introduction to partial fractions.

Core Concepts: Introduction to partial fraction.

Description: This web link to the video contains non-repeated linear factors, its solution and procedures are explained.

Core Concepts: Non-repeated linear  factors.

Description: This web link to the video contains repeated linear factors, and its solution and procedures are explained.

Core Concepts: Repeated linear factors.

Description: This web link to the video contains quadratic linear factors, its solution and procedures are explained.

Description: This web link to the video contains improper fractions with non-repeated linear factors, its solution and procedures are explained.

Core Concepts: Improper fractions with non-repeated linear factors.

Description: This web link to the web page contains worksheets on partial fraction.

Core Concepts: Partial fractions question.

#### 8. Functions

Description: This web link to the web page contains a brief introduction and history of the functions.

Core Concepts: Introduction on functions.

Description: This web link to the video contains definitions, meanings, types and examples of functions.

Core Concepts: Introduction to functions and types of functions.

Description: This web link to the video contains a vertical line test for functions.

Core Concepts: Testing for functions.

Description: This web link to the video contains definitions of functions using mapping notations.

Core Concepts: Mapping notation of functions.

Description: This web link to the web page contains a quiz on functions.

Core Concepts: Functions.

Description: This web link to the video contains concepts regarding piecewise function, its meaning and examples .

Core Concepts: Piecewise functions.

Description: This web link to the video contains finding the value of functions. The methods, examples and a few solutions.

Core Concepts: Function notation.

Description: This web link to the video contains the types and classification of functions.

Core Concepts: Classification functions.

Description: This web link to the video contains an explanation of identity functions.

Core Concepts: Identity  functions.

Description: This web link to the video contains an explanation of the modulus function.

Core Concepts: Modulus Functions.

Description: This web link to the video contains the greatest integer function.

Core Concepts: Greatest integer functions.

Description: This web link to the video contains the concept of even and odd functions with examples.

Core Concepts: Even and odd functions.

Description: This web link to the video lesson contains the inverse function.

Core Concepts: Inverse functions.

Description: This web link to the web page contains the explanation and example of operations on functions.

Core Concepts: Operation of functions.

Description: These web links to the videos contain the differences between domain, co-domain and range of functions.

Core Concepts: Function - Domains and range.

Description: This web link to the video contains how to find the domain for the function.

Core Concepts: Domain of functions.

Description: This web link to the video contains the range of the function.

Core Concepts: Range of the function.

Description: This web link contains worksheet on the domain and a range of functions.

Core Concepts: Worksheet on Domain and range of functions.

#### 9. Limits

Description: This web page link contains a brief introduction and history of the limits.

Core Concepts: Introduction on Limits.

Description: This web link to the video contains the explanation that x tends to a limit.

Core Concepts: Concepts on Limits.

Description: This web link to the video contains right-hand and left-hand limits.

Core Concepts: Right and Left Hand Limits.

Description: These web links to the videos contain checking of the existence of limits with proof.

Core Concepts: Existence of  Limits.

Description: This web link to the video contains the theorem of limits.

Core Concepts: Theorem  of  Limits.

Description: This web link contains limits by direct substitutions.

Core Concepts: Limits by direct substitution.

Description: This web link to the video contains the limits and factors.

Core Concepts: Limit and factorization.

Description: This web link to the video contains the limits by direct rationalisation methods.

Core Concepts: Limits by rationalisation methods.

Description: This web link to the video contains the limits by expansion.

Core Concepts: Limits by expansion methods.

Description: This web link to the video contains an infinity of limits.

Core Concepts: Infinity of limits.

Description: This web link to the video contains the limits of trigonometric functions.

Core Concepts: Trigonometry limits.

Description: These web links to web pages and videos contain definitions and explanations of the continuity of the functions.

Core Concepts: Continuity of the functions.

#### 10. Differentiation

Description: These web links to the video contain the history of calculus.

Core Concepts: Introduction to calculus.

Description: This web link to the web page contains the application on derivatives.

Core Concepts: Utility and scope.

Description: These web links to the videos contain the derivatives of functions .

Core Concepts: Derivatives of function.

Description: This web link contains an introduction to the derivatives using the Geogebra.

Core Concepts: Geometrical interpretation of differentiation.

Description: This web link to the video contains the derivatives of functions using the general method.

Core Concepts: Differentiation of polynomial function.

Description: These web links to the videos contain the differentiation of the functions using the product rule.

Core Concepts: Derivative using product rule.

Description: This web link to videos contains the derivatives of functions using the quotient rule.

Core Concepts: Derivative using quotient rule.

Description: This web link to the video contains the differentiation of trigonometric function.

Core Concepts: Differentiation of trigonometric functions.

Description: This web link to the video contains the application of derivatives like finding equations of tangent and normal, rate measures, etc.

Core Concepts: Application derivatives.

#### 11. Integration

Description: This web link to a PDF containing a brief introduction and history of integral calculus.

Core Concepts: Introduction of integration.

Description: This web page link contains the application of integration in real-life.

Core Concepts: Utility and scope of  integration.

Description: This web link to the video contains the definition of integration, the differences between differentiation and integration.

Core Concepts: Introduction of integration.

Description: This web link to the video contains the integration constant explaining what and why + C.

Core Concepts: Introduction of integration and its constant.

Description: This web link to the video contains a basic standard form of integration with examples.

Core Concepts: Standard of integration.

Description: This web link to the video contains the basic integration rules.

Core Concepts: Basic integration rules.

Description: This web link to the video contains integration of trigonometric function.

Core Concepts: Integrating trigonometric functions.

Description: These web links to the videos and a web page contain concepts and elaboration on the integration by substitution.

Core Concepts: Integration by substitution methods.

#### 12. Trigonometry

Description: This web link to the video contains the history and importance of trigonometry.

Core Concepts: Introduction to trigonometric function.

Description: This web page link contains the importance of learning trigonometric functions, their scope and utility in real-life situations.

Core Concepts: Utility and scope of trigonometric functions.

Description: This web link to the video contains the trigonometric sum and difference identities.

Core Concepts: Trigonometric identities.

Description: These web links to the videos contain derivatives of sum and difference formulas and their examples.

Core Concepts: Addition and subtraction  formula.

Description: This web link to the video contains a derivation of the product formula.

Core Concepts: Product formula.

Description: This web link to the video contains problems based on the transformation formula.

Core Concepts: Transformation formula.

Description: These web links to the videos contain practice questions on transformation formulas to product rules from sum or difference identities.

Core Concepts: Transformation formula  and its derivations.

Description: These web links to the videos contain derivation of the double and half angle formula supported by examples..

Core Concepts: Double and half angle formula .

Description: This web link to web pages shares the practice question on the double and half-angle formula.

Core Concepts: Double and half angle formula .

Description: These web links to videos contain derivations and solving of problems using the triple angle formula.

Core Concepts: Triple  angled formula.

Description: This web page link contains practice questions on compound angle formula.

Core Concepts: Compound angle  formula.

#### 13. Points and their Coordinates in Two-Dimension

Description: This web page contains about eh coordinate geometry focusing on its introduction including a brief introduction on the points and their coordinates in two-dimension.

Core Concepts: Coordinate Geometry: An introduction.

Description: This web page contains some examples of geometry in everyday life.

Core Concepts: Utility and scope of points and their coordinates in two-dimension.

Description: This web link to the video contains what the Cartesian Coordinate system is.

Core Concepts: Cartesian coordinates system.

Description: This web link to the video contains what the cartesian coordinate plane is..

Core Concepts: Cartesian coordinate plane.

Description: This web link to the video contains the derivation of the distance formula.

Core Concepts: Distance between two points.

Description: This web link to the video explains the concept of division and the derivation of the section formula of internal division.

Core Concepts: Section formula: internal.

Description: This web link to the video explains the derivation of the section formula of external division.

Core Concepts: Section formula: external.

Description: This web link to the video explains the deviations of the formula for the centroid formula of the triangle.

Core Concepts: Centroid and incentre of the triangle.

Description: This web link to the video explains how to find the slope for the straight lines.

Core Concepts: The slope of straight lines.

Description: This web link to the video contains findings of the angle between lines.

Core Concepts: Angle between lines.

Description: This web link to the video explains the conditions of parallelism and perpendicularity.

Core Concepts: Condition of parallelism and perpendicularity.

#### 14. Logarithm

Description: The video link contains evaluating logarithm.

Core Concepts: 11P-A2 Evaluating logarithm.

#### 15. The straight Line

Description: The web page contains a PDF to straight lines.

Core Concepts: Introduction to straight lines.

Description: This web page contains the application of straight lines in real-life .

Core Concepts: Utility and scope of straight lines.

Description: This web link to the video explains the slope-intercept form of a straight line.

Core Concepts: Slope intercepts form.

Description: The web link to the video contains a point-slope form of straight lines.

Core Concepts: Point slope form.

Description: This web link to the video contains a two-point form of straight lines.

Core Concepts: Two point form.

Description: This web link to the video contains the normal form equations of straight lines.

Core Concepts: The normal form of the equations.

Description: This web link to the video contains the derivation of intercepts form.

Core Concepts: Intercept form.

Description: This web link to the video contains finding of the distance of a point from a line.

Core Concepts: Distance formula.

Description: This web link to the video contains the finding of the distance between two parallel lines.

Core Concepts: Distance formula.

Description: This web link to the video contains the application of straight lines in the different fields.

Core Concepts: Application of straight lines.

#### 16. The Circle and Its Theorem

Description: This web link provides a video on the definition of a circle.

Core Concepts: Definition of circle.

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

Core Concepts: Concept of circle.

Description: This web link contains a video on the equation of a circle in centre-radius form.

Core Concepts: The equation of a circle in centre-radius form..

Description: This web link contains a video on the equation of a circle in its diameter form.

Core Concepts: The equation of a circle in its diameter form.

Description: This web link contains a video on determining the centre and radius of a circle from a given equation.

Core Concepts: Determining the centre and radius of a circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: a straight line drawn from the centre of a circle to bisect a chord is perpendicular to the chord.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: A straight line, drawn from the centre of a circle perpendicular to a chord, bisects the chord.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: One and only one circle can be drawn through three points not lying in the same straight line.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: Equal chords of a circle are equidistant from the centre; Chords of a circle that are equidistant from the centre are equal.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The angle subtended at the centre by an arc of a circle is double the angle which these subtends at any remaining part of the circumference.

Core Concepts: Theorem on Chords of a Circle.

Description:The web link contains an interactive GeoGebra diagram on the chords of a circle: In a circle, the angle in a semicircle is a right angle.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: Angles in the same segment of a circle are equal.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The opposite angles of a cyclic quadrilateral are supplementary.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: If a side of a cyclic quadrilateral is produced, the exterior angle so formed is equal to the interior opposite angle.

Core Concepts: Theorem on Chords of a Circle.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: The tangent at any point of a circle and the radius through this point are perpendicular to each other.

Core Concepts: Theorem on Tangent Lines and Circles.

Description: The web link contains an interactive GeoGebra diagram on the chords of a circle: If two circles touch each other, the point of contact lies on the straight line joining the centres of two circles.

Core Concepts: Theorem on Tangent Lines and Circles.

#### 17. Measures of Central Tendency

Description: This web link leads to a web page introducing the concept of central tendencies.

Core Concepts: Introduction of central tendencies.

Description: This web link leads to a web page discussing the utility and scope of central tendencies.

Core Concepts: Utility and scope of central tendencies.

Description: These web links contain videos on the meaning of central tendencies.

Core Concepts: Concept of central tendencies.

Description: This web link leads to a video on finding the mean using the shortcut method.

Core Concepts: Finding the mean of data by shortcut method.

Description: This web link contains a video on how to find the mean using the step-deviation method.

Core Concepts: Finding the mean of a data by step-deviation method.

Description: This web link contains a video on finding the central tendencies of simple distribution data.

Core Concepts: Central tendencies of simple distribution.

Description: This web link contains a video on finding the central tendencies of discrete data.

Core Concepts: Central tendencies of discrete data.

Description: This web link contains a video on finding the central tendencies of grouped data.

Core Concepts: Central tendencies of grouped data.

Description: This web link contains a video on finding the mode of grouped data.

Core Concepts: Finding the mode of grouped data.

#### 18. Dispersion

Description: This web link contains a video on measuring the dispersion of data using standard deviation.

Core Concepts: Measuring the dispersion of data using standard deviation.

Description: This web link contains a video on finding the combined mean.

Core Concepts: Finding combined mean.

#### 19. Probability

Description: This web link leads to a web page detailing the history of probability.

Core Concepts: Introduction and history of probability.

Description: This web link contains a web page detailing the utility and scope of probability.

Core Concepts: Utility and scope of probability.

Description: This web link contains a video on the introduction of probability.

Core Concepts: Probability concepts.

Description: These web links contain videos on set theory concepts.

Core Concepts: Set theory.

Description: This web link provides a video on the probability of complementary events.

Core Concepts: Probability of complementary events.

Description: This web link contains a video on the odds vs probability.

Core Concepts: Odds and Probability.

Description: This web link contains a web page with interactive questions on probability.

Core Concepts: Interactive Probability questions.

Description: These web links contain videos on the “addition rule” of probability.

Core Concepts: Addition rule of probability.

Description: This web link leads to a web page with some probability questions.

Core Concepts: Application of addition rule in probability..