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Class X - Mathematics (ICSE)

Class X - Mathematics ICSE for March 2021 Exam.

₹ 5000
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Description Instructor Pre-Requisites Syllabus Reviews Materials Discussion Forum

Description
  • The course is mainly aiming at Class X students who are enrolled in the ICSE syllabus.
  • Enjoying and Learning Maths in a fun and interesting way is the point of attraction of this course.
  • Concept learning sessions are always followed by doubt clearing sessions which will help the student to understand the concepts much better.
  • Homework discussions are conducted as well.
  • One to One doubt clearing sessions are also conducted for every student once in a week as per the requirement.
  • After completing every chapter previous year questions are also discussed which helps the students to understand the type of questions that are appearing on the exams.
What will you learn?
  • The entire Class 10 ICSE Mathematics syllabus is covered in this course along with a lot of previous year questions which will help the student to improve the knowledge and skills in this subject.
  • Mathematical Skills required for Class 11 Students.
  • Basic Mathematical Skills.
  • A Basic understanding of Commercial Mathematics, Algebra, Geometry, Mensuration, Trigonometry, and Statistics.
What knowledge and tools are required?
  • Basic Mathematical Skills
  • A Mobile or Laptop for attending the class
  • Concise Mathematics Class X- Selina Publishers is the main Textbook followed. Other textbooks can also be referred to.
  • A notebook and a Pen for taking notes and doing problems.
Who should take this course?
  • Students who are currently enrolled in Class 10 ICSE.
  • Class 10 ICSE Maths Students.
  • Students who completed ICSE IX Maths.
  • Students who are interested in Basic Mathematical Skills.
Lecture 1 :- Introduction

Understanding the syllabus and Schedule of the sessions.

  • Topics

  1. 1. Introduction to Syllabus
  2. 2. How the sessions or classes are scheduled?
  3. 3. Unit 1: Commercial Mathematics
  4. 4. Unit 2: Algebra
  5. 5. Unit 3: Geometry
  6. 6. Unit 4: Mensuration
  7. 7. Unit 5: Trigonometry
  8. 8. Unit 6: Statistics
Lecture 2 :- GST [ Goods and Services Tax ] - 1

Computation of tax including problems involving discounts, list price, profit, loss, basic/cost price including inverse cases.

  • Topics

  1. 1. Computation of tax
  2. 2. Goods and Services Tax
  3. 3. Definition of Goods/Services
  4. 4. More details about GST
  5. 5. GST Tax Calculation
  6. 6. Example Questions
  7. 7. Practice Questions
Lecture 3 :- GST [ Goods and Services Tax ] - 2

Computation of tax including problems involving discounts, list price, profit, loss, basic/cost price including inverse cases.

  • Topics

  1. 1. Input Tax Credit (ITC)
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 4 :- GST [ Goods and Services Tax ] - 3

Computation of tax including problems involving discounts, list price, profit, loss, basic/cost price including inverse cases.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 5 :- Banking (Recurring Deposit Accounts) - 1

Recurring Deposit Accounts: computation of interest and maturity value using formula

  • Topics

  1. 1. Introduction
  2. 2. Types of Accounts
  3. 3. Recurring Deposit Account (R.D Account)
  4. 4. Computing maturity value of a Recurring Deposit Account
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 6 :- Banking (Recurring Deposit Accounts) - 2

Recurring Deposit Accounts: computation of interest and maturity value using formula

  • Topics

  1. 1. More Questions
  2. 2. Previous Year Questions and Discussion
Lecture 7 :- Shares and Dividends - 1

a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium. b)Formulae

  • Topics

  1. 1. Introduction
  2. 2. Formulae
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 8 :- Shares and Dividends - 2

a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium. b)Formulae

  • Topics

  1. 1. Miscellaneous Problems
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 9 :- Shares and Dividends - 3

a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium. b)Formulae

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 10 :- Linear Inequations (In one variable) - 1

Linear Inequations in one unknown. Algebraically and writing the solution in set notation form. Representation of the solution on the number line.

  • Topics

  1. 1. Introduction
  2. 2. Linear Inequations in One variable
  3. 3. Solving a Linear Inequation Algebraically
  4. 4. Replacement Set and Solution Set
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 11 :- Linear Inequations (In one variable) - 2

Linear Inequations in one unknown. Algebraically and writing the solution in set notation form. Representation of the solution on the number line.

  • Topics

  1. 1. Representation of the solution on the number line
  2. 2. Combining Inequations
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 12 :- Linear Inequations (In one variable) - 3

Linear Inequations in one unknown. Algebraically and writing the solution in set notation form. Representation of the solution on the number line.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 13 :- Quadratic Equations - 1

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Introduction
  2. 2. To Examine Nature of Roots
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 14 :- Quadratic Equations - 2

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Solving Quadratic Equations by factorisation
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 15 :- Quadratic Equations - 3

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Solving Quadratic Equations using the formula
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 16 :- Quadratic Equations - 4

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 17 :- Quadratic Equations - 5

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Problems based on Numbers
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 18 :- Quadratic Equations - 6

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Problems based on Time and Work
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 19 :- Quadratic Equations - 7

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Problems based on Geometrical Figures
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 20 :- Quadratic Equations - 8

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Problems based on Distance, Speed and Time
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 21 :- Quadratic Equations - 9

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Miscellaneous Problems
  2. 2. Practice Questions
Lecture 22 :- Quadratic Equations - 10

a) Nature of roots. b)Solving Quadratic Equations. c)Solving simple Quadratic Equation Problems.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 23 :- Ratio and Proportion - 1

a) Proportion, continued proportion, mean proportion. b)Componendo, dividendo, alternendo, invertendo properties, and their combinations. c) Direct simple applications on proportions only.

  • Topics

  1. 1. Introduction
  2. 2. Ratio
  3. 3. Increase or decrease in a ratio
  4. 4. Commensurable and Incommensurable quantities
  5. 5. Composition of Ratios
  6. 6. Example Questions
  7. 7. Practice Questions
Lecture 24 :- Ratio and Proportion - 2

a) Proportion, continued proportion, mean proportion. b)Componendo, dividendo, alternendo, invertendo properties, and their combinations. c) Direct simple applications on proportions only.

  • Topics

  1. 1. Proportion
  2. 2. Continued Proportion
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 25 :- Ratio and Proportion - 3

a) Proportion, continued proportion, mean proportion. b)Componendo, dividendo, alternendo, invertendo properties, and their combinations. c) Direct simple applications on proportions only.

  • Topics

  1. 1. Some important properties of proportion
  2. 2. Direct Applications
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 26 :- Ratio and Proportion - 4

a) Proportion, continued proportion, mean proportion. b)Componendo, dividendo, alternendo, invertendo properties, and their combinations. c) Direct simple applications on proportions only.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 27 :- Remainder and Factor Theorems - 1

a)Factor theorem. b)Remainder theorem. c)Factorizing a polynomial completely after obtaining one factor by factor theorem.

  • Topics

  1. 1. A Basic Concept
  2. 2. Remainder Theorem
  3. 3. Factor Theorem
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 28 :- Remainder and Factor Theorems - 2

a)Factor theorem. b)Remainder theorem. c)Factorizing a polynomial completely after obtaining one factor by factor theorem.

  • Topics

  1. 1. Using the factor theorem to factorize the given polynomial
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 29 :- Remainder and Factor Theorems - 3

a)Factor theorem. b)Remainder theorem. c)Factorizing a polynomial completely after obtaining one factor by factor theorem.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 30 :- Matrices - 1

a)Order of a matrix. Row and Column matrices. b)Compatibility for addition and multiplication. c)Null and Identity Matrices. d)Addition ad subtraction of 2 x 2 matrices. e)Multiplication of a 2 x 2 matrix by 1) a non zero rational number. 2) a matrix

  • Topics

  1. 1. Matrix
  2. 2. Order of a matrix
  3. 3. Elements of a matrix
  4. 4. Types of matrices
  5. 5. Transpose of a matrix
  6. 6. Equality of matrices
  7. 7. Addition of matrices
  8. 8. Subtraction of matrices
  9. 9. Additive identity
  10. 10. Additive Inverse
  11. 11. Solving Matrix Equations
  12. 12. Example Questions
  13. 13. Practice Questions
Lecture 31 :- Matrices - 2

a)Order of a matrix. Row and Column matrices. b)Compatibility for addition and multiplication. c)Null and Identity Matrices. d)Addition ad subtraction of 2 x 2 matrices. e)Multiplication of a 2 x 2 matrix by 1) a non zero rational number. 2) a matrix

  • Topics

  1. 1. Multiplication of a matrix by a scalar
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 32 :- Matrices - 3

a)Order of a matrix. Row and Column matrices. b)Compatibility for addition and multiplication. c)Null and Identity Matrices. d)Addition ad subtraction of 2 x 2 matrices. e)Multiplication of a 2 x 2 matrix by 1) a non zero rational number. 2) a matrix

  • Topics

  1. 1. Multiplication of matrices
  2. 2. Identity matrix for multiplication
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 33 :- Matrices - 4

a)Order of a matrix. Row and Column matrices. b)Compatibility for addition and multiplication. c)Null and Identity Matrices. d)Addition ad subtraction of 2 x 2 matrices. e)Multiplication of a 2 x 2 matrix by 1) a non zero rational number. 2) a matrix

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 34 :- Arithmetic Progression - 1

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Introduction
  2. 2. Arithmetic progression
  3. 3. General term of an arithmetic progression
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 35 :- Arithmetic progression - 2

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Sum of n terms of an A.P
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 36 :- Arithmetic progression - 3

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Three or more terms in A.P
  2. 2. Arithmetic mean
  3. 3. Properties of an A.P.
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 37 :- Arithmetic progression - 4

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Word problems
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 38 :- Arithmetic progression - 5

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 39 :- Geometric Progression - 1

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Introduction
  2. 2. Geometric Progression
  3. 3. General term of an geometric progression
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 40 :- Geometric Progression - 2

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Properties of an G.P.
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 41 :- Geometric Progression - 3

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Sum of n terms of an G.P
  2. 2. Geometric means between numbers a and b
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 42 :- Geometric Progression - 4

Finding their general term. Finding the sum of their first 'n' terms. Simple applications.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 43 :- Reflection - 1

a)Reflection of a point in a line: x=0, y=0, x=a, y=a, the origin. b)Reflection of a point in the origin. c) Invariant points.

  • Topics

  1. 1. Introduction
  2. 2. Co-ordinates
  3. 3. Reflection
  4. 4. Reflection in the line y=0 i.e. in the axis
  5. 5. Reflection in the line x=0 i.e. in the axis
  6. 6. Reflection in the origin
  7. 7. Invariant point
  8. 8. Example Questions
  9. 9. Practice Questions
Lecture 44 :- Reflection - 2

a)Reflection of a point in a line: x=0, y=0, x=a, y=a, the origin. b)Reflection of a point in the origin. c) Invariant points.

  • Topics

  1. 1. Using graph paper
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 45 :- Reflection - 3

a)Reflection of a point in a line: x=0, y=0, x=a, y=a, the origin. b)Reflection of a point in the origin. c) Invariant points.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 46 :- Section and Midpoint Formula - 1

Section and Midpoint Formula, Internal Section, Co-ordinates of the centroid of a triangle.

  • Topics

  1. 1. Introduction
  2. 2. The section formula
  3. 3. Points of trisection
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 47 :- Section and Midpoint Formula - 2

Section and Midpoint Formula, Internal Section, Co-ordinates of the centroid of a triangle.

  • Topics

  1. 1. Mid-Point Formula
  2. 2. Centroid of a triangle
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 48 :- Section and Midpoint Formula - 3

Section and Midpoint Formula, Internal Section, Co-ordinates of the centroid of a triangle.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 49 :- Equation of a line - 1

Slope –intercept form y = mx + c  Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis. Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.  Conditions for two lines to be parallel or perpendicular. Simple applications of all the above.

  • Topics

  1. 1. A Basic Concept
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 50 :- Equation of a line - 2

Slope –intercept form y = mx + c  Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis. Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.  Conditions for two lines to be parallel or perpendicular. Simple applications of all the above.

  • Topics

  1. 1. Inclination of a line
  2. 2. Concept of Slope
  3. 3. Slope of a straight line
  4. 4. The slope of a straight line passing through two given fixed points
  5. 5. Parallel lines
  6. 6. Perpendicular lines
  7. 7. Condition for Collinearity of three points
  8. 8. Example Questions
  9. 9. Practice Questions
Lecture 51 :- Equation of a line - 3

Slope –intercept form y = mx + c  Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis. Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.  Conditions for two lines to be parallel or perpendicular. Simple applications of all the above.

  • Topics

  1. 1. X Intercept
  2. 2. Y Intercept
  3. 3. Equation of a line
  4. 4. Equally inclined lines
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 52 :- Equation of a line - 4

Slope –intercept form y = mx + c  Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis. Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.  Conditions for two lines to be parallel or perpendicular. Simple applications of all the above.

  • Topics

  1. 1. To find the slope and y intercept of a given line
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 53 :- Equation of a line - 5

Slope –intercept form y = mx + c  Two- point form (y-y1) = m(x-x1) Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis. Geometric understanding of ‘c’ as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.  Conditions for two lines to be parallel or perpendicular. Simple applications of all the above.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 54 :- Similarity - 1

Similarity, conditions of similar triangles. (i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models.

  • Topics

  1. 1. Introduction
  2. 2. Similar triangles
  3. 3. Corresponding sides and corresponding angles
  4. 4. Conditions for Similarity of two triangles
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 55 :- Similarity - 2

Similarity, conditions of similar triangles. (i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models.

  • Topics

  1. 1. Basic proportionality theorem with applications
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 56 :- Similarity - 3

Similarity, conditions of similar triangles. (i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models.

  • Topics

  1. 1. Relation between the areas of two triangles
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 57 :- Similarity - 4

Similarity, conditions of similar triangles. (i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models.

  • Topics

  1. 1. Similarity as a size transformation
  2. 2. Application to Maps and Models
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 58 :- Similarity - 5

Similarity, conditions of similar triangles. (i) As a size transformation. (ii) Comparison with congruency, keyword being proportionality. (iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included). (iv) Applications of Basic Proportionality Theorem. (v) Areas of similar triangles are proportional to the squares of corresponding sides. (vi) Direct applications based on the above including applications to maps and models.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 59 :- Loci - 1

Loci: Definition, meaning, Theorems and constructions based on Loci. (i) The locus of a point at a fixed distance from a fixed point is a circle with the fixed point as centre and fixed distance as radius. (ii) The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines. (iii)The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

  • Topics

  1. 1. Locus
  2. 2. Definition
  3. 3. Theorems based on symmetry
  4. 4. Applications
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 60 :- Loci - 2

Loci: Definition, meaning, Theorems and constructions based on Loci. (i) The locus of a point at a fixed distance from a fixed point is a circle with the fixed point as centre and fixed distance as radius. (ii) The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines. (iii)The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

  • Topics

  1. 1. Summary
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 61 :- Loci - 3

Loci: Definition, meaning, Theorems and constructions based on Loci. (i) The locus of a point at a fixed distance from a fixed point is a circle with the fixed point as centre and fixed distance as radius. (ii) The locus of a point equidistant from two intersecting lines is the bisector of the angles between the lines. (iii)The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

  • Topics

  1. 1. Important Points
  2. 2. Previous Year Questions and Discussion
Lecture 62 :- Circles - 1

(i) Angle Properties  The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle.  Angles in the same segment of a circle are equal (without proof).  Angle in a semi-circle is a right angle. (ii) Cyclic Properties:  Opposite angles of a cyclic quadrilateral are supplementary.  The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).

  • Topics

  1. 1. Introduction
  2. 2. Arc and its types
  3. 3. Segment and relation between arc and its segments
  4. 4. Cyclic properties
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 63 :- Circles - 2

(i) Angle Properties  The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle.  Angles in the same segment of a circle are equal (without proof).  Angle in a semi-circle is a right angle. (ii) Cyclic Properties:  Opposite angles of a cyclic quadrilateral are supplementary.  The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).

  • Topics

  1. 1. Some important results
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 64 :- Circles - 3

(i) Angle Properties  The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle.  Angles in the same segment of a circle are equal (without proof).  Angle in a semi-circle is a right angle. (ii) Cyclic Properties:  Opposite angles of a cyclic quadrilateral are supplementary.  The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 65 :- Tangents and Intersecting Chords - 1

Tangent and Secant Properties:  The tangent at any point of a circle and the radius through the point are perpendicular to each other. 76  If two circles touch, the point of contact lies on the straight line joining their centers.  From any point outside a circle two tangents can be drawn and they are equal in length.  If two chords intersect internally or externally then the product of the lengths of the segments are equal.  If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.  If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

  • Topics

  1. 1. Introduction
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 66 :- Tangents and Intersecting Chords - 2

Tangent and Secant Properties:  The tangent at any point of a circle and the radius through the point are perpendicular to each other. 76  If two circles touch, the point of contact lies on the straight line joining their centers.  From any point outside a circle two tangents can be drawn and they are equal in length.  If two chords intersect internally or externally then the product of the lengths of the segments are equal.  If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.  If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

  • Topics

  1. 1. Some important results
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 67 :- Tangents and Intersecting Chords - 3

Tangent and Secant Properties:  The tangent at any point of a circle and the radius through the point are perpendicular to each other. 76  If two circles touch, the point of contact lies on the straight line joining their centers.  From any point outside a circle two tangents can be drawn and they are equal in length.  If two chords intersect internally or externally then the product of the lengths of the segments are equal.  If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.  If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 68 :- Constructions (Circles) - 1

(a) Construction of tangents to a circle from an external point. (b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.

  • Topics

  1. 1. Construction of tangents to a given circle
  2. 2. Construction of Circumscribed and Inscribed Circles of a Triangle
  3. 3. Circumscribing and Inscribing a circle on a regular Hexagon
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 69 :- Constructions (Circles) - 2

(a) Construction of tangents to a circle from an external point. (b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 70 :- Cylinder, Cone and Sphere - 1

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Cylinder
  2. 2. Hollow Cylinder
  3. 3. Example Questions
  4. 4. Practice Questions
Lecture 71 :- Cylinder, Cone and Sphere - 2

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Cone
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 72 :- Cylinder, Cone and Sphere - 3

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Sphere
  2. 2. Spherical shell
  3. 3. Hemisphere
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 73 :- Cylinder, Cone and Sphere - 4

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Conversion of solids
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 74 :- Cylinder, Cone and Sphere - 5

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Combination of Solids
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 75 :- Cylinder, Cone and Sphere - 6

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Miscellaneous Problems
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 76 :- Cylinder, Cone and Sphere - 7

Area and volume of solids – Cylinder, Cone and Sphere. Three-dimensional solids - right circular cylinder, right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of solids included.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 77 :- Trigonometrical Identities - 1

(a) Using Identities to solve/prove simple algebraic trigonometric expressions sin2 A + cos2 A = 1 1 + tan2 A = sec2A 1+cot2A = cosec2A; 0 ≤ A ≤ 90°

  • Topics

  1. 1. Trigonometry
  2. 2. Trigonometrical Ratios
  3. 3. Relation between different trigonometrical ratios
  4. 4. Trigonometrical Identities
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 78 :- Trigonometrical Identities - 2

(a) Using Identities to solve/prove simple algebraic trigonometric expressions sin2 A + cos2 A = 1 1 + tan2 A = sec2A 1+cot2A = cosec2A; 0 ≤ A ≤ 90°

  • Topics

  1. 1. Trigonometrical Ratios of Complementary angles
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 79 :- Trigonometrical Identities - 3

(a) Using Identities to solve/prove simple algebraic trigonometric expressions sin2 A + cos2 A = 1 1 + tan2 A = sec2A 1+cot2A = cosec2A; 0 ≤ A ≤ 90°

  • Topics

  1. 1. Using the trigonometrical tables
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 80 :- Trigonometrical Identities - 4

(a) Using Identities to solve/prove simple algebraic trigonometric expressions sin2 A + cos2 A = 1 1 + tan2 A = sec2A 1+cot2A = cosec2A; 0 ≤ A ≤ 90°

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 81 :- Heights and Distances - 1

Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

  • Topics

  1. 1. Angles of elevation and depression
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 82 :- Heights and Distances - 2

Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

  • Topics

  1. 1. More Questions
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 83 :- Heights and Distances - 3

Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 84 :- Graphical Representation - 1

Graphical Representation. Histograms and Less than Ogive. • Finding the mode from the histogram, the upper quartile, lower Quartile and median etc. from the ogive. • Calculation of inter Quartile range.

  • Topics

  1. 1. Graphical Representation
  2. 2. Histogram
  3. 3. Histogram for continuous grouped data
  4. 4. Histogram for discontinuous grouped data
  5. 5. Histogram when class marks are given
  6. 6. Cumulative frequency and cumulative frequency table
  7. 7. Cumulative frequency curve or an ogive
  8. 8. Example Questions
  9. 9. Practice Questions
Lecture 85 :- Graphical Representation - 2

Graphical Representation. Histograms and Less than Ogive. • Finding the mode from the histogram, the upper quartile, lower Quartile and median etc. from the ogive. • Calculation of inter Quartile range.

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 86 :- Measures of Central Tendency - 1

Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class, and modal class for grouped data. (both continuous and discontinuous). Mean by all 3 methods included: Direct Short-cut Step-deviation

  • Topics

  1. 1. Introduction
  2. 2. Arithmetic Mean
  3. 3. Arithemetic Mean of Tabulated Data
  4. 4. 1. Direct Method
  5. 5. 2. Short-cut Method
  6. 6. 3. Step-Deviation Method
  7. 7. Example Questions
  8. 8. Practice Questions
Lecture 87 :- Measures of Central Tendency - 2

Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class, and modal class for grouped data. (both continuous and discontinuous). Mean by all 3 methods included: Direct Short-cut Step-deviation

  • Topics

  1. 1. To find Mean for Grouped Data
  2. 2. 1. Direct Method
  3. 3. 2. Short-cut Method
  4. 4. 3. Step-Deviation Method
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 88 :- Measures of Central Tendency - 3

Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class, and modal class for grouped data. (both continuous and discontinuous). Mean by all 3 methods included: Direct Short-cut Step-deviation

  • Topics

  1. 1. Median
  2. 2. Median for Raw Data
  3. 3. Median for Tabulated Data
  4. 4. Median for grouped data (Continuous and discontinuous)
  5. 5. Quartiles
  6. 6. Inter-Quartile range
  7. 7. Example Questions
  8. 8. Practice Questions
Lecture 89 :- Measures of Central Tendency - 4

Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class, and modal class for grouped data. (both continuous and discontinuous). Mean by all 3 methods included: Direct Short-cut Step-deviation

  • Topics

  1. 1. Mode
  2. 2. Mode for raw data
  3. 3. Mode for tabulated data
  4. 4. Mode for grouped data
  5. 5. Example Questions
  6. 6. Practice Questions
Lecture 90 :- Measures of Central Tendency - 5

Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean*, median class, and modal class for grouped data. (both continuous and discontinuous). Mean by all 3 methods included: Direct Short-cut Step-deviation

  • Topics

  1. 1. Previous Year Questions and Discussion
Lecture 91 :- Probability - 1

• Random experiments • Sample space • Events • Definition of probability • Simple problems on single events

  • Topics

  1. 1. Introduction
  2. 2. Some basic terms and concepts
  3. 3. Measurement of probability
  4. 4. Example Questions
  5. 5. Practice Questions
Lecture 92 :- Probability - 2

y • Random experiments • Sample space • Events • Definition of probability • Simple problems on single events

  • Topics

  1. 1. Some important concepts
  2. 2. Example Questions
  3. 3. Practice Questions
Lecture 93 :- Probability - 3

y • Random experiments • Sample space • Events • Definition of probability • Simple problems on single events

  • Topics

  1. 1. Previous Year Questions and Discussion
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Instructor Profile

Delfin Biju

Math Tutor

I try my best to keep my students enjoying the learning experience, making it fun with examples and a very beautiful approach to learning new things. I love teaching. I see myself as a student and learn as much as I can which helps my students grow with knowledge along with me. I teach Maths for class 8th to 10th ICSE and CBSE students. As I secured 100 percent marks in mathematics for my ICSE - 10th board exam, I wish that all my students could achieve the same and would try my best to make my students achieve these goals. I have completed my Bachelor in Information technology so that I love to teach Computer science as well. I hope all my students enjoy learning.With lots of love, Delfin


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