I am posting section headings of each chapter in this series to facilitate a quick revision of the material in the chapter.After you study the chapter on a day, the next day you can look at the section review sheet and recollect the material. Or you can take a print out and write down what you remember. Such a process will help in retaining the material that you studied well for a longer time. You need to revise material at frequent intervals to retain it in your memory.
I shall post the concept of each section in a separate blog.
www.iit-jee-maths.blogspot.com
Monday, May 19, 2008
R D Sharma Ch 15. Circle
Circle Sections in R D Sharma
Section Review
Find out how much you much remember about each section
1. Definition
2. Standard equation of a circle
3. Some particular cases of standard equation of a circle
4. General equation of a circle
5. Equation of a circle when the coordinates of end points of a diameter are given
6. Intercepts of the axes
7. Position of a point with respect to a circle
8. equation of a circle in parametric form
9. Intersection of a straight line and a circle
10. The length of the intercept cut off from a line by a circle
11.Tangent to a circle at a given point
12 Normal to a circle at a given point
13. Length of the tangent from a point to a circle
14. Pair of tangents drawn from a point to given circle
15. Combined equation of pair of tangents
16. Director circle and its equation
17. Chord of contacts of tangents
18. Pole and Polar
19. Equation of the chord bisected at a given point
20. Diameter of a circle – Locus of middle points of parallel chords
21. Common tangents to two circles
22. Common chord of two circles
23. Angle of intersection of two curves and the condition of orthogonality of two circles
24. Radical axis
25. Equation of a circle through the intersection of a circle and line
26. Circle through the intersection of the two circles
27. Coaxial system of circles
Section Review
Find out how much you much remember about each section
1. Definition
2. Standard equation of a circle
3. Some particular cases of standard equation of a circle
4. General equation of a circle
5. Equation of a circle when the coordinates of end points of a diameter are given
6. Intercepts of the axes
7. Position of a point with respect to a circle
8. equation of a circle in parametric form
9. Intersection of a straight line and a circle
10. The length of the intercept cut off from a line by a circle
11.Tangent to a circle at a given point
12 Normal to a circle at a given point
13. Length of the tangent from a point to a circle
14. Pair of tangents drawn from a point to given circle
15. Combined equation of pair of tangents
16. Director circle and its equation
17. Chord of contacts of tangents
18. Pole and Polar
19. Equation of the chord bisected at a given point
20. Diameter of a circle – Locus of middle points of parallel chords
21. Common tangents to two circles
22. Common chord of two circles
23. Angle of intersection of two curves and the condition of orthogonality of two circles
24. Radical axis
25. Equation of a circle through the intersection of a circle and line
26. Circle through the intersection of the two circles
27. Coaxial system of circles
R D Sharma Ch. 16. Parabola
Ch. 16. Parabola-RDS-
Section Review
Find out how much you remember about each section
1. Conic sections: Definition
2. The parabola
3. Equation of parabola in its standard form
4. Some other standard forms of parabola
5. Position of a point with respect to a parabola
6. Equation of a parabola in parametric form
7. Equation of the chord joining any two points on the parabola
8. Intersection of a straight line and a parabola
9. Equation of tangent in different forms
10. Equation of normal in different forms
11 Number of normals drawn from a point to a parabola
12. Some results in conormal points
13 Number of tangents drawn from a point to a parabola
13a. Equation of the pair of tangents from a point to a parabola
14. Equation of the chord of contacts of tangents to a parabola
15. Equation of the chord bisected at a given point
16. Equation of diameter of a parabola
17. Length of tangent, subtangent, normal and subnormal
18. Pole and Polar
19. some important results at a glance
Section Review
Find out how much you remember about each section
1. Conic sections: Definition
2. The parabola
3. Equation of parabola in its standard form
4. Some other standard forms of parabola
5. Position of a point with respect to a parabola
6. Equation of a parabola in parametric form
7. Equation of the chord joining any two points on the parabola
8. Intersection of a straight line and a parabola
9. Equation of tangent in different forms
10. Equation of normal in different forms
11 Number of normals drawn from a point to a parabola
12. Some results in conormal points
13 Number of tangents drawn from a point to a parabola
13a. Equation of the pair of tangents from a point to a parabola
14. Equation of the chord of contacts of tangents to a parabola
15. Equation of the chord bisected at a given point
16. Equation of diameter of a parabola
17. Length of tangent, subtangent, normal and subnormal
18. Pole and Polar
19. some important results at a glance
R D Sharma Ch. 17. Ellipse
Ch. 17. Ellipse Parabola-RDS-
Section Review
Find out how much you remember about each section
1. Introduction
2. Equation of ellipse in its standard form
3.Second focus and second directrix of the ellipse
4. Vertices, major and minor axes, foci, directrices and centre of the ellipse
5. Ordinate, double ordinate and latus rectum of the ellipse
6. focal distances of a point on the ellipse
7. equation of ellipse in other forms
8. Position of a point with respect to an ellipse
9 .Parametric equations and parametric coordinates
10. Equation of the chord joining any two points on an ellipse
11. Condition of a line to be a tangent to an ellipse
12. Equation of tangent in terms of its slope
13. Equation of tangent at a point
14 Number of tangents drawn from a point to an ellipse
15. Equation of normal in different forms
16 Number of normals
17. Properties of eccentric angles of the conormal points
18. Equation of the pair of tangents from a point to an ellipse
19. Equation of the chord of contacts of tangents
19a. Equation of the chord bisected at a given point
20. Equation of diameter of an ellipse
21. Some properties of ellipse
Section Review
Find out how much you remember about each section
1. Introduction
2. Equation of ellipse in its standard form
3.Second focus and second directrix of the ellipse
4. Vertices, major and minor axes, foci, directrices and centre of the ellipse
5. Ordinate, double ordinate and latus rectum of the ellipse
6. focal distances of a point on the ellipse
7. equation of ellipse in other forms
8. Position of a point with respect to an ellipse
9 .Parametric equations and parametric coordinates
10. Equation of the chord joining any two points on an ellipse
11. Condition of a line to be a tangent to an ellipse
12. Equation of tangent in terms of its slope
13. Equation of tangent at a point
14 Number of tangents drawn from a point to an ellipse
15. Equation of normal in different forms
16 Number of normals
17. Properties of eccentric angles of the conormal points
18. Equation of the pair of tangents from a point to an ellipse
19. Equation of the chord of contacts of tangents
19a. Equation of the chord bisected at a given point
20. Equation of diameter of an ellipse
21. Some properties of ellipse
27. Definite Integrals
27. Definite Integrals
Section Review
1. Definite integrals
2. Evaluation of definite integrals
3. Geometric interpretation of definite integrals
4. Evaluation of definite integrals by substitution
5. Properties of definite integrals
6. Integral function
7. Summation of series using definite integral as the limit of a sum
8. Gamma function
Section Review
1. Definite integrals
2. Evaluation of definite integrals
3. Geometric interpretation of definite integrals
4. Evaluation of definite integrals by substitution
5. Properties of definite integrals
6. Integral function
7. Summation of series using definite integral as the limit of a sum
8. Gamma function
IIT JEE Section Review Ch. 29. Differential Equations
R D Sharma Chapter 29. Differential Equations
1. Some definitions
2. Solution of a differential equation
3. Formation of differential equations
4. differential equations of first order and degree
5. Geometric interpretation of differential equations of first order and degree
6. Solution of differential equations of first order and degree
7. Methods of solving differential equations of first order and degree
I plan to post the concept review in learning Mathematics blog
1. Some definitions
2. Solution of a differential equation
3. Formation of differential equations
4. differential equations of first order and degree
5. Geometric interpretation of differential equations of first order and degree
6. Solution of differential equations of first order and degree
7. Methods of solving differential equations of first order and degree
I plan to post the concept review in learning Mathematics blog
R D Sharma Ch. 30. Vectors
30. Vectors
1. Introduction
2. Representation of vectors
3. Equality of vectors
4. Types of vectors
5. Parallelogram law of addition of vectors
6. Subtraction of vectors
7. Multiplication of a vector by a scalar
8. Position vector
9. Section formula
10. Linear combination of vectors
11. Collinear and non-collinear vectors
12. Collinear points
13. Components of a vector
14. Components of a vector in three dimensions
15. Collinearity and coplanarity
16. Linear independence and dependence of vectors
17. Angle between two vectors
18. The scalar or dot product
19. Geometrical interpretation of scalar product
20. Properties of scalar product
21. Scalar product in terms of components
22. Angle between two vectors
23. Components of a vector b along perpendicular to vector a
24. Tetrahedron
25. Application of scalar product in mechanics to find the work done
26. Definition of vector product
27. Properties of vector product
28. vector product in terms of components
29. Vectors normal to the plane of two given vectors
30. Some important results
31. Lagrange’s identity
32. Application of vector product in mechanics to find the moment of a force
33. Application of vector product to find the moment of a couple
34. Scalar triple product
35. Properties of scalar triple product
36. Scalar triple product in terms of components
37. Distributivity of cross product over vector addition
38. Volume of a tetrahedron
39. Vector triple product
40. Geometrical applications of vectors
41. Solutions of vector equations
1. Introduction
2. Representation of vectors
3. Equality of vectors
4. Types of vectors
5. Parallelogram law of addition of vectors
6. Subtraction of vectors
7. Multiplication of a vector by a scalar
8. Position vector
9. Section formula
10. Linear combination of vectors
11. Collinear and non-collinear vectors
12. Collinear points
13. Components of a vector
14. Components of a vector in three dimensions
15. Collinearity and coplanarity
16. Linear independence and dependence of vectors
17. Angle between two vectors
18. The scalar or dot product
19. Geometrical interpretation of scalar product
20. Properties of scalar product
21. Scalar product in terms of components
22. Angle between two vectors
23. Components of a vector b along perpendicular to vector a
24. Tetrahedron
25. Application of scalar product in mechanics to find the work done
26. Definition of vector product
27. Properties of vector product
28. vector product in terms of components
29. Vectors normal to the plane of two given vectors
30. Some important results
31. Lagrange’s identity
32. Application of vector product in mechanics to find the moment of a force
33. Application of vector product to find the moment of a couple
34. Scalar triple product
35. Properties of scalar triple product
36. Scalar triple product in terms of components
37. Distributivity of cross product over vector addition
38. Volume of a tetrahedron
39. Vector triple product
40. Geometrical applications of vectors
41. Solutions of vector equations
R D Sharma Ch. 31. Three Dimensional Geometry
31. Three Dimensional Geometry
1. Coordinates of a point in space
2. Signs of coordinates of a point
3. Distance formula
4. Section formulas
5. Direction cosines and direction ratios
6. Angle between two vectors in terms of their direction cosines and direction ratios
7. Straight line in space
8.Angle between two lines
9. Intersection of two lines
10. Perpendicular distance of a point from a line
11. Reflection or image of a point in a straight line
12. Shortest distance between two straight lines
13. Plane
14. Equations of a plane passing through a given point
15. Intercept form of a plane
16. vector equation of a plane passing through a given point and normal to a given vector
17. Equation of a plane in normal form
18. Angle between two planes
19. Equation of a plane passing through a given point and parallel to two given vectors
20. Equation of a plane parallel to a given plane
21. Equation of a plane passing through the intersection of two planes
22. Distance of a point from a plane
23. Equation of planes bisecting the angles between two given planes
24. Line and a plane
25. Angle between a line and a plane
26. Intersection of a line and a plane
27. Condition of coplanarity of two lines and equation of the plane containing them
28. Image of a point in a plane
1. Coordinates of a point in space
2. Signs of coordinates of a point
3. Distance formula
4. Section formulas
5. Direction cosines and direction ratios
6. Angle between two vectors in terms of their direction cosines and direction ratios
7. Straight line in space
8.Angle between two lines
9. Intersection of two lines
10. Perpendicular distance of a point from a line
11. Reflection or image of a point in a straight line
12. Shortest distance between two straight lines
13. Plane
14. Equations of a plane passing through a given point
15. Intercept form of a plane
16. vector equation of a plane passing through a given point and normal to a given vector
17. Equation of a plane in normal form
18. Angle between two planes
19. Equation of a plane passing through a given point and parallel to two given vectors
20. Equation of a plane parallel to a given plane
21. Equation of a plane passing through the intersection of two planes
22. Distance of a point from a plane
23. Equation of planes bisecting the angles between two given planes
24. Line and a plane
25. Angle between a line and a plane
26. Intersection of a line and a plane
27. Condition of coplanarity of two lines and equation of the plane containing them
28. Image of a point in a plane
Section Review Ch. 32. Probability
R D Sharma Chapter 32. Probability
section Review
1. Introduction
2.classical approach to probability
3. Axiomatic approach to probability
4. Addition theorems on probability
5. Conditional probability
6. Multiplication theorems on probability
7.Independent events
8. Some solved problems based on addition and multiplication theorems of probability
9. the law of total probability
10. Baye’s rule
11. Random variable and its probability distribution
12. Binomial distribution
13. Mean and variance of binomial distribution
14. Maximum value of P9X = r) for given values of n and p for a binomial variate X
section Review
1. Introduction
2.classical approach to probability
3. Axiomatic approach to probability
4. Addition theorems on probability
5. Conditional probability
6. Multiplication theorems on probability
7.Independent events
8. Some solved problems based on addition and multiplication theorems of probability
9. the law of total probability
10. Baye’s rule
11. Random variable and its probability distribution
12. Binomial distribution
13. Mean and variance of binomial distribution
14. Maximum value of P9X = r) for given values of n and p for a binomial variate X
Ch 33. Trigonometric Ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions
Ch 33. Trigonometric Ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions
Section Review
1. Introduction
2. Some basic formulae
3. Domain and range of trigonometrical functions
4. Sum and difference formulae
5. Sum and difference into products
6. Product into sum or difference
7. T – ratios of the sum of three or more angles
8. Values of trigonometrica ratios of some important angles and some important results
9. Expressions of sin A/2 and cos A/2 in terms of sin A
10. Maximum and minimum values of trigonometrical functions
Section Review
1. Introduction
2. Some basic formulae
3. Domain and range of trigonometrical functions
4. Sum and difference formulae
5. Sum and difference into products
6. Product into sum or difference
7. T – ratios of the sum of three or more angles
8. Values of trigonometrica ratios of some important angles and some important results
9. Expressions of sin A/2 and cos A/2 in terms of sin A
10. Maximum and minimum values of trigonometrical functions
Ch.34 properties of Triangles and circles connected with them
Ch.34 properties of Triangles and circles connected with them
1. Introduction
2. Sine rule
3. cosine formulae
4. Projection formulae
5. Trigonometrical ratios of half of the angles of a triangle
6. Area of a triangle
7 Napier’s analogy
8. Circumcircle of a triangle
9. Inscribed circle or incircle of a triangle
10. Escribed circles of a triangle
11. Orthocentre and its distances from the angular points of a triangle
12. Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
13. Area of a cyclic quadrilateral
14. Ptolemy’s theorem
15. Circum-radius of a cyclic quadrilateral
1. Introduction
2. Sine rule
3. cosine formulae
4. Projection formulae
5. Trigonometrical ratios of half of the angles of a triangle
6. Area of a triangle
7 Napier’s analogy
8. Circumcircle of a triangle
9. Inscribed circle or incircle of a triangle
10. Escribed circles of a triangle
11. Orthocentre and its distances from the angular points of a triangle
12. Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon
13. Area of a cyclic quadrilateral
14. Ptolemy’s theorem
15. Circum-radius of a cyclic quadrilateral
R D Sharma Ch. 36 Inverse Trigonometrical Functions
Ch 36. Inverse Trigonometrical Functions
1. Inverse trigonometrical functions
2. Properties of inverse trigonometrical functions
1. Inverse trigonometrical functions
2. Properties of inverse trigonometrical functions
R D Sharma Ch. 37 Solution of Triangles
Section review
1. Introduction
2. Solution of a right angled triangle
3. Solution of a triangle in general
4. Some useful results
1. Introduction
2. Solution of a right angled triangle
3. Solution of a triangle in general
4. Some useful results
R D Sharma Ch. 37 Solution of Triangles
Section Review
1. Introduction
2. Solution of a right angled triangle
3. Solution of a triangle in general
4. Some useful results
1. Introduction
2. Solution of a right angled triangle
3. Solution of a triangle in general
4. Some useful results
R D Sharma Ch. 38 Hights and distances
Section Review
1. Angle of elevation and depression of a point
2. Some useful results
1. Angle of elevation and depression of a point
2. Some useful results
Friday, May 16, 2008
Some online question pages
These question sets are very good as beginning exercises
Logarithmic equations
http://www.analyzemath.com/LogEqTest/LogEqTest.html
Trigonometric equations
http://www.analyzemath.com/Solve-Trigonometric-Equations/Solve-Trigonometric-Equat.html
Complex numbers
http://www.analyzemath.com/complex/questions.html
Polynomial inequalities
http://www.analyzemath.com/IneqTest/IneqTest.html
Probability
http://www.analyzemath.com/statistics/probability_questions.html
Derivatives
http://www.analyzemath.com/calculus_questions/derivative.html
http://www.analyzemath.com/calculus_questions/computation_derivative.html
Integration
http://www.analyzemath.com/calculus_questions/fundamental_theorem.html
http://www.analyzemath.com/calculus_questions/antiderivatives.html
Logarithmic equations
http://www.analyzemath.com/LogEqTest/LogEqTest.html
Trigonometric equations
http://www.analyzemath.com/Solve-Trigonometric-Equations/Solve-Trigonometric-Equat.html
Complex numbers
http://www.analyzemath.com/complex/questions.html
Polynomial inequalities
http://www.analyzemath.com/IneqTest/IneqTest.html
Probability
http://www.analyzemath.com/statistics/probability_questions.html
Derivatives
http://www.analyzemath.com/calculus_questions/derivative.html
http://www.analyzemath.com/calculus_questions/computation_derivative.html
Integration
http://www.analyzemath.com/calculus_questions/fundamental_theorem.html
http://www.analyzemath.com/calculus_questions/antiderivatives.html
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