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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