5. Coordinate Chemistry

a) Locus

a) Locus

b) Translation of axes

b) Translation of axes

c) Rotation of axes

c) Rotation of axes

c-1) Straight Line

c-1) Straight Line

d) Pair of Straight Lines

d) Pair of Straight Lines

e) Circles

e) Circles

f) System of circles

f) System of circles

g) Conics

g) Conics

h) Parabola

h) Parabola

i) Hyperbola

i) Hyperbola

j) Normal

j) Normal

k) Polar at any point of these conics

k) Polar at any point of these conics

l) Asymptotes of hyperbola.

l) Asymptotes of hyperbola.

m) Polar Coordinates

m) Polar Coordinates

n) Coordinates in three dimensions and tetrahedron

n) Coordinates in three dimensions and tetrahedron

o) Direction Cosines and direction ratios of a line – angle between two lines

o) Direction Cosines and direction ratios of a line – angle between two lines

p) Cartesian equation of a plane in (i) general form

p) Cartesian equation of a plane in (i) general form

(ii) normal form

(ii) normal form

(iii) intercept form

(iii) intercept form

q) Sphere – Cartesian equation – Centre and Radius

q) Sphere – Cartesian equation – Centre and Radius

1. Algebra

a) Functions – Types of functions

a) Functions – Types of functions

b) Mathematical induction and Applications

b) Mathematical induction and Applications

c) Permutations and Combinations – linear and circular permutations

c) Permutations and Combinations – linear and circular permutations

d) Binomial theorem for any rational index – applications

d) Binomial theorem for any rational index – applications

e) Partial fractions

e) Partial fractions

f) Exponential

f) Exponential

g) Quadratic expressions, equations.

g) Quadratic expressions, equations.

h) Theory of equations: Relations between the roots and Coefficients in any equation

h) Theory of equations: Relations between the roots and Coefficients in any equation

I) Transformation of equations – reciprocal equations

I) Transformation of equations – reciprocal equations

j) Matrices and determinants: Types of matrices

j) Matrices and determinants: Types of matrices

k) Properties of determinants

k) Properties of determinants

l)The three variables

l)The three variables

m) Consistency and inconsistency of simultaneous equations

m) Consistency and inconsistency of simultaneous equations

n) Complex numbers and their properties : Applications

n) Complex numbers and their properties : Applications

2. Trigonometry

a) Trigonometric functions

a) Trigonometric functions

b) Trigonometric ratios of compound angles

b) Trigonometric ratios of compound angles

c) Multiple and Sub-multiple Angles

c) Multiple and Sub-multiple Angles

d) Transformations

d) Transformations

e) Trigonometric equations

e) Trigonometric equations

f) Inverse trigonometric functions

f) Inverse trigonometric functions

g) Hyperbolic and inverse hyperbolic functions

g) Hyperbolic and inverse hyperbolic functions

h) Properties of Triangles

h) Properties of Triangles

i) Heights and distances

i) Heights and distances

3. Vector Algebra

a) Algebra of vectors

a) Algebra of vectors

b) Scalar and vector product of two vectors

b) Scalar and vector product of two vectors

c) Scalar and vector triple products

c) Scalar and vector triple products

d) Scalar and vector products of four vectors

d) Scalar and vector products of four vectors

4. Probability

a) Random experiments – Sample space – events – probability of an event – addition and multiplication theorems of probability – Conditional event and conditional probability

a) Random experiments – Sample space – events – probability of an event – addition and multiplication theorems of probability – Conditional event and conditional probability

b) Random variables

b) Random variables

6. Calculus

a) Functions – limits – Continuity

a) Functions – limits – Continuity

b) Differentiation – Methods of differentiation

b) Differentiation – Methods of differentiation

c) Successive differentiation – Leibnitz’s theorem and its applications

c) Successive differentiation – Leibnitz’s theorem and its applications

d) Applications of differentiation

d) Applications of differentiation

e) Partial differentiation including Euler’s theorem on homogeneous functions

e) Partial differentiation including Euler’s theorem on homogeneous functions