Intermediate 2nd Year Mathematics

MATHEMATICS IIA SYLLABUS

Unit 1: Complex Numbers

Complex Numbers as Ordered Pairs of Real Numbers – Fundamental Operations – Representation in the form a + ib – Modulus and Amplitude – Geometrical and Polar Representation – Argand Plane and Argand Diagram.

Unit 2: De Moivre’s Theorem

De Moivre’s Theorem for Integral and Rational Indices – nth Roots of Unity – Geometrical Interpretations and Applications.

Unit 3: Quadratic Expressions

Quadratic Expressions – Quadratic Equations in One Variable – Sign of Quadratic Expressions – Change of Signs – Maximum and Minimum Values – Quadratic Inequalities.

Unit 4: Theory of Equations

Relations Between Roots and Coefficients – Equations with Related Roots – Equations with Real Coefficients – Complex Conjugate Roots – Transformation of Equations – Reciprocal Equations.

Unit 5: Permutations and Combinations

Fundamental Principle of Counting – Linear and Circular Permutations – Permutations of n Dissimilar Objects – Permutations with Repetition – Combinations and Related Theorems.

Unit 6: Binomial Theorem

Binomial Theorem for Positive Integral Index – Binomial Theorem for Rational Index – Approximations Using Binomial Theorem.

Unit 7: Partial Fractions

Partial Fractions with Non-Repeated Linear Factors – Repeated Linear Factors – Irreducible Quadratic Factors.

Unit 8: Measures of Dispersion

Range – Mean Deviation – Variance – Standard Deviation – Coefficient of Variation – Analysis of Frequency Distributions. 

Unit 9: Probability

Random Experiments and Events – Classical Definition of Probability – Axiomatic Approach – Addition Theorem – Independent and Dependent Events – Conditional Probability – Multiplication Theorem – Bayes’ Theorem.

Unit 10: Random Variables and Probability Distributions

Random Variables – Binomial Distribution – Poisson Distribution.

MATHEMATICS IIB SYLLABUS

Unit 1: Circle

Equation of Circle – Centre and Radius – Circle Through Three Non-Collinear Points – Parametric Equations – Position of a Point Relative to a Circle – Power of a Point – Tangents and Normals – Chord of Contact – Pole and Polar – Conjugate Points and Lines – Relative Position of Two Circles – Common Tangents – Centres of Similitude.

Unit 2: System of Circles

Angle Between Two Intersecting Circles – Radical Axis – Common Chord – Common Tangent – Radical Centre – Intersection of a Line and Circle.

Unit 3: Parabola

Conic Sections – Standard Equation of Parabola – Different Forms of Parabola – Parametric Equations – Tangents and Normals – Conditions for Tangency.

Unit 4: Ellipse

Standard Equation of Ellipse – Parametric Equations – Tangents and Normals – Conditions for Tangency.

Unit 5: Hyperbola

Standard Equation of Hyperbola – Parametric Equations – Tangents and Normals – Conditions for Tangency – Asymptotes.

Unit 6: Integration

Integration as the Inverse Process of Differentiation – Standard Integrals – Properties of Integrals – Substitution Method – Integration by Parts – Partial Fractions Method – Reduction Formulae.

Unit 7: Definite Integrals

Definite Integral as Limit of Sum – Area Interpretation – Fundamental Theorem of Integral Calculus – Properties – Reduction Formulae – Applications to Area.

Unit 8: Differential Equations

Formation of Differential Equations – Degree and Order – Variable Separable Method – Homogeneous Differential Equations – Non-Homogeneous Differential Equations – Linear Differential Equations.