1) Matrices and Determinants (15 periods)
Order - Types of matrices - Addition and subtraction of matrices and Multiplication of a matrix by a scalar - Product of matrices. Evaluation of determinants of order two and three - Properties of determinants (Statements only) - Singular and non singular matrices - Product of two determinants.
2) Algebra (20 periods)
Partial fractions - Linear non repeated and repeated factors - Quadratic non repeated types. Permutations - Applications - Permutation of repeated objects - Circular permutaion. Combinations - Applications - Mathematical induction - Summation of series using ∑n, ∑n2 and ∑n3. Binomial theorem for a positive integral index - Binomial coefficients.
3) Sequences and series (20 periods)
Harnomic progression - Means of two positive real numbers - Relation between A.M., G.M., and H.M. - Sequences in general - Specifying a sequence by a rule and by a recursive relation - Compound interest - Nominal rate and effective rate - Annuities - immediate and due.
4) Analytical Geometry (30 periods)
Locus - Straight lines - Normal form, symmetric form - Length of perpendicular from a point to a line - Equation of the bisectors of the angle between two lines - Perpendicular and parallel lines - Concurrent lines - Circle - Centre radius form - Diameter form - General form - Length of tangent from a point to a circle - Equation of tangent - Chord of contact of tangents.
5) Trigonometry (25 periods)
Standard trigonometric identities - Signs of trigonometric ratios - compound angles - Addition formulae - Multiple and submultiple angles - Product formulae - Principal solutions - Trigonometric equations of the form sin θ = sinα, cosθ = cosα and tanθ = tan α - Inverse trigonometric functions.
6) Functions and their Graphs (15 Periods)
Functions of a real value - Constants and variables - Neighbourhood - Representation of functions - Tabular and graphical form - Vertical line test for functions - Linear functions - Determination of slopes - Power function - 2x and ex - Circular functions - Graphs of sinx, ,cosx and tanx - Arithmetics of functions (sum, difference, product and quotient) Absolute value function, signum function - Step function - Inverse of a function - Even and odd functions - Composition of functions
7) Differential calculus (30 periods)
Limit of a function - Standard forms Lt
xa xaxa nn → − − , Lt xx x
0 1 1
e xx x → − 0
1lo g( )
Continuity of functions - Graphical interpretation - Differentiation - Geometrical interpretation - Differtentiation using first principles - Rules of differentiation - Chain rule - Logarithmic Differentitation - Differentiation of implicit functions - parametric functions - Second order derivatives.
8) Integral calculus (25 periods)
Integration - Methods of integration - Substitution - Standard forms - integration by parts - Definite integral - Integral as the limit of an infinite sum (statement only).
9) Stocks, Shares and Debentures (15 periods)
Basic concepts - Distinction between shares and debentures - Mathematical aspects of purchase and sale of shares - Debentures with nominal rate.
10) Statistics (15 Periods)
Measures of central tendency for a continuous frequency distribution Mean, Median, Mode Geometric Mean and Harmonic Mean - Measures of dispersion for a continuous frequency distribution - Range - Standard deviation - Coefficient of variation - Probability - Basic concepts - Axiomatic approach - Classical definition - Basic theorems - Addition theorem (statement only) - Conditional probability - Multiplication theorem (statement only) - Baye’s theorem (statement only) - Simple problems.