RPET-2015 syllabus: Mathematics

Algebra:

• Complex number as an ordered pair of real numbers; real and imaginary parts, absolute value, graphical representation of complex numbers, triangle inequality, complex conjugate co-ordinates, roots of a complex number.
• Theory of quadratic equations and expressions; relation between roots and coefficients.
• Arithmetic, geometric and harmonic progressions. Permutations and combinations. Elementary applications of mathematical induction. Binomial theorem. Determinants of order two and three and their elementary properties.

Matrices:
definition, addition, subtraction and multiplication, transpose and adjoint of a matrix, inverse of a matrix.
Trigonometry:
De Moivre's theorem and its applications; hyperbolic and inverse hyperbolic functions, separation of real and imaginary parts of a complex quantity.
Co-ordinate Geometry:

• Rectangular cartesian co- ordinates, distance between two points, area of a triangle.
• Straight lines, angle between two lines, parallel and perpendicular lines. Circle, equation of tangent and normal to a circle. Pole, polar, radical axis. Parametric representation. Parabola, tangent and normal, its properties.
• Coordinate axes and planes in three-dimensional space, coordinates of point in space, distance between two points, section formula, direction cosines & direction ratios of a line joining two points, projection of the join of two points on a line, angle between two lines, whose direction ratios are given.

Calculus:

• Functions; into, onto and one-one function, polynomial, rational, trigonometric, logarithmic and exponential functions.
• Notion of limit and continuity of a function, derivative of a function at a point; derivatives of sum, difference, product and quotient of functions, derivatives of composite functions, implicit functions and inverse trigonometrical, logarithmic and exponential functions. Logarithmic differentiations. Geometrical interpretation of derivative; successive differentiation, tangents and normals. Sign of the derivative and monotonicity.
• Maximum and minimum values of a function.
• Integration as the inverse process of differentiation; integration by parts and by substitutions; definite integral and its application for the determination of areas (simple cases), properties of definite integrals.

Vectors:
Addition of vectors, multiplication by a scalar; scalar product, cross product and scalar triple product with geometrical applications.
Probability:
Probability; sum and product laws; conditional probability.