NATIONAL SCHOOL OF SCIENCES
Department of Mathematics
Syllabus for First Terminal Examination – 2074
Sets, Real number system and Logic:
- Definition of set, Specification of sets, Types of sets, Relation between sets, Operation on sets, Algebra of sets, Properties of union, intersection, Inclusion and equality relation, De Morgan's Law, Distribution, compliment, difference laws, Symmetric difference of sets
- Distance formula, section formula, slope of a line, equation of a locus, collinearity, intersection of two lines, concurrent lines, Angle between two lines, Length of perpendicular from a point to the line, Bisectors of angle between two lines.
- Ordered pair, Cartesian product, Relation, Definition of function, Image and pre-image of elements, Domain, co-domain and range of a function, Types of function (one-one, onto, bijective), inverse of a function, composition of function, real valued function, exponential and logarithmic functions, properties of logarithmic functions.
- Theorems on quadratic equations, Nature of roots, Relation between roots and coefficients, Formation of quadratic equation, Condition for the common roots.
Limits and Continuity:
- Definition of limits, limits of a function, Indeterminate forms, theorem on limits of algebraic and trigonometric function, limits of algebraic and trigonometric functions.
Matrix and Determinant:
- Definition of matrix, Types of matrix, Operation on matrices, transpose of a matrix, minors and cofactors, determinant of order 3, Sarrus rule, properties of determinants.