Seta, relations, functions | - Sets (their representation), various kinds of sets, algebra of sets
- Complement, intersection, symmetric difference of sets (their algebraic properties)
- Laws by De-Morgan on intersection, union, difference (practical problems on them)
- Function as special case of relation
- Function as mapping, codomain, domain
- Different range of functions
- Even/odd functions
- Into/onto/one-to-one functions
- All special functions
- Difference, product, sum, & composition of functions
- Invertible functions
|
Algebra | - Complex number algebra
- Triangle inequality
- Unity cube roots
- Geometric interpretations
- Multiplication/addition/conjugation/polar representation properties of modulus
- Fundamental theorem of algebra’s statement
- Quadratic equation with real coefficients
- Roots & coefficients relationship
- Quadratic equations formation with given roots
- Roots symmetric functions
- Geometric/arithmetic progression
- Arithmetic/geometric means
- Finite arithmetic & geometric progression sums
- Infinite geometric series
- First N natural numbers sum
- Squares & cubes of first N number sum
- Logarithms (its properties)
- Combinations/permutations
- Binomial theory for a positive integral index
- Binomial coefficients properties
|
Matrices | - Matrices equality
- Matrices as rectangular array for real numbers
- Multiplication/addition by a scalar & product of matrices
- Elementary column/row transformations
- Adjoint of matrix
- Square matrix determinant of order up to three
- Square matrix inverse of order up to three
- Matrix operations properties
- Symmetric/diagonal/skew symmetric matrices (their properties)
- Simultaneous linear equations solutions in two/three variables
|
Probability & Statistics | - Random experiment
- Sample space
- Different kinds of events
- Multiplication/addition probability rules
- Conditional probability
- Events independence
- Total probability
- Theorem by Baye
- Use permutation & combinations for computation of probability
- Dispersion and central tendency measurement
- Mean/median/standard deviation/mean deviation
- Variance of ungrouped/grouped data
- Frequency distribution data analysis with same mean but different variance
- Random variable/variance & mean of the random variable
|
Trigonometry | - Trigonometric functions (periodicity & graph)
- Subtraction/addition formula
- Formula involving sub multiple & multiple angles
- Trigonometric equations general solutions
- Inverse trigonometric functions (elementary properties)
|
Analytical geometry | - Two dimension: Catersian coordinates/two points distance/section formula/shift of origin
- Various forms of equation of straight line
- Angle between 2 lines
- Distance of point from line
- Lines via the point of intersection of two lines
- Equation of bisector for angle between 2 lines
- Lines concurrency
- Centroid/orthocentre/incentre/circumcentre of triangle
- Equation of circle in various forms
- Circle’s parametric equations
- Intersection of circle with circle/straight line
- Parabola equation
- Hyperbola/ellipse in standard form
- Parametric equations/equations of tangent and circle
- Three dimensions: Two points distance, Direction ratios/cosines, equation of straight line in space
- Two lines shortest distance
- Skew lines
- Plane equation
- Distance of point from plane
- Angle between two planes/lines/ a line & plane
- Coplanar lines
|
Differential calculus | - Function’s continuity
- Limit of function at real number
- Sum’s limit & continuity
- Two functions difference/product/quotient
- Rule of L Hospital evaluation limits of functions
- Composite functions continuity
- Continuous functions intermediate value property
- Functions/sum derivative
- Product, difference, & quotient of 2 functions
- Rule of chain
- Polynomial/Rational/inverse trigonometric/ trigonometric/exponential & logarithmic functions
- Normals & tangents
- Decreasing/increasing functions
- Order two derivatives
- Function maximum & minimum values
- Theorem of rolle’s & mean value theorem of Lagrange
- Two theorem geometrical interpretation
- Derivatives till order two of implicit functions
- Derivatives geometric interpretation
|
Integral calculus | - Integration, the inverse process of differentiation
- Standard function’s indefinite integrals
- Definite integrals like limit of sums
- Definite integrals (its properties)
- Integral calculus fundamental theorem
- Integration by parts
- Integration by partial function and substitution methods
- Definite integral applications to the determination of areas held up simple curves
- Ordinary differential equations formation
- Homogeneous differential equations of first order & first degree solutions
- Variable methods separation
- Linear first order differential equations
|
Vectors | - Scalar multiplication
- Vectors addition
- Cross/dot products
- Vector triple/scalar products (their geometrical interpretation)
|
