## MySkill Academy |

12thMat-1 Course Topics

Unit 7 : Applications of Derivatives | 7.1 Derivatives as Slope and Rate of Change - meaning of derivative as slope, equations of tangent and normal, meaning of derivative as rate of change and related rates; Mean Value Theorem - Rolle’s theorem, Lagrange’s Mean Value Theorem, geometrical meaning, applications | Indeterminate forms - a limit process - l’ Hôpital Rul, evaluating the limits; Sketching of elementary curves - increasing / decreasing – first derivative test, concavity / convexity – second derivative test, Asymptotes and symmetry, sketching of polynomial, rational, trigonometric, exponential and logarithmic curves | Extrema of functions - Extrema: Maxima and Minima using first and second derivative test, applications to optimization |

Unit 6 : Vectos-2 | 6.1 Scalar Triple Product - definition of scalar triple product, geometric meaning and determinant form , properties, problems and applications | Vector Triple Product - definition of vector triple product, geometric meaning, properties, problems and applications; Straight lines - vector and cartesian equations of a straight line: two points form, one point and parallel to a vector form, direction ratios and cosines, angle between two lines, coplanar lines (intersecting, perpendicular, parallel), non-coplanar lines, distance between two parallel lines, two non–coplanar lines, a point and a line | Planes - vector and cartesian equations of a plane (Normal form, given one point and two parallel vectors, given two points and one parallel vector, given three points, passing through intersection of two planes), angle between two planes, angle between a line and a plane, meeting point of a line and a plane, distance between a point and a plane, distance between two parallel planes |

Unit 5 :Two Dimensional Analytic Geometry - II | 5.1 Conic sections - definition of a conic, general equation of a conic, sections of a cone; Circle - general form, standard forms, parametric form, verifying position of a given point | Parabola - standard equation: four types, properties, parametric form, simple problems and applications; Ellipse and Hyperbola - standard equation, parametric form, properties, simple problems and applications | |

Unit 4 : Trigonometric functions and Inverse Trigonometric functions | 4.1 Periodic functions - definition and examples, domain and Range of a function; Odd and Even functions - definitions and examples | Graphs of Trigonometric functions - graphs of sine, cosine, tangent, secant, cosecant, cotangent functions | Properties and graphs of inverse Trigonometric functions - domain and Range of Inverse Trigonometric functions, properties of Inverse Trigonometric functions, Simple problems, graphs of Inverse of sine, cosine, tangent, secant, cosecant, cotangent functions |

Unit-3 Theory Equations | Quadratic Equations - relation between roots and coefficients, conditions for rational, irrational and complex roots, solving equations reducible to quadratic equation, graph of a quadratic function, minimum and maximum values, quadratic inequalities and sign of quadratic expression | Polynomial equations - fundamental theorem of algebra, formation of equation for the given roots, equations with rational coefficients when some of the irrational or complex roots are given, roots of third or higher degree polynomial equations when given in partly factorised form | Graphical approach to equations - using continuity of polynomial functions to find real roots by finding where the function changes sign, counting the number of positive, negative and complex roots using Descartes’ rule of signs (no proof) |

Unit-2 Complex Numbers | Demoivre’s theorem - statement of Demoivre’s theorem, Euler’s formula, notation and polar form of unit circle, square roots, cube roots and fourth roots of unity, problems involving the cube roots of unity | ||

Unit-2 Complex Numbers | Introduction to Complex Numbers - need for complex numbers; complex numbers as ordered pairs of real numbers | basic arithmetic operations on complex numbers; Algebra of complex numbers - conjugate of a complex number, modulus of a complex number, triangle inequality, problems | Polar form - argand plane as an extension of the real number line, geometrical representation of complex numbers, conjugate, modulus, addition and subtraction, polar form of a complex number and principal value of the argument |

Unit-1 Matrices and determinants -II | Inverse of a Matrix - cofactor of a matrix, adjoint of a matrix, inverse of a matrix, uniqueness of inverse; Elementary Transformations - rank of a matrix | echelon form, inverse of a matrix using elementary transformations; System of linear equations - linear equations in matrix form | solving equations using Matrix Inverse method, consistency of the system of equations by Determinant method and Rank method |

12thMat-1 Course Plan