Differential Equations | Formation of differential equations, variable separable form, solution of differential equations of first order and first degree, homogeneous differential equations. |
Matrices | Matrix, types of matrices, inverse of a matrix, operations on matrices, determinant, solution of linear equations using matrices. |
Coordinate Geometry | Straight lines, normal to a circle, distance of a point from a line, section formula, distance formula, slope of a line, angle between two lines, equation of a line in various forms, intersection of lines, circle, general form, parametric form, equation of a circle in standard form, tangent to a circle. |
Three-Dimensional Geometry | Coordinate system in space, direction cosines and direction ratios of a line, the distance between two points, equation of a line in vector form and Cartesian form, the angle between two lines, equation of a plane, the angle between a line and a plane, distance of a point from a plane. |
Application Of Integrals | Definite integral, integration by parts, definite integral as the limit of a sum, integration by substitution, definite integral as the limit of a sum, integration using trigonometric identities, and integration using partial fractions. |
Application of Derivatives | Tangents and normals, maxima and minima, rate of change. |
Determinants | Determinant of a square matrix, Cramer's rule, properties of determinant. |
Vectors | Vectors in two and three dimensions, vector triple product, dot product, cross product, direction cosines and direction ratios, scalar triple product. |
Limits and Derivatives | Limits of functions, differentiation rules, derivatives of functions, derivatives of trigonometric functions, logarithmic functions, inverse trigonometric functions, and exponential functions. |
Conic Sections | Parabola, hyperbola, ellipse, their properties, equations in standard form. |
