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Curriculums/Geometry
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UNIT 1: POLYGONS
Introduction to polygons, Curves and the concept of polygons Basic properties of convex polygons Regular polygons Quadrilaterals and their basic properties Trapezoids Parallelograms Rhombi and rectangles Squares and Kites
UNIT 2: CIRCLES
The concept of circle fundamental concepts of the circle Corresponding position of a line and a circle in the same plane Properties related to chords of a circle. Properties of tangents of a circle Corresponding position of two circles Arcs and angels of the circle Circumference and arc length of circles Calculation of tangent lengths of circles Power of a point Circles of triangle Inscribed and circumscribed quadrilaterals
UNIT 3: ANALYTIC ANALYSIS OF CIRCLE
Equation of circle, parametric equation of circle Construction of a circle whose equation is given Equation of circle whose three points are given Corresponding positions of a line and a circle Equations of Tangents and Normals
UNIT 4: AREAS OF POLYGONAL REGIONS
Concept of polygonal regions Area of triangular regions Area of triangular regions Properties related to area of triangles and some conclusions Areas of quadrilaterals Area of some special quadrilaterals Area of regular polygons Area of circles, sectors, segments and rings Area of segments and rings Area of circles and sectors, segments and rings
Unit 1: AREAS AND VOLUMES OF SOLIDS
Prisms Regular, rectangular, right and oblique prisms Area and volume of prism Cavalier's Principle Cylinders Right cylinder and oblique cylinder Area and volume of a cylinder Pyramids Regular pyramid Regular tetrahedron, regular Octahedron Area and volume of a pyramid Area and volume of Frustum of a pyramid
Cones Right and oblique cone Area and volume of a cone Area and volume of a Frustum of a cone
Spheres Corresponding position and crossection Determination of a sphere Area of Zone, Lune and spherical segment Volume of spherical segment and Wedge
Unit 2: ANALYTICAL ANALYSIS OF THE CONES
ELLIPSE Definition of ellipse and the axes of the ellipse Eccentricity of the ellipse Equation of the ellipse with center of the origin Equation of the tangent and the normal Parametric equation of the ellipse
HYPERBOLA Definition of hyperbola Eccentricity of the hyperbola Equation of the hyperbola with center at the origin Equation of the tangent and the normal Asymptotes of the hyperbola Rectangular hyperbola
PARABOLA Definition of parabola Focus and directrix of a parabola Equations of the tangent and the normal an
Unit 3: VECTORS
Vectors in space, analytical analysis of the line and the plane Position vector The vector determined by two points Norm of the vector and unit vector Operations on the set of vectors Multiplication of the vectors by scalars Linear combination of vectors (dependence and independence) Parallel vectors, inner product function Euclidean inner product, Schwarz inequality
Unit 4: MATRICES
Definition of a matrix Operation with matrices Addition, subtraction, multiplication of matrices Properties of matrix multiplication Identity matrix Transpose of a matrix Properties of transposes Inverse of a matrix by Gaussian Jordan method
Unit 5: DETERMINANTS
Minors and cofactors of a matrix Properties of Determinant Determinant of a transpose Ad joint of a matrix Determinant and inverse of a matrix Determinant of a transpose
SYSTEMS OF LINEAR EQUATIONS
Solution set of a system of linear equations Methods of solution of system of linear equations Cramer's rule
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