Mathematics: Analytical Geometry-

Coordinate Systems- Cartesian Coordinate System, Polar Coordinate System, Cylindrical Coordinate System, Spherical Coordinate System, Geographic Coordinate System, Curvilinear Coordinate Systems.

Distance Formula- Euclidean Distance, Three-Dimensional Euclidean Distance, Manhattan Distance, Minkowski Distance, Chebyshev Distance.

Midpoint Formula- Midpoint Formula for Two-Dimensional Space (Cartesian Plane), Midpoint Formula for Three-Dimensional Space, Midpoint Formula for Complex Numbers, Midpoint Formula for Vectors, Midpoint Formula for Parametric Curves.

Equations of Lines- Slope-Intercept Form, Point-Slope Form, General Form, Two-Point Form, Parallel and Perpendicular Lines, Intercept Form, Parametric Form.

Parallel and Perpendicular Lines- Parallel Lines:- Horizontal Parallel Lines, Vertical Parallel Lines, Oblique Parallel Lines. Perpendicular Lines:- Vertical and Horizontal Lines, Diagonal Perpendicular Lines.

Slope of a Curve (Possibly)- Positive Slope, Negative Slope, Zero Slope, Undefined Slope, Increasing Slope, Decreasing Slope, Constant Slope, Instantaneous Slope, Average Slope, Tangent Slope.

Conic Sections- Circle, Ellipse, Parabola, Hyperbola.

Transformations of Graphs- Translation (Shift), Dilation (Stretch/Compression), Reflection, Rotation, Vertical Stretch/Compression, Horizontal Stretch/Compression, Combination of Transformations.

Symmetry- Reflection Symmetry (Line Symmetry), Rotational Symmetry, Translational Symmetry, Point Symmetry (Central Symmetry), Glide Symmetry, Helical Symmetry, Fractal Symmetry.

Applications of Analytical Geometry- Graphing Equations, Distance and Midpoint Formulas, Equations of Lines and Planes, Curve Fitting and Regression Analysis, Vector Analysis, Transformation Geometry, Optimization Problems, Conic Sections, Analyzing Curves and Surfaces, Geometric Modeling.