Points and vectors
Part I: - Points and vectors in plane and in space
- Length of a vector
- Operations with vectors – sum, scalar multiple
- Linear combination of vectors
- Linear dependence of vectors
- Line segment – center, length
- Triangle – centroid, centers of sides, lengths of sides, perimeter
Part II: - Scalar product (dot product) of vectors in plane and in space
- Perpendicular vectors
- Angle of vectors
- Applications – plane shapes, solids in coordinate system
Part III: - Vector product of vectors
- Area of a plane region, area of a face of a solid
- Volume of a solid (parallelepiped, pyramid, tetrahedron)
- Complex problems covering whole topic
Plane geometry
Part I: - Line – parametric description, general equation, point-slope form equation
- Direction vector and normal vector of a line
- Line segment, half-line – parametric description
- Relative position of two lines
- Perpendicularity of lines
- Parallelity of lines
Part II: - Distance of a point from a line
- Distance of two parallel lines
- Angle of two lines
- Triangle – medians, heights (altitudes), side perpendicular bisectors
- Line and point reflection, translation
Part III: - Angles and distances – more complex problems
- Complex problems covering whole topic
Space geometry
Part I: - Line – parametric description
- Plane - parametric description, general equation
- Intersection of two lines
- Intersection of a line and a plane
- Intersection of two planes
- Relative position of points, lines and planes
Part II: - Intersection of two planes – more complex problems
- Perpendicularity of lines and planes
- Parallelity of lines and planes
- Angles of lines and planes
Part III: - Complex problems on perpendicularity
- Point, line and plane reflection
- Distance of a point from a plane
- Distance of a point from a line
- Metric problems on solids
Conics
Part I: - Circle (center and radius)
- Ellipse (center, semi-major and semi-minor axis, foci, vertex and co-vertex)
Part II: - Parabola (vertex, directrix, focus)
- Hyperbola (center, foci, vertices, semi-major and semi-minor axis, eccentricity)
Part III: - Tangent line to a conic
- Conic and a line
- Conic passing through given points
