MATH IIA: GEOMETRY
This course develops geometry as a system of logical reasoning using clear definitions, postulates, theorems and corollaries to foster creative and critical thinking. Geometric elements, structure and relationships are presented and integrated with algebra, trigonometry, logic and arithmetic. Deductive reasoning is introduced and applied to geometry to develop formal mathematical proofs. The topics of congruence, parallelism, quadrilaterals, circles, similarity, areas, regular polygons, coordinate geometry and locus are studied from geometric, algebraic and graphic perspectives for the improvement of reasoning. This course amply covers all the geometry necessary for achievement on the SAT I.
MATH II: INFORMAL GEOMETRY
This is a course in which the principles of logical reasoning are introduced before the study of proof. Students develop their deductive reasoning skills throughout the course by providing informal justifications and informal arguments. Real-life applications illustrate geometric concepts. Specific subject areas of study include: parallel lines and planes, congruent triangles, quadrilaterals, right triangles, circles, and similar polygons. Also developed is the study of transformations and determining the area of plane figures as well as the area and volume of solids. Trigonometry involving triangles is also introduced. This course amply covers all the geometry necessary for achievement on the SAT I.
Students construct and study the properties of the circle, parabola, ellipse and hyperbola. Students also study the equations of conic sections to match equations to graphs. History of the mathematicians who contributed to conic sections as well as real world usages will be explored throughout the seminar.