LC Math 2 Advanced P - MA5034

This is the second course in an accelerated common core based college preparatory math sequence. It is the next course for students that have taken LC Math 1 Advanced. This course focuses on the exploration of geometric concepts through visual, numerical and analytic lenses. Applications that utilize algebraic problem solving developed in LC Math 1 Advanced will be included throughout the course to reinforce and strengthen students’ proficiency on these topics prior to enrollment in AP Precalculus. Students interact with plane Euclidean geometry both synthetically (without coordinates) and analytically (with coordinates) throughout the course, with an emphasis on the proof of theorems used to describe relationships that can be reasoned inductively.

 

After a brief introduction to the language, notation and reasoning skills that define geometry, students use a transformational approach to define congruence of figures and apply that congruence specifically to triangles. Students use this knowledge to analyze the characteristics of quadrilaterals and angles formed when parallel lines are cut by a transversal. Non-rigid transformations are used to introduce the concept of a dilation, which allows students to define similar figures, including circles. After an exploration of the arcs formed by various angles inscribed in a circle, students use right triangles to develop definitions for the trigonometric functions and unit circle. Circular trigonometry is investigated using the sine and cosine functions and their behavior over various angles. Vectors, which were used to define translations earlier in the course, are applied to real-world problems involving directional forces and the Law of Sines and Law of Cosines is used to find the magnitude and direction of resultant vectors. The course concludes with an exploration of various locus points, both inside a triangle and in the plane (which lead to the derivation of the equations of conic sections), and a deepening of understanding related to three-dimensional figures that were introduced in 8th grade, including the use of Cavalieri’s Principle to calculate the volume of a three-dimensional figure.