This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Topics include: 1. Quadratic Relations of the Form y ax2 = + bx + c By the end of this course, students will: • determine the basic properties of quadratic relations; • relate transformations of the graph of y = x2 to the algebraic representation y = a(x – h)2 + k; • solve quadratic equations and interpret the solutions with respect to the corresponding relations; • solve problems involving quadratic relations. 2. Analytic Geometry By the end of this course, students will: • model and solve problems involving the intersection of two straight lines; • solve problems using analytic geometry involving properties of lines and line segments; • verify geometric properties of triangles and quadrilaterals, using analytic geometry 3. Trigonometry By the end of this course, students will: • use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity; • solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem; • solve problems involving acute triangles, using the sine law and the cosine law.