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.
