MAD501: Math Analysis (2011-2012)
CURRICULUM PROGRAM: Mathematics
COURSE TITLE: Math Analysis
CALENDAR YEAR: 2011-2012
GRADE LEVEL: 11-12
COURSE LENGTH: 36 weeks
Major Concepts/Content: This course will involve students in units and topics of study of operations with functions and equations, circular functions, vectors, applications of matrices, complex and polar coordinates, recursion, advanced proof ideas, rates and areas, statistical interference, algebra and algorithms. Problem solving in real world applications involving these units of study will be the beginning and focal points of lessons. Connections will be made of graphs with equations with real world situations. Reasoning in trigonometry, probability, discrete math, mathematical structure, and the conceptual underpinnings of calculus is a major emphasis in this course.
Major Instructional Activities: Students will be involved in communicating ideas through conjecture and validation of thinking in functions, models, matrices, probability, and statistics. They will be engaged in cooperative groups, whole class settings, or individually to reinforce concepts in functions, polar coordinates, advanced proof ideas, and algebraic algorithms. Students should have access to graphing calculators at all times.
Major Evaluative Techniques: Many evaluative processes will be used to assess students’ written and oral work. These include multiple-choice, short-answer, discussion, or open-ended questions; structured or open-ended interview; homework; projects; journals; essays; dramatization; and class presentations. Testing formats will include restricted-time written tests, two-staged tests, take-home tests, oral tests and student-produced tests. Assessment methods can be supplemented by student-produced analysis of problem situations, solutions to problems, reports on investigations and journal entries. Calculators should be available in most assessment situations.
Course Objectives: Upon successful completion of the mathematical analysis course, the student should be able to:
- Solve equations symbolically, graphically, and numerically and knows how to use the quadratic formula for solving quadratic equations
- Uses matrices to solve systems of equations
- Evaluate f(x) for complex arguments
- Visualize objects, paths, and regions in space, including intersections and cross sections of three-dimensional figures, and describes these using geometric language
- Use and apply vector geometry
- Use coordinate geometry techniques to graph conic sections
- Graph polar and parametric coordinates and equations
- Determine the behavior of a function, its maximum and minimum, its interval and its critical points
- Use arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively
- Define, use and manipulate expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities
- Recognize, draw, and analyze graphs of trigonometric functions
- Organize, analyzes, and displays single-variable data choosing appropriate frequency distribution, circle graphs, line plots, histograms, and summary statistics
- Interpret representations of data, compares distribution of data, and critiques conclusions and uses of statistics, both in school materials and public documents
- Explore questions of experimental design, use of control groups, and reliability
- Use matrix theory with graphics calculators to solve systems of equations, transformations, and finite functions
- Use and analyze trigonometric principles, properties, and laws
- Solve problems using the Law of Sines and Law of Cosines.