Mathematics Department

Essential Knowledge and Skills

Students in Advanced Placement Calculus BC study single-variable calculus at a level equivalent to at least a semester of calculus at most colleges and universities. Students in Advanced Placement Calculus BC study limits, the techniques and applications of the derivative, techniques and applications of the definite integral, the Fundamental Theorem of Calculus and basic differentials. Students also study parametric, polar, and vector functions; integration by parts and partial fractions; and improper integrals. Polynomial approximations and series including concepts of series, series of constants, and the Taylor series are also studied. Algebraic, numerical, and graphical representations are emphasized throughout the course.

Indicators of Student Learning

Upon the completion of this course, students will:

Problem Solving

• Select appropriate method for problem solving.

• Choose from and employ a variety of problem solving strategies including: diagrams lists and tables, looking for and identifying patterns, eliminating possibilities, solving a similar problem, guessing and checking.

• Use analytical process to organize information, establish problem solving strategies, solve the problem, and analyze the results.

• Calculate slope of a tangent line, area under the curve, and volumes of solids of revolution.

• Represent and solve routine and non routine problems verbally, numerically, graphically, and algebraically.

Reasoning and Proof

• Understand properties, definitions, theorems and prove applicable to problem.

• Explain and justify problem-solving procedures

• Make and investigate mathematical conjectures

• Realize that a mathematical conjecture does not constitute a proof

Communication

• Express calculus concepts using correct terminology and differential and integral symbols in oral, pictorial, and written form.

• Use the language of mathematics to clearly express mathematical ideas.

• Build calculus vocabulary by exploring concepts and adding understanding.

• Use communication strategies to facilitate retention of information such as repeating information, constructing mnemonics and taking notes.

• Synthesize information to answer questions, solve problems, and communicate ideas.

• Share ideas and information in small groups and whole class discussions, visual presentations, and written response especially prior to tests.

• Use writing as a learning tool, i.e. journals, learning logs, paraphrasing, summarizing, and notebooks.

Technology

• Use a graphing calculator efficiently and accurately for computation, graphing and modeling a variety of mathematical concepts

• Be able to use technology to solve problems, experiment, interpret results, and verify conclusions Assessment Upon the completion of this course, students will:

• Demonstrate competency in problem solving by using appropriate methods and techniques, generating a solution and checking the reasonableness of that solution.

• Demonstrate competency in reasoning and proof by using appropriate properties and theorems to obtain a solution.

• Demonstrate competency in communication by using correct terminology, expressing ideas clearly, explaining analytical process, presenting ideas and information in written response.

• Demonstrate competency in technology by using graphing calculators.