Topics of Study

Limits & Continuity

• piecewise defined functions
• finding limits graphically
• finding limits algebraically
• continuity
• limits involving infinity

The Derivative

• tangent lines
• the derivative
• differentiation techniques: power rule, product and quotient rules, chain rule
• implicit differentiation
• higher order differentiation

Applications of the Derivative

• curve analysis
• optimization
• related rates
• growth and decay

Transcendental Functions

• derivatives of trig functions
• derivatives of exponential functions
• derivatives of logarithmic functions

Integration

• antiderivatives
• definite and indefinite integral
• integration techniques

Applications of Integration

• finding area under a curve
• finding area between curves
• volume of solids of revolution

Mathematical Competencies

Reasoning and Analyzing

• estimate reasonably
• use reason and logic to analyze and apply mathematical ideas
• use tools or technology to analyze relationships, test conjectures, and check solutions

Understanding and Solving

• develop a conceptual understanding of ideas
• visualize to explore and illustrate concepts and relationships
• apply flexible strategies to solve problems

Communicating and Representing

• communicate mathematical thinking in many ways
• use mathematical language to contribute to mathematical discussions
• represent ideas in various ways (written, symbolic, pictorial)
• explain and justify ideas

Connecting and Reflecting

• reflect on mathematical thinking
• connect mathematical concepts to each other