Parametric Equations, Polar Coordinates, and Vector-Valued Functions – Unit 9

Unit 9 includes all the topics listed in the title. These are BC only topics (CED – 2019 p. 163 – 176). These topics account for about 11 – 12% of questions on the BC exam. Comments on Prerequisites: In BC Calculus the work with parametric, vector, and polar equations is somewhat limited. I always…

Linear Motion (Type 2)

For updated information for the special 2020 exams click here. AP  Questions Type 2: Linear Motion We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, person, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity…

Type 2 Questions: Linear Motion

We continue the discussion of the various type questions on the AP Calculus Exams with linear motion questions. “A particle (or car, or bicycle) moves on a number line ….” These questions may give the position equation, the velocity equation (most often), or the acceleration equation of something that is moving, along with an initial…

A Note on Speed

A quick note on speed. The idea of differentiating speed to determine where it is increasing or decreasing is perfectly reasonable. . Then, Since the denominator is positive, and speed is increasing when  and have the same sign, and and speed is decreasing when they have different signs. As a practical matter, this is the…

Parametric and Vector Equations

In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations  or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement in the x- and y-direction is given by the vector . The vector…