ASSESSMENT OF STUDENTS' UNDERSTANDING OF RELATED RATES PROBLEMS Costanza Piccolo and Warren J. Code University of British Columbia, Vancouver This study started with a thorough analysis of student work on problems involving related rates of change in a first-year differential calculus course at a large, research- focused university. In two sections of the course, students' written solutions to geometric related rates problems were coded and analyzed, and students' learning was tracked throughout the term. Three months after the end of term, "think-aloud'' interviews were conducted with some of the students who completed the course. The interviews and ...
RELATED RATES PRACTICE NAME: SOLUTIONS March22,2017 STEPS FOR SOLVING PROBLEMS WITH RELATED RATES (1) Drawapicturerepresentingtheproblem. (2) Write down what you knowandwhatyouneedtondout. (3) Label your picture with the known and unknown variables. (4) Find the equation that relates the variables. (5) Take the derivative of the equation relating the variables with respect to t. RememberyourDerivativeRules! (6) Substitute the given values into the equation from Step 5. (7) Use the equation from Step 4 to nd the missing pieces of information. (8) Solve for the nal missing piece and you’re done! (1) If the radius of a balloon is increasing ...
Math 220 Groupwok 10/12/17 Related Rates Word Problems SOLUTIONS (1) One car leaves a given point and travels north at 30 mph. Another car leaves 1 HOUR LATER, and travels west at 40 mph. At what rate is the distance between the cars changing at the instant the second car has been traveling for 1 hour? z x y Set up the problem by extracting information in terms of the variables x, y, and z, as pictured on the triangle: • First sentence: dx = 30 and x(t) = 30t. dt • Second: dy = 40 and y(t) = 40(t&minus ...
Stony Brook University MAT125 Mathematics Department Calculus A About this course This course, MAT 125 (Calculus A), is the rst course in the calculus sequence MAT 125, MAT 126, MAT 127. It covers limits and continuity, derivative, dierentiation rules, implicit dierentiation, applications of dierentiation: linear approximations and dierentials, related rates and optimization problems, shapes of curves, l’Hopital’s rule, antiderivatives. All the material in MAT 125 is also covered by MAT 131 (which also does some of the MAT 126 material), although the posted material here is distinct. This course contains 26 Video Lectures (given by David Khan) with ...
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