AP Calculus AB / Mr. Hansen 2/1/2005

Name: _________________________

Practice Test on Chapter 6
Instructions: No calculator allowed. Do not answer the questions on the first pass; simply
estimate the score you think you would earn (0 to 5) if this were a real test.

1.	A differential equation (usually abbreviated ____________ ) is an equation that __________ ______________________________________________________________ (multiple words needed). A general solution to a differential equation is a ________________________________________________ that satisfy the differential equation, whereas a __________ solution is a single ___________ or ___________ that not only satisfies the ___________ _____________ itself, but also _________ one or more ___________ _____________ .
2.(a)	Solve the differential equation dy/dx = .074y subject to the initial condition (0, 5.28).
(b)	The relationship that y exhibits with respect to independent variable x in part (a) is called __________________ ________________ .
(c)	If x measures time periods, then what x value (approximately) corresponds to a y value of 10.56? (A) 8 (B) 10 (C) 12 (D) 14 (E) 16
3.	State the formula for integration by parts.
4.	Use integration by parts to compute ò 3x ln 2x dx. Show your work.
5.	Showing your work, verify that ò ln z dz = z ln z – z + C.
6.	A cup of coffee cools in 30 minutes from 80° C. to 35° C. in a room whose temperature is 30° C. The cooling satisfies Newton’s differential equation, dT/dt = –k(T – Tambient). Write an expression for the proportionality constant.
7.	Consider the differential equation .
(a)	Sketch the slope field, using the window [–10, 10] ´ [–10, 10]. Label the axes.
(b)	On your slope field, sketch the solution that passes through the point (1, 5).
(c)	Continuing with the assumptions given above, use Euler’s Method with a step size of –0.1 to estimate M when t = 0.8. You need not simplify.
(d)	Would an answer to (c) be too high or too low? Explain.