AP Calculus MATH 136-04

Exam #2

Wednesday, Nov. 3, IN CLASS

The second exam covers Sections 3.8 and 3.9, Chapter 4 (excluding Sections 4.4 and 4.7), and Sections 5.1 - 5.7. It is recommended that you go over the homework problems (HW#4 - 6) and quizzes (#4 - 6), as well as your class notes. Many of the problems and questions we discuss in class are excellent examples of test questions. The solutions to your WebAssign problems on HW#4 - 6 can be seen by clicking "View Key" near the top of each assignment. You can click ``Practice Another Version'' after each problem to try the same problem but with different numbers.

I have also listed some sample problems from the Chapter 3, 4 and 5 Review Exercises below. The odd answers are in the back of the book while the evens are listed here. The Concept-Check at the end of each chapter (before the exercises) is also a source for good questions. The exam will be designed to take the full class period (45-50 minutes).

Exam Review: We will review for the exam on Monday, Nov. 1, during class. Please come prepared with specific questions.

Note: You will be given a scientific calculator for the exam which does NOT have graphing capabilities so be prepared to answer questions without your personal calculator.

Chapter 3 Review Exercises, pp. 248 - 250
Problems:   68 (a,b,c,e), 73, 75a

The answers to the evens are:
68.   (a) v = 3t^2 - 12, a = 6t, (b) upward: t > 2, downward: 0 < t < 2, (c) 23, (e) speeding up: t > 2, slowing down: 0 < t < 2.

Chapter 4 Review Exercises, pp. 324 - 326
Problems:   1, 2, 3, 7, 8, 9, 10, 27, 29, 31, 32, 33, 36, 37, 39, 40, 44, 47, 51, 53, 54, 55, 57, 58

The answers to the evens are:
2.   f(-1) = -sqrt{2} is the absolute min and f(2/3) = 2 sqrt{3}/9 is the absolute max.
8.   (a) no asymptotes, (b) increasing on (-3,0), (0, infinity), decreasing on (-infinity, -3), (c) local min at f(-3) = -27, no local max, (d) concave up on (-infinity, -2), (0, infinity), concave down on (-2, 0), inflection points at (-2,-16) and (0,0)
10.   (a) vertical asymptotes at x = 1,-1 and horiz. asymp. at y = 0, (b) decreasing on (-infinity, -1) and (-1, 0), increasing on (0, 1) and (1, infinity), (c) local min at the point (0,1), no local max, (d) concave up on (-1, 1) and concave down on (-infinity, -1), (1, infinity), no inflection points.
32.   0
36.   dh/dt = 8/(9 Pi) cm/sec
40.   The point is (4,2).
44.   Pi/6
54.   f(u) = (1/2)u^2 + 2u^(1/2) + 1/2
58.   s(t) = -sin(t) - 3cos(t) + 3t + 3

Chapter 5 Review Exercises, pp. 425 - 427
Problems:   1, 3, 5, 8, 9, 11, 12, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 32, 33, 34, 39, 40, 41

The answers to the evens are:
8.   (a) e^(Pi/4) - 1, (b) 0, (c) e^(arctan x)
12.   1/10
18.   2/(3 Pi)
20.   -ln(4)/3
22.   4 ln 2 - 15/16
24.   25/9 - (100/9) e^(-3)
26.   2/81
32.   x arctan(x) - (1/2)ln(1+x^2) + c
34.   arctan(e) - Pi/4
40.   cos^3 x/(1 + sin^4 x)