AP Calculus MATH 136-04

Exam #1

Wednesday, Sept. 29, IN CLASS

The first exam covers Chapter 1 (excluding Section 1.4), Chapter 2, and Chapter 3 (excluding Sections 3.8 and 3.9). It is recommended that you go over the homework problems (HW#1 - 3) and quizzes (#1 - 3), 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#1 - 3 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 1, 2 and 3 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, Sept. 27, 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 1 Review Exercises, pp. 81 - 82
Problems:   1, 2, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 23, 24, 25, 26, 27, 31

The answers to the evens are:
2.   (a) 3, (b) passes horizontal-line test, (c) 0.25, (d) [-1,3.5], (e) reflect the graph of g about the diagonal
6.   Domain: [-2,2], Range: [0,4].
8.   Domain: (-infinity, infinity), Range: [2,4].
12.   Graph the ln(x) function, shift it right by 2 units and stretch it vertically by a factor of 3.
16.   This is a piecewise function which is continuous at x = 0. The left piece is a line with slope -1 and the right piece is a shifted exponential.
24.   The inverse is (1-x)/(2x-1).
26.   (a) ln 5, (b) e^2, (c) ln(ln(2))

Chapter 2 Review Exercises, pp. 165 - 168
Problems:   1, 3, 4, 5, 7, 9, 10, 13, 14, 16, 18, 21, 23, 27, 29, 30 (a and b), 33, 34, 35, 36, 37 (a and b), 39, 40, 42

The answers to the evens are:
4.   0
10.   -1
14.   1/3
16.   0
18.   -1
30.   (a) f'(2) = 10, (b) y = 10x - 16
34.   Your graph should be positive (above the x-axis) until a small positive x-value, then become negative (below the x-axis).
36.   Your graph should be discontinuous at the cusp since the function is not differentiable at that point.
40.   a = f, b = f'' and c = f'.
42.   This is just like Nixon's statement on inflation. The first derivative of the cost of living function is positive since the cost rises but the second derivative is negative because it is rising at a slower rate (slopes decreasing means concave down).

Chapter 3 Review Exercises, pp. 248 - 250
Problems:   1, 2, 3, 4, 7, 9, 11, 12, 13, 15, 16, 20, 21, 23, 25, 27, 28, 33, 34, 35, 37, 41, 42, 51, 52, 65

The answers to the evens are:
2.   -sin(tan x) sec^2(x)
4.   (3x + 5)/(2x + 1)^(3/2)
12.   4(arcsin 2x)/sqrt(1 - 4x^2)
16.   (y - 2x cos y)/(2 cos(2y) - x^2 sin y - x)
20.   [(ln x)^(cos x)]*[cos x/(x ln x) - sin x * ln(ln x)]
28.   -sin(x) e^(cos x) - e^x sin(e^x)
34.   1/(1 + (arcsin sqrt(x))^2 ) * 1/sqrt(1 - x) * 1/(2 sqrt(x))
42.   y = -1
52.   (a) -2, (b) -3/8, (c) 6