Calculus 1, MATH 135-01

Prof. Gareth Roberts

Exam #1

Thursday, Feb. 25, In Class

The first exam covers Chapter 1 (excluding Section 1.7) and Sections 2.1 and 2.2. It is recommended that you go over homework problems (HW #1 - 3), class notes, and worksheets. 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 also click on "Practice Another Version" to redo some homework problems.

In addition, some review problems from the Chapter 1 and 2 Review Exercises are listed below. The odd answers are in the back of the book while the evens are listed here. The exam will be designed to take roughly one hour although you will have 90 minutes if needed.

Exam Review Session: Monday, Feb. 22, 7:00 - 8:30 pm in Smith Labs 154, led by Jake Alofs.
Please come prepared with specific questions.

Note: You will be allowed a scientific calculator for the exam which does NOT have graphing capabilities. Please bring your own calculator with you to the exam.

Chapter 1 Review Exercises, pp. 53 - 54
Problems:   2, 3, 6, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 23, 24, 25, 27, 30, 35, 36, 40, 42, 43, 44 (a and b), 52, 53, 57, 58

The answers to the evens are:
2.   (a) (1, 9), (b) [-1, -1/5].
6.   Shift the graph of the standard parabola 2 units to the left and 1 unit down.
8.   The first graph is compressed vertically by a factor of 2. The second graph is stretched horizontally by a factor of two (sketch it over the domain [0, 8]).
10.   An odd function is symmetric with respect to the origin.
16.   (a) even, (b) neither, (c) even.
24.   y = 5.
30.   h(z) = -2(z - 3)2 + 21, so the maximum value of h(z) is 21.
36.   The graph of y = 10-x is an exponential decay function with y approaching 0 as x approaches infinity.
40.   h(g(x)) = cos(x-1), with domain x ≠ 0. g(h(x)) = sec(x), with domain x ≠ ± π/2, ± 3π/2, ± 5π/2, etc.
42.   (a) 2π/3 corresponds to 120 degrees and has coordinates (-1/2, sqrt{3}/2).
(b) 7π/4 corresponds to -45 degrees and has coordinates (1/sqrt{2}, -1/sqrt{2}).
(c) 7π/6 corresponds to 210 degrees and has coordinates (-sqrt{3}/2, -1/2).
The 6 standard trig functions are easily obtained from the coordinates of each point.
44.   (a) tan(θ) = -4/3, (b) sin(2θ) = -24/25. Use the formula sin(2θ) = 2sin(θ)cos(θ).
52.   (a) (ii), (b) no match, (c) (iii), (d) no match.
58.   (a) yes, (b) yes, f-1(x) = x + 1 if x < 0, ex if x ≥ 0 (piecewise function).

Chapter 2 Review Exercises, pp. 110 - 112
Problems:   1, 5, 8, 9, 15, 21, 26, 41, 45

The answers to the evens are:
8.   0.33
26.   5