Math 1155
Spring 05
Exam 1 Study Guide
Here's a brief overview of what I consider to be important in the various
sections on the exam.
In general, you should know that I like geometric, conceptual questions.
We'll do plenty of computations throughout the semester, including on
exams, but my tests often have lots of pictures. Sometimes I ask you to
draw them, and sometimes I'll give you a picture and ask you to interpret
it.
Section 1.1
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You should familiar with everything in this section. Distance and
midpoints could show up; more importantly, everything in the later
sections depends on your being comfortable talking about x- and
y-coordinates, points, and so on.
Section 1.2
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You should know what the graph of an equation is, and how to tell if a
certain point is on a graph. Concepts like x- and y- intercept could
easily arise on an exam, and symmetry certainly will. You also need to be
very comfortable with the equation for a circle centered at radius (h,k)
with radius r. It's conceivable you'd have to work with the general form
of the equation, in the box on page 18. That might mean completing the
square to get the standard (or "nice") form of the equation on page 16.
See example 15.
Section 1.3
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You need to know the point-slope and slope-intercept equations of lines.
(Given one, how could you change to the other? If I give you either a
point and a slope, or two points, could you write down the equation of the
line in both forms?) You should know what slopes are and how to interpret
them.
Section 2.1
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Essentially this entire class will be spent studying functions, so a basic
understanding of this material is important for the rest of the semester,
let alone this exam.
Section 2.2
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As with the graphs in section 1.2, you need to know what the graph of an
equation is, and how to find its intercepts. As with 2.1, if you don't
understand this section you'll have difficulty with everything else, so
spend a little time to make sure everything makes sense here.
Section 2.3
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This is a long section with a lot of important concepts. We spent a fair
amount of time in class on odd and even functions, so you should know
those definitions and expect that to come up on the exam. We also talked
about functions increasing and decreasing, so that's fair game, along with
minima and maxima.
Section 2.4
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If I ask you to work with a function given by a specific equation, it
would likely be one of the ones in this library. These functions are sort
of the "basic building blocks" that we'll use all semester long, so you
should be familiar with them. Also pay attention to piecewise-defined
functions.
Section 2.5
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As promised, anything from this section will be fairly basic. You might
have to shift a function around reflect it, but don't worry about (for
example) horizontal compressions for now.