Summary for Midterm One - Math 120

Here are some thoughts I was having while considering what to put on the first midterm.
The core of your studying should be the assigned homework problems: make sure you really
understand those well before moving on to other things (like the old midterms on the test
archive).

• Chapter 1 -Warm Up

– One of the most important ideas of this chapter is that of multiplying by one as a
means of unit conversion. This idea makes all unit conversions have a common
method, and helps one’s notekeeping.

• Chapter 2 - Imposing Coordinates

– This chapter introduced the use of the coordinate system and the distance formula.

– A classic problem from this chapter is one in which two objects are moving and we
need to describe the distance between them, like problems 2.3, 2.13 and 2.14.

• Chapter 3 - Three Simple Curves

– This chapter introduces circles and horizontal and vertical lines. You should be sure
you are comfortable finding the equation of a circle from a variety of descriptions.

– You should be able to find the intersection of a circle with a vertical or horizontal
line.

– The classic problems from this chapter are 3.4 and 3.7.

• Chapter 4 - Linear Modeling

– In this chapter, we get the general line definition. Be sure you are able to find the
intersection of a given circle with a general line.

– We also have the idea of perpendicular lines, and the method for finding the shortest
distance between a line and a point not on that line.

– Especially good problems are 4.8, 4.12, 4.14 and 4.15.

• Chapter 5 - Functions and Graphs

– Here the function is introduced.

– Every function has a domain, range and graph. Be sure to know what each is, and
how to determine it for a given function. As we said, finding the range and graph
can be hard; rest assured, if asked to find the range or graph of a given function, it
will be doable.

– You should be comfortable with multipart functions (what are they, how to evaluate
one, how to solve equations involving them, etc.) What’s an example of a multipart
function?

– I like problem 5.10 particularly.

• Chapter 6 - Graphical Analysis

– Chapter 6 talks about a variety of graph-related topics.

– You should understand how to graph a multipart function, where each part is linear.

– Especially good problems are 6.3, 6.4, 6.5, 6.6 and 6.8.

• Chapter 7 - Quadratic Modeling

– The quadratic function is introduced. You should know the significance of the vertex
and how to find it. You should be able to sketch the graph of a given quadratic
function.

– You should be able to determine the maximum and minimum value of a quadratic
function on a specified interval.