Math 120
"Explanation Exam" Prep #1
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Directions:
For exam #1, you will be provided with an exam consisting of some number of
questions. For each question, you will be given not only the question, but also the answer, and
some space to explain how one gets from the question to the answer. Your grade will depend
on your ability to explain all the steps that are needed in order to fully, completely, and as
correctly as you can, answer the question.
Prior to exam #1, you will do several "Exam Preparations", or "Preps" for short. The
objective here is to help you figure out how much detail you will need to provide on an actual
exam, so that you know how to do this type of exam prior to exam day.
You should do this Prep in the following manner:
1. Go through the sample questions, and for each question, explain the answer to each
question to the best of your ability
a. This is an Open-Book Prep: you are allowed to use any notes, books, homework,
etc that you've got.
Remember that the objective is to figure out how to explain things, not to regurgitate
things.
b. Since the objective here is to familiarize yourself with this type of exam, if you get
stuck on something, skip it and go on to another question. Try to answer at least one
question completely, in order to get the maximum benefit from this prep.
c. The actual EXAM is not open book. Your instructor has/will make clear what
you're allowed to bring into the exam, if anything.
d. Please use English sentences to clarify why your math is correct. Don't just
write in number & equations: explain how you get from one to another.
2. Once you're done, get a sample solution.
3. Next, find a someone else who is also done (your prep partner), and exchange papers with
them. Go through the other person's explanations, and compare it to the solution.
a. Notice that each step in the solution is numbered
b. As you're going through their solution, when you find the part of their explanation that
corresponds to one of the numbered steps, write down that number on their paper,
and circle it.
4. When you get your paper back, examine it closely.
Did you include all the steps listed on the sample solution?
Did your partner find all those steps?
What can you do differently next time, in order to both make sure that you include all the
steps, and that your partner can easily identify which parts of your work match up with each
step?
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Math 120
"Explanation Exam" Prep #1
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5
, where θ is in the second quadrant,
13
find all the other trig functions using definitions:
1) Given Sin θ =
(At each step in your explanation, keep all numbers in fraction form (i.e., no decimal numbers from
your calculator))
5
13
13
Csc θ =
5
Sin θ =
Answers:
12
Cos θ = 
13
13
Sec θ = 
12
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5
12
12
Cot θ = 
5
Tan θ = 
Math 120
"Explanation Exam" Prep #1
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5
, where θ is in the second quadrant,
13
find all the other trig functions using trig identities:
2) Given Sin =
(At each step in your explanation, keep all numbers in fraction form (i.e., no decimal numbers from
your calculator))
5
13
13
Csc θ =
5
Sin θ =
Answers:
12
Cos θ = 
13
13
Sec θ = 
12
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5
12
12
Cot θ = 
5
Tan θ = 
Math 120
"Explanation Exam" Prep #1
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3) You're sitting in class one day, and you overhear a classmate, Bob, explaining a problem to
someone else. What you hear is the following:
"Tangent of 30 degrees? Without using a calculator? No problem. You just draw out your handydandy 30-60-90 triangle like this, and notice that the side adjacent to 30° is 3 , the opposite is 1,
adjacent
and the hypotenuse is 2. We could just use the definition of tan, namely that tan =
, but
opposite
2
hypotenuse
cos
where's the fun in that? Let's use the fact that tan =
, and that Sin 
(which is ),
sin
1
opposite
2
2
hypotenuse
and that cos θ =
(which is
). Plug those into the equation for tan, get 1 , which
2
adjacent
3
3
1
simplifies to
- Voila!"
3
List all the mistakes that Bob has made:
Explain why Bob still got the right answer (feel free to use write out some math, in order to help you
explain this)
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