PreCalculus
Midterm
Name
For each box you are to choose which question you want to answer and show all work for that prompt only.
Answer only one of the questions in each section!
1.
As a submarine at the surface of the ocean makes a
dive, its path makes a 21º angle with the surface. If
the submarine goes for 300 m along its downward
path, how deep will it be? How many meters along
this path must it go to reach a depth of 1000 m?
2.
Determine the 201st term of the sequence:
79,  76,  73,  70, ...
Solve the equation on the interval 0    2 :
2cos  2   3  0
List the next 3 terms of the sequence:
 363  726  1089
,
,
7
7
7
3.
Determine the exact value of each expression:


3 
tan sec1  
 
 3  

4.
After being struck with a hammer, a gong vibrates 22
vibrations in the first second and in each second
2
thereafter makes
as many vibrations as in the
3
previous second. Find how many vibrations the gong
makes before it stops vibrating.
Find the exact value of the tan 870 (No decimals
here, use an identity and unit circle knowledge)
Consider an equilateral triangle with sides of 40
centimeters. Connect the midpoints of the sides of the
triangle. Continue to connect midpoints of each
successive triangle. List the perimeters of the first
four triangles formed. What is the sum of the
perimeters of the first n triangles?
5.
Use a Double-Angle Formula to determine the exact
5
value of tan  2  given sec    , sin   0 .
2
6.
Determine the sum of the following series:
a.
1 2 4 8
8192
     
5 5 5 5
5
Determine the exact value of cos(   ) :
3 
2

sin   ,     ; cos   , 0    .
5 2
5
2
Every March the NCAA holds their National
Championship Women’s Basketball Tournament which
allows 64 universities to participate. Each game consists
of two teams and only the winner of each game advances
to the next round of competition.
9
b.
 100 (1.08)
n 0
4
c.
 ( 2 n  4)
n




n 1



Write a sequence for the number of games played
in each round.
Is this arithmetic or geometric?
Is this sequence finite or infinite?
How many rounds are needed to crown a
champion?
Write the series related to your sequence?
What is the sum of this series?
What does this sum represent?
7.
The roof of a house is being reconstructed to
accommodate heavy snows. The current 32-foot
roofline makes an 18.2 angle with the horizontal.
The owner has decided to construct the new roof so
that it makes a 50 angle with the horizontal. What
will be the length of the new roofline?
8.
A software program requires users to login with a case
sensitive 6-character password with no spaces. Using
a “QWERTY” keyboard (see handout), find the
number of possible passwords the program will
accept.
A surveyor marks off measurements shown below for
a triangle shaped courtyard in a new community.
Determine the angle at C two different ways, then find
the lengths of the distances marked a and b.
A electrical outlet has a 98% reliability rating
(meaning when an appliance is plugged in it will work
98% of the time.) Suppose you make toast each
morning for one week using the same outlet. Find the
probability of the outlet not working exactly 2 of these
days.