MTE 180 Place label
hereel her
Phil Clark
No note
cards!
Scratch paper
is provided.
Use of
calculators is encouraged.
This test is 8
pages and includes 10 problems.
Instructions:
To receive credit, you must show all work and explain all your reasoning. If you use you calculator, tell me how. If you guess-and-check, tell me how.
Honor Statement:
By
signing below you confirm that you have neither given nor received any
unauthorized assistance on this exam.
This includes any use of a graphing calculator beyond those uses
specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this
exam with anyone until the exam testing period is over. In addition, your calculator’s program
memory and menus may be checked at any time and cleared by any testing center
proctor or Mathematics Department instructor.
Signature Date
1. True and False [2 pts each]
a) If a sequence is geometric then an exponential function can be found T F
to model it.
b) The Fibonacci sequence is arithmetic. T F
c) The converse of a statement is logically equivalent to the original T F
statement.
d) A proper subset of a given set A can have the same amount of elements T F
as the set A.
e) A function is a relationship between two sets which takes each T F
element in the domain and matches it with exactly one element in the
range.
2.
Michael’s
dad said his allowance would start at a dollar for the first month and that he
would triple it each month after that.
a)
Write
the first six terms of the sequence that represents the number of dollars of
Michael’s allowance each month(starting with the first year). [4 pts]
b)
What
type of sequence is this (circle one) ? [2 pts]
ARITMETIC GEOMETRIC NEITHER
c)
Write
a formula for the nth term of your sequence in part (a). [4pts]
d)
In
what month will Michael make more than $100?
[4 pts]
3. You have 5 pounds of ground beef in your refrigerator and want to make hamburgers for your guests at a cookout.
a) If each hamburger is going to be 2/3 pound, how many people can you serve at the cookout? Explain your reasoning. [5 points]
b) How many pounds (if any) of ground beef will you have left over? Explain. [5 points]
4.
Farmer
Fred wants to fence in a rectangular area that is against a mountainside so he
only needs fence for the other 3 sides.
He wants the longest side to be opposite the mountain and 40 feet longer
than the other 2 sides. He has 280 feet
total of fence. What should the
dimensions of his fence be? Explain how
you got your solution. [8 pts]
5.
In
Springfield, Oh. there are 100 total people.
Of those people 45 own a car, 55 own a truck and 30 own a horse. Now 15 of these people own both a truck and
a car; another 10 own both a car and a horse; 10 of them own a truck and a
horse; and 5 of them own all three.
a)
How
many people from Springfield either own a car or a truck? Explain your reasoning. (hint: you can use a
Venn Diagram to explain your reasoning.)
[5 pts]
b)
What
percent of the people in the area do not have any of the
aforementioned modes of transportation?
Explain your reasoning. [5 pts]
6. Determine whether the arguments below are valid or invalid. If a problem is invalid give a brief explanation or counterexample of why it is invalid. Circle the correct answer. [3 pts each]
a) All math classes are fun.
Phil teaches math class.
Therefore, Phil is fun.
VALID INVALID
b) If Jane walks to class, she will be late.
Jane was not late for class.
Therefore, Jane did not walk.
VALID INVALID
c) All the members of the band play instruments.
Steven plays an instrument
Steven is a member of the band.
VALID INVALID
d) If a number is divisible by 10, then it is divisible by 5.
X is not divisible by 10.
Therefore it is not divisible by 5.
VALID INVALID
7. For each of the following, form a conclusion that follows logically from the given statements. [3 pts each]
a) All college students are poor.
Helen is a college student.
b) Every equilateral triangle is isosceles.
There exist triangles that are isosceles.
8. Poppa Joes pizza offers 5 different toppings for their original crust pizza.
a) How many different types of original crust pizzas can they make if there is no restriction on how many toppings you can order? [5 pts]
b) Poppa Joes offers a special on their two topping, original crust pizza. How many different types of two topping, original crust pizzas can be made? [5 pts]
9. To rent a van it costs $250 and then an additional 35 cents per mile.
a) Write an expression for the cost function C(x) that gives the total cost to rent the van for a trip of x miles. [4 pts]
b) Say you are heading to Las Vegas (about 350 miles), what would be the total cost of your trip? Explain your methods. [4 pts]
c) What is the furthest mileage you could travel if you only had $500 to spend (round to the nearest mile)? [4 pts]
10. You are to create your own sequence that follows some logical pattern.
a) Give the first 6 terms of your sequence. [3 pts]
b) Tell whether your sequence is Arithmetic, Geometric or Neither. [2 pts]
c) If possible give an equation to find the nth term of the sequence otherwise describe the pattern as if you were telling a friend over the phone how to recreate the sequence. [3 pts]