EXAM 2: MATH 0465
Question 1. The year is 2024 and located on the Moon in Mallory Crator a school is opening up. The school
president Dr. Chan Kaifang estimates the current enrollment of 634 students will increase 5% each year for
the next 10 years. General Mark R. Naird has allocated enough resources for 1100 students.
(a) Write the function of time t, in years, that models the number of students.
(b) Use the functions to nd how many students will be present in 8 years.
(c) Use the functions to nd how many students will be present in 10 years.
(d) Use the past information to explain why between 8 and 10 years there could be 1000 students at the
school.
1
EXAM 2: MATH 0465 2
Question 2. A student has the following total points per category:
Category Homework Quiz Turn-In Project Exam Final Attendance Participation Total
Earned 190 155 35 50 130 105 45 50
Available 200 160 50 100 250 200 50 50
(a) What is the average amount of points the student earned out of the total available?
(b) If Homework is 10% of the grade, Quiz is 15% of the grade, Turn-In is 10% of the grade, Project is
15% of the grade, Exam is 20% of the grade, nal is 20% of the grade, attendance is 5% of the grade,
and the participation is 5% of the grade. Find the weighted average for the students grade.
(c) Give a reason why the last two answers are not the same. Also, if the weighted total is what is counted
at the end of the semester, does the student pass with a 70% or higher?
EXAM 2: MATH 0465 3
Question 3. State when to use the commutative, associative, and/or distributive property to simplify the
following expressions and then perform the action:
(a) 4x
p
7wy + 5xwy + 7x
p
7wy
(b)
57x2y + 66xy2
3xy
(c)
15x8y4
5xy
2
EXAM 2: MATH 0465 4
Question 4.
(a) Claim: (a+b)2 = a2+b2 for all real numbers a and b. If this is true, use deductive reasoning to support
your conclusion. Otherwise, provide a counterexample.
(b) Use the distributive property and combine like terms to simplify the expression: (x2 + y2)(x2 y2).
EXAM 2: MATH 0465 5
Question 5. Dene your variable and construct an equation to answer the following question (do not
solve):
Suppose a particular city estimates that only
7
9
of its eligible voters went to the polls. If 72,394
voters were at the polls, how many eligible voters does the city have?
Question 6. Write an algebraic expression to represent the following calculation. Use x to represent the
number.
Take a third of a number, subtract 15, then decrease the total by 10%, and then increase 25%.
Question 7. Show why the solution to the following equation is all real numbers.
3(x 1) = (3 3x)
EXAM 2: MATH 0465 6
Question 8. Consider the following equation:
x 5
5
= 10
(a) Find the error:
x5
5
= 10
x = 10
(b) According to order of operations, and assuming x is known, what is the rst and second thing that must
be done in order to evaluate
x 5
5
?
(c) Solve:
x 5
5
= 10
Question 9. Solve the equation
3 p
x = x3
by completing the following table, round your values two decimal places.
Input -5 -4 -3 -2 -1 0 1 2 3 4 5
3 p
x
x3
List all of your solutions:
EXAM 2: MATH 0465 7
Question 10. Consider the following formula, which calculates the monthly payment for a mortgage:
M = P
1 +
r
n
nt
r
n
1 +
r
n
nt
1
M is the monthly payment, P is the principal or amount borrowed, n is the number of payments per year, t
is the number of years, and r is the annual interest rate as a decimal.
Find the monthly payment for a loan of $782,740 at 4.23% for 30 years (compounded monthly). Remember
dollar amounts are rounded 2 decimal places. For full credit replace all the variables with the appropriate
numbers.
Extra Credit
Question 11. The following formula calculates the electric force between two charges based on their charges
(q1 and q2) and the distance between them (r):
F =
1
40
q1q2
r2 :
The variables q1 and q2 have units of Coulomb (C), and r has units of meters (m). What units must the
constant 0 have in order for the units on F to be newtons (N)? Show how to determine this algebraically.
Question 12. Suppose you get a $100 gift card and have already spent $4.95 on songs. With the remaining
money on the gift card suppose you want to buy more songs at $1.49 per song and has an additional sales tax
charge of 9.5% in your state. Furthermore, there is a 3% electronic service charge. How many more songs
can you buy with the gift card?
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