Math 1090-002 Final Practice Problems
Spring 2013
Instructor:Jie Ma
***********THINGS YOU NEED TO KNOW***********
(1) Final Exam Date, Time and Location: 04/29/2013, 3:30-5:30p.m., Regular classroom: AEB 350.
(2) You must bring your student ID.
(3) You must bring your Scientific Calculator. The use of Cell phones will
be prohibited.
(4) You can bring a 4x6 inches double-sided index card, on which you can
write down anything you want. Any cards that exceed the presumed size
will be thrown away.
(5) I will be in my office all day the Monday the test is held on from
10:00a.m.-3:00p.m.
(6) I will make seat assignments for the final exam. I will post that seating
chart the night before the test and please check my website to find your
seat.
(7) I reserve the rights to say that this practice test might be or might not
be similar to the final exam. Other than this practice test, you should
also review your notes, all your midterm exams and their practice exams,
and also the final review on page 339-346 in the book.
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1. Solve these equations.
(a)
2(x+3)
5 − 4x = 9 + 3x
(b) 101 ∗ e2013x+429 − 10e = −4
(c) log(x2 ) + 1 = log(3x + 1)
(d) ln(x + 1) = 3 + ln x + ln 5
2


µ
¶
µ
¶
2 0
2 3 −1 0
7 3 1


2. Let A = −1 0 , B =
, and C =
.
1 4 0 1
−5 1 2
1 5
(a) Determine the size of each matrix:
size of A:
size of B:
size of C:
(b) Is AC defined? If so, calculate it.
AC =
(c) Is BA defined? If so, calculate it.
BA =
(d) Find AT + 2C if possible. If not possible, explain why.
AT + 2C =
3
3. Find the maximum and minimum of the objective function F = 2013x −
429y subject to the following constraints.
5x + 8y ≤ 64
x−y ≤5
y≥0
x≥0
(a) Graph the feasible region.
(b) List all the intersection points.
(c) Calculate both the maximum value and minimum values. Where do they
occur?
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4. Answer the following questions:
(1) If the cost of a uniform is $35.00, then there should be 3,750 uniform
purchased and that if the cost of a uniform is $110.00, then there should
be 750 uniform purchased. The supply equation for the company is: p
1
= 50 q + 30. Find the equilibrium point for this problem.
(2) The sock smurfs have started a business. They sneak into people’s laundry rooms and steal their left socks. Then they repair the socks and sell
them to the one-footed dufflepuds. The smurf business cost function is
C(x) = x2 − 25x + 4000 and the revenue function is R(x) = 105x, where
x is the number of left socks sold.
(a) What is the smurfs’ profit function?
(b) How many left socks must the smurfs sell to break even?
(c) How many left socks must the smurfs sell to maximize profit?
(d) What is the maximum profit?
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5. For
8x + 11y = 10
2x + 3y = 4
(a) Rewrite this system of linear equations in the form A ( xy ) = B, where A
and B are matrices.
(b) Use the inverse matrix of A to solve for x and y.
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6. Answer the following questions.
x+1
1
(1) Let f (x) = x3 + 1, g(x) = x−2 , h(x) = x+1 .
(a) Calculate (h ◦ g ◦ f )(x).
(b) Calculate [(hg) + (2f − g)](2)
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7.Given an equation: 4y − x = x + 3
(1) What is the slope-intercept form of the given equation?
(2) What is the slope of the line?
(3) What is the x-intercept of the equation ?
(4) What is the y-intercept of the equation ?
(5) What is the line that passes through the point(1, 0) and is parallel to the
given line?
(6) What is the line that passes through the point(2, 5) and is perpendicular
to the given line?
(7) What is the equation of the line that is perpendicular to x = 4 and passes
through (5, 2013)?
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9. Answer the following questions:
(1) The calico Band was a warm up bad for the Rolling Stones in the 1970s.
The band never made it big. Only one of the band members has any
money left. He deposited $50, 000 in a money market account earning
12% interest, compounded monthly in 1980. In 2010, what is the value
of this account?
(2) You find a bargain house which sells for $133, 000.
(a) What are your monthly payments for a 30-year loan at 3.75% interest
compounded monthly?
(b) What is the total finance charge (interest) for this 30-year loan?
(3) The Bryan Landscaping company earned $10, 000 in its first year of business which it deposited in a cd account earning 6% compounded daily for
four years. What is the value of this account after the four year period?
(from practice test 3)
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(4) Answer the following questions:
(a) Dr. Ma wants to buy a machine which will support his future research. He decides to create an account to save money for that. He
wants to have $100, 000 saved after 5 years. The account pays 4%
interest every year, compounded quarterly and he will make deposits
at the end of each quarter. How large must each deposit be to reach
their goal?
(b) Imagine he has reached his goal (from part (a)). How much money
can he receive from the account each quarter if he plans to use all
the money in 2 years?
(5) Creative Ideals International Company predicts it will have a tax bill of
$15, 000 in one year. What monthly payments must be deposited into an
account at the end of every month that pays 6% interest compounded
monthly in order to pay the taxes at the end of the year?
(6) Barney is saving for college. He is 10 years old and plans to go to college
when he’s 18. He saves his allowance, $300 a month. He has the family
butler deposit this into an annuity at 8% interest compounded monthly.
How much will Barney have in his college account when he’s 18? (from
practice test 3)
(7) Amelia just inherited $250, 000 as a death benefit from her mother’s life
insurance. She has deposited this amount in a savings account that pays
10% interest compounded monthly. How much can Amelia withdraw
monthly if she intends to access this account for the next 20 years? (from
practice test 3)
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(8) Larry’s daughter, Jeri, is engaged and will get married in three years. She
wants a large, expensive wedding that will cost about $25, 000. In order
to save for the wedding, Larry has found a relatively safe investment that
pays 9% compounded monthly. What monthly payment must he make
to this account in order to pay for Jeri’s wedding?(from practice test 3)
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