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Math 1090-002 Summer 2015
Pratice Final Exam
1. Write the equation of the line
(a) which passes through the two points (20, −55) and (−4, 17).
(b) is perpendicular to the line in part (a).
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Math 1090-002 Summer 2015
Pratice Final Exam
2. Given functions f (x) = log(x + 1) and g(x) =
(a) Find the domain of f (x) and g(x)
(b) (g ◦ f )(x)
(c) (f + g)(1)
(d) f −1 (x)
2
2
x+1
Math 1090-002 Summer 2015
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3. Let A = 1
0
Pratice Final Exam

1 0
−4 8
−1 1
(a) find A−1
(b) find A2
(c) find AT
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Math 1090-002 Summer 2015
Pratice Final Exam
4. For the function g(x) = 4(x − 1)2 − 2
(a) find the vertex and axis of symmetry
(b) find the x- and y- intercepts
(c) how to transform the base graph of f (x) = x2 to get g(x)
(d) graph g(x)
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Math 1090-002 Summer 2015
Pratice Final Exam
5. Solve the following equations:
(a) − log4 (x) + log4 (x + 1) = 1
2
(b) ex
−x−2
=1
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Math 1090-002 Summer 2015
Pratice Final Exam
6. Given the geometric sequence 4, −2, 1, − 12 , . . .
(a) find the iterative formula for the nth term
(b) find the sum of the first 10 terms
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Math 1090-002 Summer 2015
Pratice Final Exam
7. A gardener has two fertilizers that contain different concentrations of nitrogen. One is 10% nitrogen. The other is 25% nitrogen. How many
pounds of each should he mix together to get 42 pounds of fertilizer with
concentration 15% nitrogen?
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Math 1090-002 Summer 2015
Pratice Final Exam
8. If 100 feet of fence is used to fence a rectangular yard. Determine the
width and length that give the maximum area.
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Math 1090-002 Summer 2015
Pratice Final Exam
9. Ibuprofen is an anti-inflammatory drug which degrades exponentially in
the blood stream with a half-life of 2.5 hours.
(a) Write a function which describes how much Ibuprofen you have in
your bloodstream at time t ≥ 0 if you take 600 mg now.
(b) How many hours will it take for the initial dose of 600 mg to be
reduced to just 1 mg?
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Math 1090-002 Summer 2015
Pratice Final Exam
10. Suppose a bank advertises an investment opportunity that doubles your
money after ten years.
(a) If the bank is offering simple interest, what must be the annual interest rate for this investment?
(b) If the bank is offering compound interest, compounded quarterly,
what must be the annual interest rate for this investment?
(c) If the bank is offering compound interest, compounded continuously,
what must be the annual interest rate for this investment?
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Math 1090-002 Summer 2015
Pratice Final Exam
11. You just bought your dream home for $280,000. You obtain a loan which
requires that you pay exactly 3.5% of the total value as a down payment.
You must pay the rest back in monthly payments at an annual interest
rate of 4.45%.
(a) What is the amount of your monthly payment if the loan term is
30 years? What is the payment with the same interest rate over 20
years?
(b) How much will you pay in interest over the life of the 30-year loan?
(c) How much would you save in total with the 20-year loan?
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