Math 100A Fall 2012 Practice Final Exam
(5 points) 1. Mary and Tommy were told to find the prime factorization of the same natural number.
When Mary factored the number completely into primes, she had exactly three 2’s in her
factorization. When Tommy factored the number completely into primes, he had exactly five
2’s in his factorization. Can they both be correct? Explain why or why not.
(15 points) 2. For each of the following, insert parentheses to make the statement true.
(a) − 4 2 = 16
(b) 2 + 3 · 4 − 2 = 8
(c) − 4 + 3 2 − 5 = − 4
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Math 100A
Practice Final Exam (Continued)
(8 points) 3. Write an algebraic expression for the sequence of operations.
(a) Three less than five times a number x.
(b) Twice the sum of a number t and 4.
(7 points) 4. Caitlyn and Kathryn go to the grocery store together. They each pick up a kiwi, a loaf of bread,
and jar of peanut butter. Caitlyn calculates their total cost (without tax, since Nebraska has
no sales tax on food purchased at a grocery store) by taking the sum of the price of a kiwi, a
loaf of bread, and a jar of peanut butter, then doubling it. Kathryn calculates their total cost
by adding twice the price of a kiwi, plus twice the price of a loaf of bread, plus twice the cost
of peanut butter. Who has correctly calculated the total cost? Explain.
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Math 100A
Practice Final Exam (Continued)
(10 points) 5. Expand the following expressions completely.
(a) (2x2 + 1)(3x3 − 5x2 − x + 4)
(b) (3y + 2)(7y − 4)
(10 points) 6. Factor completely, if possible.
(a) 2x3 − 6x2 + x − 3
(b) 6x2 + 7x + 2
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Math 100A
Practice Final Exam (Continued)
(10 points) 7. Solve each equation for the indicated variable.
1
1
(x + 2) = (x − 3), for x
3
2
(b) ac + 2f = 4e − bc, for c
(a)
(10 points) 8. Let f (d) be a function describing the number of bottles of soda a company manufactures on
day d. Explain what the following expressions involving the function f mean.
(a) f (d) + 2
(b) f (d) − f (d − 1)
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Math 100A
Practice Final Exam (Continued)
(5 points) 9. On a warm winter day, the height (in feet) of a snowman is 5 − 0.1h, where h is the number
of hours since 8:00 AM. Identify the initial value and the rate of change, and explain their
meanings in practical terms. Make sure to include units!
(8 points) 10. Douglas is going to work two jobs in the spring semester. The first will offer 20 hours per week
and pay $12.50 per hour. The second job has flexible hours and pays $10 per hour. If Douglas
wants to earn $300 dollars every week, how many hours should he work at the second job?
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Math 100A
Practice Final Exam (Continued)
(10 points) 11. How many solutions does each equation have? Show your work.
(a) 4x − 11(x − 2) = 3x − 10 + 2(2x + 1)
(b)
2
1
(x − 34) = (3x + 10)
17
34
(8 points) 12. Without evaluating the function f (x) = 9 + 4(x − 3) at a point, find the slope and a
point other than the y-intercept on the graph. Then sketch the graph.
y
✻
5
✲
−10
−5
5
−5
−10
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x
Math 100A
Practice Final Exam (Continued)
(8 points) 13. Find the set of all x such that the sum of 7 times x and 15 is greater than negative 13. Express
your answer in interval notation.
(9 points) 14. Solve the system of linear equations.
3x + 4y = 12
7x + 2y = 10
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Math 100A
Practice Final Exam (Continued)
(8 points) 15. Determine whether the points within the following table can be represented by a linear function. If you answer yes, show your work with at least three calculations. If you answer no,
only two supporting calculations are necessary.
x
y
10
4
13
0
16
−4
19
−8
(10 points) 16. Find a possible formula for the linear function h(x) if h(10) = −15 and h(−5) = 40.
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Math 100A
Practice Final Exam (Continued)
(9 points) 17. Give the domain and range of the following relation. Is it a function?
{(−1, 5), (2, 3), (0, 0), (1, 0), (−1, 0), (5, −1)}
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