(15 points) 1. Factor completely, if possible.
(a) x2 − 2x − 63
(a)
(b) 16w4 − 1
(b)
(c) 6z 2 + 13z − 5
(c)
(7 points) 2. Expand ((x − y) + 3)((x + y) − 3) and simplify your answer.
2.
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Math 100A
Exam #2 (Continued)
(10 points) 3. Solve the equations for the indicated variable. If no solution exists, so state.
(a) 5x + 7 − 3x =
1
(34x − 12), for x.
17
(a)
(b) pq + np = k, for p.
(b)
(5 points) 4. Using complete sentences, explain the difference between an equation and an expression.
(8 points) 5. Find the set of all y such that the sum of twice y and 7 is greater than 14. Express your
solution in interval notation.
5.
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Math 100A
Exam #2 (Continued)
1
(10 points) 6. Given f (n) = n(n + 1), evaluate at the indicated point and simplify completely.
2
(a) f (100)
(a)
(b) f (n + 1).
(b)
7. Michael’s investment portfolio includes stocks and bonds. Let the function v(t) be the dollar
value after t years of the portion held in stocks, and let the function w(t) be the dollar value
held in bonds after t years.
(6 points)
(a) Write a complete sentence explaining what the following expression tells you about the
investment:
w(t)
v(t) + w(t)
(4 points)
(b) Write an expression in terms of the functions w and v that gives the difference in value
of the stock portion of the investment in year t and the bond portion of the investment
the preceding year.
(b)
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Math 100A
Exam #2 (Continued)
(10 points) 8. Solve each linear inequality. Express your solution using interval notation.
(a) 8x + 3 ≥ 5x − 8.
(a)
(b) −3(2x + 1) < 2[3x − 2(x − 5)].
(b)
(7 points) 9. Ann has been saving nickels and dimes. She opened up her piggy bank and determined that
it contained 48 coins worth $4.50. Determine how many nickels and dimes were in the piggy
bank by writing and solving an equation. (If work in the form of an equation is
not provided, you will receive no credit. Be sure to define your variables!)
9.
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Math 100A
Exam #2 (Continued)
(8 points) 10. Consider the following relation.
{(−4, 5), (20, 7), (−3, 10), (20, 10)}
(a) Does the relation represent a function? Explain why or why not.
(a)
(b) State the domain and range of the relation.
(b)
(10 points) 11. Abby and Leah go on a 5-hour drive for 325 miles at 65 mph. After t hours, Abby calculates
the distance remaining by subtracting 65t from 325, whereas Leah subtracts t from 5, then
multiplies by 65.
(a) Write expressions for each calculation.
(a)
(b) Do the expressions in (a) define the same function? Explain why or why not.
(b)
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