Questions

For the first three problems, determine how many real roots each have.

1) Real cubed roots of –27

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2) Real square roots of 13

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3) Real fourth roots of –28

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4) Find the value.

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5) Find the value.

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6) Simplify using positive exponents. State the letter of the correct answer.

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7) Simplify using positive exponents. State the letter of the correct answer.

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8) Simplify using positive exponents. State the letter of the correct answer.

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9) Simplify using positive exponents. State the letter of the correct answer.

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10) Simplify using positive exponents. State the letter of the correct answer.

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11) Change to radical form.

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12) Change to radical form.

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13) Rationalize the denominator.

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14) Define an algebraic equation.

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15) Solve the equation for “x”.

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16) Solve the equation for “x”.

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17) Solve for “S”.

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18) Find two consecutive even integers whose sum is 90.

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19) The perimeter of a rectangular lawn is 112 meters and the length is 4 meters less than twice the width. Find the length and the width.

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20) Suppose you wish to produce a 40-gram bar of metal that is 15% silver by melting together parts of one bar that is 20% silver an another that is 12% silver. How many grams of each should be used?

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21) Solve the system.

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22) Use the definition of equality of complex numbers to solve for “x” and “y”.

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23) Use the definition of equality of complex numbers to solve for “x” and “y”.

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24) Use the definition of equality of complex numbers to solve for “x” and “y”.

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25) Perform the indicated operation.

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26) Perform the indicated operation.

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27) Perform the indicated operation.

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28) Identify the conjugate, and then write the standard form.

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29) Perform the indicated operation, and then express the answer in standard form.

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30) Perform the indicated operation, and then express the answer in standard form.

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31) Find the real zeros of the function by factoring.

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32) Find the real zeros of the function by factoring.

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33) Divide using synthetic division. State the letter of the correct answer.

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34) Use the factor theorem to determine if D(x) is a factor of P(x). If it is not, give the value found.

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35) Explain how you determined the answer to the previous problem.

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36) Find all rational roots using a graph and synthetic division or the factor theorem.

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37) Find all zeros. State the letter of the correct answer.

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For the next three problems, find the (a) domain, (b) vertical asymptotes, (c) horizontal asymptotes and (d) any holes in the graph.

38) Solve the rational function for its (a) domain, (b) vertical asymptotes, (c) horizontal asymptotes and (d) any holes in the graph.

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39) Solve the rational function for its (a) domain, (b) vertical asymptotes, (c) horizontal asymptotes and (d) any holes in the graph.

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40) Solve the rational function for its (a) domain, (b) vertical asymptotes, (c) horizontal asymptotes and (d) any holes in the graph.

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41) What type of function is described in the question below?

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42) A town in Ohio has a population of about 24,500 people. It is estimated that the growth rate is 2.1% per year. Find the estimated population in 5 years. Round the answer to the nearest whole number.

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43) If $20,000 is deposited at a 12% interest compounded continuously for 8 years, what will the final amount be?

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44) Solve for “x”.

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45) Solve for “x”.

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46) Solve for “x” using the properties of logarithms.

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47) Solve for “x” using the properties of logarithms.

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48) In trigonometry, when an angle is rotated in a plane, what is the difference between a 100 degree angle and a -100 degree angle?

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For the next two problems, determine the coterminal angle(s), and then determine the reference angle.

49) Determine the coterminal angle(s), and then determine the reference angle.

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50) Determine the coterminal angle(s), and then determine the reference angle.

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51) Convert the given radian measure to degrees.

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Solve triangle MNO, and then answer the next three problems. Round all answers to the nearest whole number.

52) What is the length of side MN?

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53) What is the length of side MO?

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54) What is the measure of angle M?

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55) Find the exact values of the six trig functions of “theta” for the information given below.

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56) Solve the problem given below. State the letter of the correct answer.

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