MATH Advanced Math  - Unit 36: Second Semester Final
Unit #19

For the first three problems, match the correct trigonometric ratio with the diagram below.

1) What is the “trig” ratio for:

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2) What is the “trig” ratio for:

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3) What is the “trig” ratio for:

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4) Convert 112 degrees to radians. State the letter of the correct answer.

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5) Convert 700 degrees to radians. State the letter of the correct answer.

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6) Convert the following radian measure to degrees. State the letter of the correct answer.

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7) Convert the following radian measure to degrees. State the letter of the correct answer.

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8) Determine the measures of the unknown angle in the triangle below to three decimal places using the arcsine, arccosine or arctangent keys on your calculator.

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9) Determine the measures of the unknown angle in the triangle below to three decimal places using the arcsine, arccosine or arctangent keys on your calculator.

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For the next two problems, determine measures of the unknown sides in each triangle below to three decimal places using the sin, cos, and tan keys on your calculator.

10) “x” = ?

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11) “x” = ?

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Unit #20

Use the formulas for special right triangles to find the lengths of the unknown sides in the diagrams below to one decimal place:

12) “k” = ?

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13) “w” = ?

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14) “g” = ?

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15) “x” = ?

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For the next five problems, refer to the list of choices below to determine the value of the given “trig” function. Answers may be used more than once or not at all. State the letter of the correct answer.

16) What is the value for?

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17) What is the value for?

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18) What is the value for?

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19) What is the value for?

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20) What is the value for?

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21) What is the value for?

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Unit #21

Refer to the curve given below to solve the next three problems. State the letter of the correct answer.

22) What is the “amplitude”?

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23) What is the “period”?

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24) What is the “phase shift”?

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For the next two problems, calculate the “starting and ending values” for the function given below.

25) What is the “starting value”?

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26) What is the “ending value”?

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Unit #22

For the next two problems, graph the inverse trigonometric curve given below on your calculator. Determine the restrictions on the domain and range of each curve in order to make the original function and its inverse 1-1. State the letter of the correct answer.

27) What is the domain?

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28) What is the range?

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Unit #23

For the next five problems, match the steps in the process to verify the given Identity.

29) #29 is _____. State the letter of the correct answer.

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30) #30 is _____. State the letter of the correct answer.

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31) #31 is _____. State the letter of the correct answer.

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32) #32 is _____. State the letter of the correct answer.

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33) #33 is _____. State the letter of the correct answer.

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34) Find the exact value of the following trigonometric expression using the sum or difference identities. State the letter of the correct answer.

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35) Find the exact value of the following trigonometric expression using the sum or difference identities. State the letter of the correct answer.

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Unit #24

36) Use any identity or combination of identities to find the exact value of the following trigonometric expression. State the letter of the correct answer.

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For the next thirteen problems, match the steps in the process to verify the given Identity. (Not all choices are used; others are used more than once.)

37) #37 is _____. State the letter of the correct answer.

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38) #38 is _____. State the letter of the correct answer.

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39) #39 is _____. State the letter of the correct answer.

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40) #40 is _____. State the letter of the correct answer.

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41) #41 is _____. State the letter of the correct answer.

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42) #42 is _____. State the letter of the correct answer.

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43) #43 is _____. State the letter of the correct answer.

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44) #44 is _____. State the letter of the correct answer.

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45) #45 is _____. State the letter of the correct answer.

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46) #46 is _____. State the letter of the correct answer.

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47) #47 is _____. State the letter of the correct answer.

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48) #48 is _____. State the letter of the correct answer.

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49) #49 is _____. State the letter of the correct answer.

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To solve the next two problems, use the Law of Sines and the information given below. (It helps to draw and label the triangle with the given information.)

50) What is the length of “a”?

51) What is the measure of angle C? State the letter of the correct answer.

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Unit #25

52) Use trigonometric area formulas and Law of Sines to find the area of the triangle below.

For the next two problems, solve the trigonometric equations as instructed below.

53) Solve for “theta”. State the LETTERS of the correct answer.

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54) Solve for “theta”. State the LETTERS of the correct answer.

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Unit #26

55) Find the rectangular coordinates of the following polar points. State the letter of the correct answer.

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56) Find the rectangular coordinates of the following polar points. State the letter of the correct answer.

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For the next two problems, find the “polar coordinates” for the “rectangular point” given below. First determine the radius, and then find the correct value of “theta”. Be sure your calculator is in DEGREE MODE. State the letter of the correct answer.

57) What is the radius?

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58) What is the approximate value of “theta”?

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For the next two problems, find the “polar coordinates” for the “rectangular point” given below. First determine the radius, and then find the correct value of “theta”. Be sure your calculator is in DEGREE MODE. State the letter of the correct answer.

59) What is the radius?

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60) What is the value of “theta”?

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61) Transform the following Polar Equation to rectangular form. State the letter of the correct answer.

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62) Transform the following rectangular equation to polar form. State the letter of the correct answer.

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Unit #27

For the next three problems, convert the given Polar Equation to a rectangular form, and then determine the vertex and focus of its graph.

63) Which is the correct rectangular equation? State the letter of the correct answer

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64) What is the “vertex”? State the letter of the correct answer.

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65) What is the “focus”? State the letter of the correct answer.

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Unit #28

66) Convert the complex number to polar form (express the argument in degrees). State the letter of the correct answer.

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67) Convert the Polar Complex Number to rectangular coordinates (use degree or radian measure as appropriate). State the letter of the correct answer.

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Recall DeMoivre's Theorem:

68) Solve using DeMoivre's Theorem. State the letter of the correct answer.

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Recall the variation of DeMoivre's Theorem:

69) Use the variation of DeMoivre’s Theorem to find all complex roots of the expression given below. Leave answers in Polar Form with the arguments in degrees. State the letter of the correct answer.

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Unit #29

70) Use laws of exponents and the theorem for this unit to solve the following for “x”. State the letter of the correct answer.

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71) Use laws of exponents and the theorem for this unit to solve the following for “x”. State the letter of the correct answer.

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Unit #30

72) Rewrite the following exponential expression as a logarithm using the inverse relationship between exponential and logarithmic expressions. State the letter of the correct answer.

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73) Rewrite the following exponential expression as a logarithm using the inverse relationship between exponential and logarithmic expressions. State the letter of the correct answer.

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74) Rewrite the following logarithmic expression as an exponential expression using the inverse relationship between exponential and logarithmic expressions. State the letter of the correct answer.

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75) Rewrite the following logarithmic expression as an exponential expression using the inverse relationship between exponential and logarithmic expressions. State the letter of the correct answer.

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76) Solve the following logarithmic equation for the indicated variable. Consider any restrictions or non-solutions. State the letter of the correct answer.

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77) Solve the following logarithmic equation for the indicated variable. Consider any restrictions or non-solutions. State the letter of the correct answer.

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Unit #31: No Exam Questions for this unit.

Unit #32

78) Using the inverse relationship for the natural exponential and logarithms to find the unknown value. State the letter of the correct answer.

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79) Using the inverse relationship for the natural exponential and logarithms to find the unknown value. State the letter of the correct answer.

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80) How long will it take an initial investment of $25,000.00 to grow to $80,000.00 with an interest rate of 4.35% compounded monthly? State the letter of the correct answer.

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81) Solve. State the letter of the correct answer.

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Unit #33

82) Find the sum of the following Arithmetic Sequence for the first 100 terms.

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Find an approximation for the twenty-third term in the following Geometric Sequence, and then answer the next two questions.

83) What is the common ratio? State the letter of the correct answer.

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84) What is the twenty-third term? State the letter of the correct answer.

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Unit #34

85) Find an exact fraction for the following repeated decimal. State the letter of the correct answer.

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86) Write the following infinite sequence as a single expression in terms of “n”. State the letter of the correct answer.

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87) Use the Comparison Test to find the following limit. State the letter of the correct answer.

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88) Find the value of the following Continued Fraction. State the letter of the correct answer.

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Unit #35

For the next two problems, use any combination of the Ratio Test and the Polynomial Quotient Test (PQT) to determine if the given series converges or diverges.

89) What is the Limit of the series? State the letter of the correct answer.

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90) Does the series converge or diverge?

91) Use the Binomial Theorem and Pascal’s Triangle to find the expanded form of each binomial expression. State the letter of the correct answer.

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