MATH Advanced Math  - Unit 18: First Semester Final
For all of the problems in this unit, state the letter of the correct answer, when necessary.

Unit #1

For the first two problems, solve the following expressions for the indicated variables.

1) Solve for “y”.

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2) Solve for “y”.

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3) Simplify.

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4) Simplify.

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5) Simplify.

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Unit #2

Use the following equation for the next three problems.

6) Find the standard form of the ellipse (determine if the ellipse is horizontal or vertical).

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7) Find the “center”.

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8) Find the two “foci”.

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Use the following equation for the next four problems.

9) Find the standard form of the hyperbola.

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10) Determine if the hyperbola is “vertical” or “horizontal”.

11) Find the “center”.

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12) Find the two “foci”.

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13) Find the equations of the “asymptotes”.

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Unit #3

Refer to the sets below to solve the next two problems. Determine the intersections and/or unions in the order presented in the problem.

14) Solve.

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15) Solve.

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For the next six questions, match each term with the statement that defines it. Note: Some choices may not be used. State the letter of your choice for each statement.

16) ___ Both endpoints are included.

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17) ___ Neither endpoint is included.

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18) ___ Any collection of the elements of the original set.

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19) ___ What two sets have in common.

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20) ___ A collection of no elements.

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21) ___ The combination of sets.

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Unit #4

For the next two problems, determine the symbols for each type of number. State the letters of the answer choices for each symbol. (Hint: Find the bottom position of the numbers on the number tree and follow its path upward). Not all blanks will be filled with choices.

22) The given number is a member of which sets of numbers?

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23) The given number is a member of which sets of numbers?

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For the next five problems, find the following unions or intersections for the types of numbers. State the letter of the answer choice for each symbol. Note: Some choices may be used twice or may not be used at all.

24) ____ Find the union or intersection.

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25) ____ Find the union or intersection.

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26) ____ Find the union or intersection.

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27) ____ Find the union or intersection.

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28) ____ Find the union or intersection.

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Unit #5

29) Solve.

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30) Solve.

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31) Solve.

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32) Solve.

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33) Solve.

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34) Solve.

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Unit #6

35) From the given graph, determine a domain and range that would restrict that graph to be a function. If the given graph is already a function, then state the domain and range as it appears on the graph. Consider only the points that are labeled.

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36) From the given graph, determine a domain and range that would restrict that graph to be a function. If the given graph is already a function, then state the domain and range as it appears on the graph. Consider only the points that are labeled.

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Unit #7

37) Use the following expression to estimate a restricted domain and range for the bottom half of the ellipse to be a function.

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Unit #8

38) Determine if the function is an inverse function.

39) Determine if the function is an inverse function.

40) Solve.

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41) Solve.

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Unit #9

42) Which table is the correct table of values for the given problem?

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43) For the same problem in the previous question, which graph is the graph of the function?

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44) Which graph is the graph of the given piecewise function?

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Unit #10

Use derived formulas for conic sections and the calculator equations for the next four questions. Graph the following pairs of curves on your calculator and estimate their points of intersection. Enter the value rounded to three decimal places.

45) What is the x-value of the left most point of intersection?

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46) What is the y-value of the left most point of intersection?

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47) What is the x-value of the right most point of intersection?

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48) What is the y-value of the right most point of intersection?

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Unit #11

For the next two problems, solve each Matrix element for x and y.

49) What is the x-value?

50) What is the y-value?

For the next three problems, find each product if it exists. Make sure you have the correct number of rows and columns.

51) Find the product.

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52) Find the product.

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53) Solve.

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Unit #12

54) Is the pair of matrices inverses of one another?

55) Is the pair of matrices inverses of one another?

56) Solve the system of equations by using matrices.

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57) Solve the system of equations by using matrices.

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Unit #13

Use your graphing calculator to complete the following activity, and then answer the next two problems.

58) What is the x-value of the vertex?

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59) What is the y-value of vertex?

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Unit #14

60) Use partial fraction decomposition to resolve the given rational expression into a sum or difference of fractions. Identify the numerator of each fraction (A, B values).

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Unit #15

For the next two problems, restrict the values of the radical expressions for only real number solutions.

61) What are the restricted values?

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62) What are the restricted values?

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63) Simplify the following rational expression by multiplying by the conjugate.

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64) Simplify the following rational expression by multiplying by the conjugate.

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Unit #16

65) Find the product.

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66) Find the quotient.

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67) Graph the complex number on the complex plane and find its vector magnitude using the Pythagorean Theorem.

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68) Graph the complex number on the complex plane and find its vector magnitude using the Pythagorean Theorem.

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Unit #17

For the complex numbers given below, perform the necessary calculations. Follow the instructions for the information given, and then answer the next five questions.

69) What is:

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70) What is:

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71) What is:

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72) What is the angle of rotation for:

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73) What is the angle of rotation for:

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For the complex numbers given below, perform the necessary calculations. Follow the instructions for the information given, and then answer the next five questions. .

74) What is:

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75) What is:

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76) State the letter of the correct answer.

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77) What is the angle of rotation for:

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78) What is the angle of rotation for:

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