# Math 102: College Mathematics Final Exam

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#### Question 1 1. Which simplification in the options provides the following result?

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Question 2
2.
Subtract: (*x*2 + 3*x* + 4) - (7*x*2 - 5*x* + 2)

#### Question 3 3. Which of the following functions best describes this graph?

#### Question 4 4. If f(x) = 5 + 3x and g(x) = 5 - 9x, find f(g(2)).

#### Question 5 5. What is the domain of √(x)?

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#### Question 6 6. Use f(x) and g(x) to find f(x) + g(x): f(x) = -x + 5 and g(x) = 3x + 2

#### Question 7 7. Estimate the coordinates of the midpoint of the line segment below:

#### Question 8 8. The distance formula is a condensed version of:

#### Question 9 9. Find the midpoint of the line segment with endpoints (6,-2) and (6,4).

#### Question 10 10. What does the statement, 'We will go get ice cream if and only if you clean your room' mean?

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#### Question 11 11. What kind of reasoning uses two unrelated events to prove a point?

#### Question 12 12. When is a contrapositive statement true?

#### Question 13 13. This graph corresponds to which inequality?

#### Question 14 14. The solution set is all values of x, such that x is greater than 30, and less than 45. Express the solution set for this compound inequality using set notation.

#### Question 15 15. What makes solving inequalities different from solving equations?

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#### Question 16 16. Expand the logarithm:

#### Question 17 17. Which part of the logarithmic expression shown is the base?

#### Question 18 18. Logarithmic properties make logarithms easier to work with because they allow us to _____ logarithms.

#### Question 19 19. What is the solution to the system of equations shown in the graph below?

#### Question 20 20. Four lines are represented by equations: Y = 2X+12, Y = 4X +12, Y = 8X + 12 and Y = 12X + 12. Their graphs are randomly shown below. Which one pertains to the equation Y = 2X + 12?

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#### Question 21 21. The graph represents a line (blue line) with _____

#### Question 22 22. Which one of the following pairs of sets is equivalent?

#### Question 23 23. Use the Venn Diagram.

#### Question 24 24. Which one is the correct denotation of an empty set?

#### Question 25 25. Subtract and simplify.

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#### Question 26 26. When you divide a rational expression you must remember to _____ the second fraction.

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Question 27
27.
Solve for x:

(6/(x+3)) + (7/(x+4)) = 116/(2x^2+14x+24)

#### Question 28 28. The following is a simplification of:

#### Question 29 29. Which of the following is equivalent to the expression below?

#### Question 30 30. Simplify:

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#### Question 31 31. While playing with a standard deck of playing cards, what is the probability that Jim's 5th card will be red after selecting 4 cards that were also red and not replacing them? (Hint: There are 52 cards in a deck which contains 26 red and 26 black cards.)

#### Question 32 32. Twenty students compete in a school-wide marathon and each student is of comparable running ability. Of the 20 students, 15 were boys and 5 were girls. What is the probability that girls will place 1st, 2nd, and 3rd in the marathon?

#### Question 33 33. The probability of selecting a green ball from a bag is 1 out of 8. If you select 3 balls, what is the probability of at least one of them being green?

#### Question 34 34. Simplify:

#### Question 35 35. Which number is represented by the graph below?

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#### Question 36 36. Which number is represented by the graph below?

#### Question 37 37. Use the Area Method to multiply the binomial (3x+2)(2x-4). Do not forget to combine like terms for your final answer!

#### Question 38 38. Which of these is NOT a step for using the FOIL method to multiply binomials?

#### Question 39 39. Which criteria is required for a problem to be a quadratic inequality?

#### Question 40 40. What is the area of ABCDE, as shown in the diagram?

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Question 41
41.
Right triangles *ABC*, *DEF* and *GHI* have congruent angles and proportional sides. The length of the base of triangle *ABC* is 5 in, the base of triangle *DEF* is 6 in and *GHI* is 10 in. Which triangle has the greatest area?

#### Question 42 42. Which combination of triangle is pictured?

#### Question 43 43. Divide using synthetic division.

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Question 44
44.
The graph of the function -*x*3 + 2x2 + 3*x* -2 is _____

#### Question 45 45. What is the shorthand way of writing the least common multiple?

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Question 46
46.
Which type of logical fallacy is illustrated in the example below?

I will get an A in math class because I spent many sleepless nights studying.

#### Question 47 47. What is the solution for the following compound inequality?

#### Question 48 48. In an exponential function, the exponent is a(n) _____.

#### Question 49 49. What is the equation of a line that passes through the points (2, 4) and (-2, 6)?

#### Question 50 50. Which one of the following pairs of sets is equal?

#### Math 102: College Mathematics Final Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!