MGF 1106

1. MGF 1106 Final Exam Review and Practice Test Solutions

2. Information about the Final Exam Length: 25 questions (multiple−choice). Each question is worth 4 points. If you miss the test: Students who do not take the final exam will receive a zero on the final exam unless prior arrangements have been made for a rare incomplete. If you miss the final and do not email me by the day of the exam, I will assume you wish to take a zero on your final exam. Question Order: The questions on the final exam will be scrambled. The order will NOT be the same as it appears on this review. Calculator Policy: A scientific calculator or non-symbolic graphing calculator is required. The TI-83/84 Series is fine but TI-89’s and TI-92’s are not permitted. Under no circumstances is a cell phone or other communication device to be used as a calculator.  

3. Formula Sheet(provided at the exam) circumference of a circle is C = πd The area of a circle is nPr = nCr= S.D. =

4. How to Study for the Exam • Review your notes. Set up a study system to review important definitions, procedures, and notation. • Complete the practice test questions and be prepared to go over the answers in class on the date of the final exam review. • Continue to review by working the suggested textbook problems and checking your answers with the key at the back of the book. • Review the corresponding questions from the tests.. • Redo the sample questions (especially the ones you missed).

5. Exam Topics 1 – 10

6. Exam Topics 11 – 20

7. Exam Topics 21 – 25

8. Important Ideas 1 – 10

9. Important Ideas 11 – 20

10. Important Ideas 21 – 25

11. Final Exam Practice Solutions

12. 1) Find the next number: 3, 5, 6, 10, 12, 20, _____ 24 B) 40 C) 18 D) 30

13. 2) Find the number of subsets and the number of proper subsets for the set {x | x ∈ N and 3 ≤ x < 6}3,2 B) 7,6 C) 8,7 D) 18, 17 C) 8, 7

14. 3) Let U = {a, b, c, d, e, f, g, h} A = {a, b, e, g} Find A’{e, f, g, h} B) {c, d, f, h} C) {a, b, c, d, e} D) {b, d, e, g} B) {c, d, f, h}

15. 4) Let U = {a, b, c, d, e, f, g, h} A = {a, b, e, g} B = {a, c, e, g} Find A ⋂ B’. {a, b, c, d} B) {d, f, h} C) {b} D) { } C) {b}

16. 5) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 2, 3, 4, 5} B = {2, 4, 5, 8, 9, 10} C = {1, 3, 5, 7, 9} Find A) {5} B) {1,3, 7, 9} C) {3, 4, 5} D) {7, 9, 10}

17. 6) 80 people were surveyed to determine what brand of coffee they prefer. How many preferred exactly one brand?A)17 B) 53 C) 75 D) 58 D) 58

18. 7) Negate the following statement: All toys are made with plastic. A) Some toys are made with plastic. B) All toys are not made with plastic. C) Some toys are not made with plastic. D) No toys are made with plastic. C) Some toys are not made with plastic.

19. 8) Let p: Jim likes oranges q: Petra likes strawberries r: Julie likes mangoes.Express the statement in symbolic form: If Jim does not like oranges, then Petra likes strawberries or Julie does not like mangoes. A) p ↔ (q ⋁ r) B) ~p → (q ⋁ ~r) C) p ↔ (q ⋁ ~r) D) ~p → (q ⋀ ~r) B) ~p → (q ⋁ ~r)

20. 9) Write the inverse of the statement: If it is raining, the car will get wet. A) If the car does not get wet, it is not raining. B) If it is raining, the car will not get wet. C) If the car will get wet, it is raining. D) If it is not raining, the car will not get wet. ~p → ~q D) If it is not raining, the car will not get wet.

21. 10) Write the negation of the statement: The dog is barking and the cat is not afraid. A) The dog is not barking and the cat is not afraid. B) The dog is not barking or the cat is not afraid. C) The dog is not barking and the cat is afraid. D) The dog is not barking or the cat is afraid. The negation of an “And” statement is an “Or” statement. D) The dog is not barking or the cat is afraid.

22. Answers 1 – 10

23. 11) Consider the following argument.All students are commuters.All faculty members are commutersTherefore, no students are faculty members. The argument is A) Valid B) Invalid One possible diagram that shows the argument is invalid B) Invalid

24. 12) The measure of an angle is 22 more than its complement. Find the measure of the larger angle.A) 68∘ B) 158∘ C) 34∘ D) 56∘ D) 56∘

25. 13) If m∠B = 42∘, find the measure of ∠A in the diagram below. The diagram is not drawn to scale.A) 48∘ B) 138∘ C) 58∘ D) none of these A) 48∘

26. 14) A tree is 30 feet from a flagpole. The tree is 8 feet tall and casts a shadow of 6 feet. How tall is the flagpole?A) 216 feet B) 64 feet C) 48 feet D) 20 feet C) 48 feet

27. 15) Find the cost to fence a square pen if a side of the square measures 18 feet and fencing costs $1.75 per foot.A) $126.00 B) $72.00 C) $58.50 D) $30.75 A) $126.00

28. 16) The figure below is not necessarily drawn to scale. Find the area of the figure. A) 120 m2B) 144 m2C) 168 m2D) 192 m2 A) 120 m2

29. 17) Find the cost to install sod in a square pen if a side of the square measures 18 feet and sod costs $1.50 per square foot.A) $108.00 B) $121.50 C) $388.50 D) $486.00 D) $486.00

30. 18) Jim is planning a two−part trip. In part one, he has three transportation options: airplane, train, or bus. In part two, he has four transportation options: tour bus, rental car, boat, or train. In how many ways can the two− part trip be made?A) 7 B) 14 C) 28 D) 12 D) 12

31. 19) Five runners enter a race. In how many different ways first, second, and third place medals be awarded? A) 6 B) 60 C) 600 D) none of these B) 60

32. 20) In how many ways can a committee of 4 students and 4 faculty members be formed from 10 students and 6 faculty members?A) 1, 814, 400 B) 3,150 C) 960 D) 12,870 B) 3,150

33. Answers 1 – 20

34. 21) (page 646: 46) The table below shows the educational attainment of the U.S. population, ages 25 and over, in 2007. Use the data in the table (expressed in millions) to determine the probability that randomly selected American, aged 25 or over, has completed four years of high school (only) or is a woman. A) B) 0 C) D) 1 C)

35. 22) Suppose an ice chest has eight bottles in it. Three bottles have orange juice, two have soda, two have milk, and one has water. If two bottles are chosen from the ice chest at random without replacement, find the probability that both are soda bottles.A) B) C) 0 D) A)

36. 23) What is the expected payoff or loss in the following game? Please round your answer to the nearest cent. A spinner is set up with six equally likely regions. Two of the regions are colored red, two are colored blue, one is colored green, and one is colored yellow You pay $6 for one spin. If the spinner stops on a red space, you win $9. Otherwise, you win nothing. A) $3 B) −$6 C) −$3 D) $6 OR C) −$3

37. 24) Find the average of the following data set: 2, 7, 3, 6, 7, 5, 3, 7, 4, 6A) 6 B) 5.5 C) 5 D) 4 C) 5

38. 25) Find the standard deviation of the following data set: 2, 7, 3, 6, 7, 5, 3, 7, 4, 6. Round your answer to the nearest tenth.A) 7 B) 5.5 C) 5 D) 1.9 D) 1.9

39. Answers 1 – 25

40. Final Exam Extra Practice

41. 1) p. 38: 8 Find the next number.

42. 1) p. 38: 8 Find the next number.

43. 2) p. 100: 31 Find the number of subsets and the number of proper subsets.

44. 2) p. 100: 31 Find the number of subsets and the number of proper subsets.

45. 3) p. 74: 7 Find C’. a, b, c, d, e, f, g}

46. 3) p. 74: 7 Find C’. a, b, c, d, e, f, g}

47. 4) p. 100: 35 Find

48. 4) p. 100: 35 Find

49. 5) P. 100: 47 Find

50. 5) P. 100: 47 Find