1. Thursday, December 17, 2015 Unit 4 Practice Test Answer Key

2. 1 The number of students who watch less than 1 hour or more than 7 hours of television is approximately what percent of the number of students who watch television each night? 2 3 9 7 = 0.24 = 24% Percent ≈ 25% Students watch

3. 2 The graph shows the number of people in the family of each student enrolled at the local high school. About how many students live in a family of fewer than 4 people? Total Percentage = 11.7% + 13.3% = 25% Number of students = 25% of 1,500 = 0.25  1,500 = 375

4. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #1 Let x = Fifth test score (1)(333+x) = (85)(5) 333 + x = 425 x = 92 3

5. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 83.6≠ 85 NO 3

6. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 84.2≠ 85 NO ? 3

7. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 84.6≠ 85 NO ? ? 3

8. Harrison has grades of 87, 83, 74, and 89. What grade must he get on his fifth test so that his average will be 85? Method #2Test each answer A.85 B.88 C.90 D.92 E.93 ? = 85 NO ? ? ? YES 3

9. 4 Tom and Karen ate lunch at the ballpark. Tom ordered a frankfurter, fries, and a soda. Karen ordered a hamburger and a soda. They divided the total bill evenly. What was the difference between what Karen paid and what she should have paid?

10. 4 Total Bill = $4.50 + $3.50 = $8.00 Tom Frankfurter$2.00 Fries$1.50 Soda$1.00 Total$4.50 Karen Hamburger$2.50 Soda$1.00 Total$3.50 Bill divided evenly = $8.00  2 = $4.00 What Karen paid – What Karen should have paid $4.00 – $3.50 = $0.50

11. 5 The graph shows students in the twelth-grade honor roll from 1992 to 1996. What was the percent increase in the number of students who made honor roll from 1993 to 1995? Increase amount 125 135 = 135 – 125 = 10 Percent Increase = 0.08 = 8%

12. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? Average of 11 tests (1)(Sum of 11 tests) = (85)(11) Sum of 11 tests = 935 6

13. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? 85 + 1 = 86 Let x = Jame’s test score Sum of 11 tests = 935 Average with Jame’s test Sum of 11 tests + Jame’s test Number of tests = Average with Jame’s test 6

14. The average grade on a class test taken by 11 students is 85. When James (who was absent) took the test, his score raised the class average by 1 point. What was James’ score? 85 + 1 = 86 Let x = Jame’s test score Sum of 11 tests = 935 Average with Jame’s test 1(935 + x) = (86)(12) 935 + x = 1032 –935 x = 97 6

15. 7 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car? Let x = Total Monthly Expenses 25% of total monthly expenses is food cost 25% of x = 450.25x = 450 x = 1800.25.25x 450.25 =

16. 7 The circle graphs shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car? Let x = Total Monthly Expenses x = 1800 20% of 1800 = 0.20  1800 = 360 Car Expense

17. 8 The average of 7 test scores is 86. Four of the scores are 80, 83, 86, and 92. Which of the following could NOT be the other scores? Total Points = 7  Average = 7  86 = 602 Four scores total = 80 + 83 + 86 + 92 = 341 Total Points – Four scores total = Other scores total 602 – 341 = 261 Test A80 + 90 + 91 = 261YES Test B75 + 88 + 98 = 261YES Test C85 + 84 + 93 = 262NO

18. 9 Based on the chart, which best approximates the total number of video rentals by premium members at Store B during the years 2000–2002? Premium Members Store B / 2000 – 2002 Total Video Rentals Store B / 2000 – 2002 12(500)+15(1000) +20(1250) = 46,000

19. 10 The average of a and b is 5, and the average of c, d, and 10 is 24. What is the average of a, b, c, and d? Average of a and b is 5 Average of c, d, and 10 is 24 –10 Average of a, b, c, and d

20. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount Alyse $14,500 Discount = 8% of $22,000 = 0.08  22,000 = $1760 = 5% of $14,500 = 0.05  14,500 = $725

21. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount = $1760 Alyse $14,500 Discount = $725 Discount Price = $22000 – $1760 = $20240 = $14500 – $725 = $13775

22. 11 Salespeople at Victory Motors give discounts based on the retail price of the car to repeat customers, such as Todd and Alyse. If Todd buys a car with a retail price of $22,000 and Alyse buys a car for $14,500, what is the difference in the discounted prices of the cars? Todd $22,000 Discount = $1760 Alyse $14,500 Discount = $725 Discount Price = $20240 Discount Price = $13775 Difference in Discounted Prices $20240 – $13775 = $6465

23. 12 If x = 2 and y = 3, what is the value of the median of the following set? 2x + y, 2y – x, 2(x + y), 3x + y 2(2) + 3 4 + 3 7 2(3) – 2 6 – 2 4 2(2 + 3) 2(5) 10 3(2) + 3 6 + 3 9 4, 7, 9, 10 Write numbers in order: Median = 7 + 9 2 = 16 2 = 8

24. 13 What was the average (arithmetic mean) amount of money, rounded to the nearest dollar, raised by all the clubs in 1996? 600400 1996 Average 400350 250200     

25. 14 If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a? a = 2bb = 3c a = 2(3c) a = 6c (1)(10c) = (40)(3) 10c = 120 c = 12

26. If a = 2b and b = 3c and the average of a, b, and c is 40, what is the value of a? a = 2bb = 3c a = 2(36) Substitute c = 12 b = 3(12) b = 36 a = 2b a = 72 14

27. 15 The table shows the total number of copies of Book B that were sold by the end of each of the first 5 weeks of its publication. How many copies of the book were sold during the 3 rd week of its publication? Total Copies Sold End of 1 st week 3200 End of 2 nd week 5500 End of 3 rd week 6800 End of 4 th week 7400 End of 5 th week 7700 Copies Sold Each Week (Total Copies Sold present week minus total copies sold previous week) 1 st week 3200 2 nd week 5500 – 3200 = 2300 3 rd week 6800 – 5500 = 1300

28. 16 A doll’s wardrobe consists of 40 possible outfits consisting of a shirt, pants, and a pair of shoes. If there are 5 shirts and 2 pairs of shoes, how many pairs of pants are in the doll’s wardrobe? Possible Outfits = ShirtsPantsShoes  40 = 5Pants2  40 = 10Pants  4 =

29. 17 The diagram shows the Washington, D.C. attractions visited by a social studies class. If 22 students visited the Capitol, how many students visited the Smithsonian? Capitol = x + 2 + 9 + 6 22 = x + 2 + 9 + 6 22 = x + 17 5 = x Smithsonian = 5 + 2 + 3 + 10 Smithsonian = 20

30. 18 A bag contains 3 round blue pegs, 2 round red pegs, 5 square red pegs, 4 square yellow pegs, and 6 square blue pegs. One peg dropped out of the bag. What is the probability that it was red or round? P(red OR round) P(red) OR P(round) + == red

31. 19 A circular target is inscribed in a square base. The radius of the circle is 3. Assuming that a dart randomly strikes the figure, what is the probability that it lands in the circle? 6 A = s 2 A = 6 2 A = 36 A =  r 2 A =  3 2 d = 6 A =  9 A = 9  P(circle) Circle area Square area P(circle)

32. Students studying neither = 30 – 22 = 8 20 There are 30 students in Mary’s homeroom. Of these students, 15 are studying Spanish, 10 are studying Latin, and 3 are studying both languages. How many students are studying neither language? Spanish Latin 12 7 3 Students studying languages = 12 + 7 + 3 = 22

33. Each sector in the spinner is of equal size and there is no overlap. The spinner is equally likely to stop on any sector. What is the probability that the spinner will land on a sector labeled with a prime number? P(landing on prime number) 21

34. 22 In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license? Students = MalesFemales + Males = 2x Females = x 24 = 2xx + 24 = 3x 8 = x 8 2(8) = 16

35. In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license? Males with D.L. = ¼ Males  Males = 16 Females = 8 Males with D.L. = ¼ 16  Males with D.L. = 4 Females D.L. = Males D.L. – Students D.L. Females D.L. = 4 – 12 Females D.L. = 8 Females Without D.L. = 0 22

36. 23 A class roster lists 15 boys and 12 girls. Two students are randomly selected to speak at a school assembly. If one of the students selected is a boy, what is the probability that the other student selected is a girl? There are 15 boys. One boy is selected. There are now 14 boys. P(selecting girl)

37. A box contains colored jellybeans. There are 14 red, 6 yellow, and x blue jellybeans in the bag. If the probability of drawing a yellow jellybean is, what is the value of x? P(yellow) 24 (1)(x + 20) = (6)(4) x + 20 = 24 –20 x = 4

38. If a die is rolled twice, what is the probability that is lands on 5 both times? P(#5 on 1 st roll AND #5 on 2 nd roll) 25 P(#5 on 1 st roll) AND P(#5 on 2 nd roll)  =

39. 26 A box contains 50 marbles. Twenty-five are red, 15 are white, and 10 are blue. Steve took a marble without looking. What is the probability that the marble is not blue? P(not blue) P(red OR white) P(red) OR P(white) + ==

40. 27 A target is made up of concentric circles as shown in the figure. Assuming that a dart randomly strikes the target, what is the probability that it will strike the shaded region? A =  3 2 A =  9= 9  P(shaded) A =  r 2 Big area P(shaded) A =  2 2 A =  4= 4  A =  r 2 Small area

41. 28 The Venn Diagram illustrates a relationship between cake, cookie, and pie orders at a bakery. Cake Pie 4 Cookies 3 5 1 6 2 0

42. 28a How many people ordered pies and cookies? Cake Pie 4 Cookies 3 5 1 6 2 0 3 + 1 = 4

43. 28b Cake Pie 4 Cookies 3 5 1 6 2 0 How many people ordered pies or cookies? 5 + 2 + 3 + 1 + 0 + 4 = 15

44. 28c How many people ordered cookies and no cake? Cake Pie 4 Cookies 3 5 1 6 2 0 4 + 1 = 5

45. 29 Find the number of ways you can arrange two letters in the word MATH. ___ 1 st letter 2 nd letter 4 Number of choices 3  = 12 Answer: 12 arrangements

46. 30 There are four black cats and five grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black? P(1 st black AND 2 nd black) P(1 st black) P(2 nd black) AND   = Each cat leaves the cage without replacement.

47. Find the 10th term of the sequence. 31 19 25 31 37 +6 19, 25, 31, 37, … Term1st2nd3rd4th5th +6 43 Term6th7th8th9th10th 6th +6 49 +6 55 +6 61 +6 67 +6 73 Method #1

48. Find the 10th term of the sequence. 19, 25, 31, 37, … a n = a 1 + d(n – 1) a 1 = 19 d = a n = 19 + 6(n – 1) a n = 19 + 6n – 6 a n = 6n + 13 First: Find formula Next: Find 10 th term a n = 6n + 13 a 10 = 6(10) + 13 = 60 + 13 = 73 +6 6 31 Method #2

49. Find the 12th term of the sequence. 32 4 9 14 19 +5 4, 9, 14, 19, … Term1st2nd3rd4th5th +5 24 6th +5 29 +5 34 +5 39 +5 44 +5 49 Method #1 Term6th7th8th9th10th 11th 12th +5 54 +5 59

50. Find the 12th term of the sequence. 4, 9, 14, 19, … a n = a 1 + d(n – 1) a 1 = 4 d = a n = 4 + 5(n – 1) a n = 4 + 5n – 5 a n = 5n – 1 First: Find formula Next: Find 12 th term a n = 5n – 1 a 12 = 5(12) – 1 = 60 – 1 = 59 +5 5 32 Method #2

51. What term of the sequence is 25? 33 1, 4, 7, 10, … a n = a 1 + d(n – 1) a 1 = 1 d = a n = 1 + 3(n – 1) a n = 1 + 3n – 3 a n = 3n – 2 First: Find formula Next: Let a n = 25 a n = 3n – 2 25 = 3n – 2 +2 +3 3 27 = 3n 9 = n

52. Which set is not a geometric sequence? 34 A. {48, 24, 12, 6, …} × ½ Geometric B. {2, –6, 18, –54, …} Geometric × –3

53. Which set is not a geometric sequence? 34 C. Geometric ×2 D. {4, 2, 0, –2, …} Not Geometric –2

54. The 8 th term of the geometric sequence {243, 81, 27, 9, …} is 35 243 × ⅓ 81279 Term1st2nd3rd 4th 9 × ⅓ Term4th 31 × ⅓ 7th8th5th 6th

55. What is the tenth term of the geometric sequence 36 × -2 Term1st2nd3rd –12 × -2 –4 4th5th 6th × -2 8 8 Term6th –1632 × -2 9th10th7th 8th –64128

56. If {1, –2, 4, …} is a geometric sequence, what is the sum of the first seven terms? 37 1 × -2 Term1st2nd3rd –24–8 × -2 16 4th5th 16 × -2 Term5th –3264 6th 7th Sum = 1 + (–2) + 4 + (-8) + 16 + (-32) +64 Sum = 85 +(-42) = 43