Day 1 Day 2 1. Which of the following situations involve opposite quantities combining to make 0? 3. On a number line, which of the following sums is to the left of the first number in the sum? Stella has a new piggy bank. She adds 3 quarters on Tuesday, and then adds another 3 quarters on Thursday. Devon opens a new checking account with $30. His first purchase, made with his new debit card, totals $28. 9 + 1 1 6 4 3 C) Joe makes 1 1 liters of lemonade and drinks it 2 all during the afternoon. Brittany is writing a novel. She wrote 4 new pages to finish Chapter 1. When she reviews Chapter 1, she discards these 4 pages and an additional 4 pages. C) 7 2 3 4 15+( 8) E) 2 + 6 2. What is the location of the sum 11 + (-5) with respect to 11 on a number line? five units to the left of 11 five units to the right of 11 C) 11 units to the left of zero 11 units to the right of zero 4. Becky adds gallon of gasoline into her snow thrower s empty fuel tank. She uses " gallon for the snowstorm on Friday, and then uses another " gallon for the snowstorm on Sunday. Is the fuel tank empty after Becky uses the snow thrower on Sunday? Explain. If her fuel tank is not empty again, what single action could have been changed so that it is empty again? Explain. Mathematics, Science, & Gifted Department Page 1
Day 3 Day 4 5. Which of the following expressions give the distance between the endpoints of the segment shown on the number line below? 7. Which properties are used to simplify as without first finding a common denominator? 3 5 4 5 Commutative Property of Multiplication C) Commutative Property of Addition C) Associative Property of Addition E) Multiplicative Inverse Property E) Additive Inverse Property F) Additive Identity Property 6. How does the expression 9 -(-5) relate to the numbers -5 and 9 on the number line? The expression shows that 9 is greater than -5. The expression shows that -5 is to the left of 0 and 9 is to the right of 0 on the number line. C) The expression represents the sum of -5 and 9. The expression represents the distance between -5 and 9 on the number line. 8. Which of the following demonstrates using the associative property of addition to simplify? Select all that apply. (-13.36 + 2.17) + 7.83 = -13.36 + 10 9 + (1.4 + 14.3) + 15.7 = 9 + 1.4+ 30 C) 21.36 + 15.32-1.36 = 20 + 15.32 [12.3 + (-24.6)] - 15.4 = 12.3 + (-40) E) 10.14-10.14 + 28.93 = 28.93 Mathematics, Science, & Gifted Department Page 2
Day 5 9. Which of the following is always the result of dividing an integer by an integer when the divisor is nonzero? Integer Day 6 11. Which of the following equations use the distributive property correctly to multiply rational numbers? Whole number C) Rational number 0 10. Kelsey s bank charged her $17.50 for using her debit card at ATMs that are not owned by her bank 7 times in the last month. C) What is the interpretation of the quotient Kelsey s bank loses $2.50 each time Kelsey uses her debit card at an ATM that is not owned by her bank. Kelsey is charged $2.50 each time she uses her debit card at an ATM that is not owned by her bank. 12. Determine the property of multiplication that is used in each step to simplify the expression " Associative C) Kelsey earns $2.50 each time she uses her debit card at an ATM that is not owned by her bank. Kelsey is charged $17.50 each time she uses her debit card at an ATM that is not owned by her bank. a. b. c. d. e. f. Mathematics, Science, & Gifted Department E) " " Identity $250? Inverse 7 Commutative $1750 " " " " Page 3
Day 7 Day 8 13. Suppose the repeating pattern in 0.020020200202002... continues forever. Is this number rational? Yes, because the number can be written as the quotient of two integers. Yes, because the number is a terminating decimal. C) No, because the number is not a terminating decimal. No, because the number is not a repeating decimal. 16. Which of the following expressions have a result that is greater than 5? C) " 14. Which of the following rational numbers have three digits that repeat in its decimal equivalent? " " C) " " E) " E) 17. A type of bolt weights about " ounce. If a collection of these bolts weights pounds, how many bolts are in the collection? Explain. 15. Which of the following is greater than "? " " C) " " E) " " Mathematics, Science, & Gifted Department Page 4
Day 9 Day 10 18. A car rental agency initially offers a car that can go 304 miles on " gallons of gasoline. There are other vehicles available at the agency, shown below. Which of the other cars have a greater unit rate of miles per gallon than the recommended car? 20. Tell whether the relationship is a proportional relationship. Explain why or why not. 187 miles on " gallons 357 miles on " gallons C) 216 miles on " gallons 209 miles on gallons E) 115 miles on gallons 19. Derek applies grass seed to acre in many acres can Derek cover per hour? hour. How The relationship is proportional because a single line can be drawn through all the points and the line passes through the origin. The relationship is proportional because a single line can be drawn through all the points. C) The relationship is not proportional because a single line can be drawn through the points but it does not pass through the origin. The relationship is not proportional because a single line cannot be drawn through all the points. 21. Which of the following situations form a proportional relationship? 5 DVDs for $9 and 15 DVDs for $27 6 cups of coffee for $8 and 9 cups of coffee for $12 C) 3 pocketbooks for $60 and 5 pocketbooks for $90 12 cans for $3 and 30 cans for $7.50 E) 2 ink cartridges for $25 and 4 ink cartridges for $75 Mathematics, Science, & Gifted Department Page 5
Day 11 Day 12 22. The amount Antwan earns mowing lawns depends on the number of hours he works, and the relationship is proportional. Antwan earns $69.00 for working 6 hours. Complete the table. Then give the value of the constant of proportionality, and explain its meaning in this situation. Time (hours) 3 8 11 Earnings (dollars) 57.50 97.75 138.00 23. The ordered pairs show equal amounts of money in U.S. dollars and euros. 24. Marsha is selling frozen yogurt at a town concert to help raise money for the local library. The earnings for the library y are proportional to the number of frozen yogurts x she sells. a. Complete the table below. Frozen Earnings Yogurts (dollars) 2 14 6 21 28 10 b. Write an equation for this relationship. c. Plot the points from Part A, and draw the line of the equation from part b onto the graph below. What other ordered pair on this graph would show the unit rate? What does the ordered pair represent in this situation? (1, 0.78); 0.78 dollar equals 1 euro. (1, 0.78); 0.78 euro equals 1 dollar. C) (1, 1.28); 1.28 dollars equals 1 euro. (1, 78); 78 euros equal 1 dollar d. If Marsha wants to raise $245 for the library, how many frozen yogurts would she have to sell? Explain how you found your answer. Mathematics, Science, & Gifted Department Page 6
Day 13 Day 14 25. A department store has a discount on shoes based on a percentage of the price. Suppose one pair of shoes is marked down from $70 to $49. What is the price for a $110 pair of shoes after the discount is applied? $89.00 $73.33 C) $77.00 $33.00 26. A $45.00 purchase in Iowa totals $47.70 with tax and a $35.00 purchase in Tennessee totals $37.45 with tax. Which state has a greater sales tax percentage? Explain your reasoning. In questions 27-30, match the situation with the percent of discount. 20% 25% C) 30% 35% E) 40% F) 45% 27. A $55.00 purse is on sale for $30.25. 28. A $98.00 power inverter is on sale for $78.40. 29. A $44.00 video game is on sale for $28.60. 30. A $37.50 dress is on sale for $26.25. Day15 Mathematics, Science, & Gifted Department Page 7
31. Which of the following uses the associative property of addition to simplify? C) 5 3 3 5 5 3 1 4 11 1 4 11 4 0.4y + (3.6y - 0.6) = 4y - 0.6 4 5 5 4 12 5 12 5 Day 16 33. Jamie is selling tickets for a whale watch at a local beach. The tickets cost $24.40 for an adult and $14.50 for a child. Jamie earns a 30% commission on all ticket sales. Write an expression that uses parentheses to represent how much Jamie earns from selling tickets, where a is the number of adult tickets sold and c is the number of children s tickets sold. Use the distributive property to simplify the expression. E) 7.8x - 1.3-1.8x = 6x - 1.3 32. Which properties are used to simplify " Associative property of addition Associative property of multiplication C) Commutative property of addition Commutative property of multiplication E) Distributive Property Mathematics, Science, & Gifted Department Page 8
Day 17 Day 18 34. Which of the situations described below can be modeled by the equation: n + 0.5 n - 0.3 n = 1.2 n, where n is the number of nickels originally in the jar? 35. Which of the following expressions represent the sum of the areas of the triangles shown? Amanda takes out 50% of the nickels in the jar on Friday and adds a number of nickels that is equal to 30% of the remaining number of nickels in the jar on Monday. There are 20% fewer nickels in the jar after Monday than before Friday. Amanda takes out 50% of the nickels in the jar on Friday and adds a number of nickels that is equal to 30% of the original number of nickels in the jar on Monday. There are 20% fewer nickels in the jar after Monday than before Friday. C) Amanda adds 50% of the original number of nickels to the jar on Friday. The number of nickels Amanda takes out on Monday is equal to 30% of the new number of nickels. There are 20% more nickels in the jar after Monday than before Friday. Amanda adds 50% of the original number of nickels to the jar on Friday. The number of nickels Amanda takes out on Monday is equal to 30% of the original number of nickels. There are 20% more nickels in the jar after Monday than before Friday. C) 3[(x + 4) + (x - 2)] 3(2x + 2) E) 12x + 12 36. A rectangle has a length of 8 feet and a width of 6 feet. If its length and width increase by 50% each, what is the area of the new rectangle? 24 square feet 48 square feet C) 72 square feet 108 square feet Mathematics, Science, & Gifted Department Page 9
Day 19 Day 20 37. An airplane takes off 12.5 miles south of a city and flies due north at a constant speed of 170 miles per hour. What is the plane s position relative to the city after 45 minutes? 39. Solve the equation " " for y. 115 miles south 115 miles north C) 140 miles south 140 miles north 40. Which of the following inequalities has the set of positive numbers as part of its solution set? 38. Which of the following equations have a solution that is negative? " C) " " " " " C) " " " E) E) " " Mathematics, Science, & Gifted Department Page 10
Day 21 Day 22 41. Determine whether the following inequalities have a solution set of. " " C) " " " " E) " 43. A fence is shown on a blueprint and has sides of length 17 cm, 18 cm, 15 cm, and 19 cm. If the scale on the blueprint is 2 cm:7 m, what is the total length of the fence? Show your work. 44. The scale drawing has a scale of 1 inch:9 yards. What is the total area of the composite figure? 42. Erin is training for a marathon and wants to run at least " miles. She has already run miles and starts to jog at a steady rate of miles per hour. Write an inequality using the time t, in hours, to find the possible amounts of time remaining for her jog. 51 square inches 459 square yards C) 4,131 square yards 4,860 square yards Mathematics, Science, & Gifted Department Page 11
Day 23 Day 24 45. Which of the following side lengths forms a unique triangle? 5 cm, 5 cm, 10 cm 11 cm, 14 cm, 17 cm C) 109 cm, 214 cm, 414 cm 2 m, 7 m, 8 m E) 8 miles, 15 miles, 26 miles 46. Determine whether or not the figure described forms a triangle. If so, determine whether the triangle with the given characteristics forms a unique triangle or more than one triangle. Given Characteristics a. A triangle with 5 cm and 7 cm side lengths and an included "# Not a Triangle Unique Triangle More Than One Triangle b. A triangle with "# and "#$ angles and an included side of 10 m c. A triangle with "#and "#$ angles and a non-included side of 48 yards d. A triangle with 14 in. and 24 in. side lengths and a non-included "#$angle e. A triangle with "#, "#, and "angles f. A triangle with side lengths 5 cm, 10 cm, and 18 cm Mathematics, Science, & Gifted Department Page 12
Day 25 Day 26 47. Determine whether the following geometric shapes are possible cross sections for a right rectangular prism, where the lengths of the dimensions are not equal to each other. (The plane intersecting the prism is not necessarily parallel to the faces of the prism.) Circle Parallelogram C) Rectangle Square E) Trapezoid F) Triangle 48. Determine which of the cross sections shapes below are possible for a right rectangular pyramid, where the length and width of the base are not equal. 49. Are all of the vertical slices of a rectangular pyramid the same kind of shape? Explain your reasoning. Circle Hexagon C) Rectangle Square E) Trapezoid F) Triangle Mathematics, Science, & Gifted Department Page 13
Day 27 Day 28 50. A wheel has a radius of 9 inches and travels as it spins. How far does the wheel travel in one revolution? Show your work. Use 3.14 for # and round to the nearest inch. 53. The measure of "# is "# and the measure of "# is "#. What is "#? Justify your answer. 51. Rewrite the formula for the circumference of a circle C = 2 # r in terms of its diameter d. Show your work. 54. In the figure below, "# and "# are complementary angles. What is "#? Show your work. 52. The sprinkler in Rob s sprinkler system waters a circular area. The sprinkler is in an open part of Rob s lawn and waters up to 18 feet away. What is the area the sprinkler can water? Show your work. Use 3.14 for # and round to the nearest square foot. The sprinkler i. Mathematics, Science, & Gifted Department Page 14
Day 29 Day 30 55. What is the surface area of the right rectangular prism shown in the figure? 143 m2 C) 315 m2 286 m2 486 m2 58. A politician running for mayor in her city wants to know her chances of winning an upcoming election. To figure this out, her campaign team wants to ask a sample of people in the city who they will vote for in the election. What method is likely to give the campaign team a random sample of the population? Ask all of the people who live in a particular neighborhood. Ask people who live in different neighborhoods throughout the city. C) Ask people who take public transportation. Ask all of the people who shop at the same store. 56. What is the volume of the right triangular prism shown? 27 yd3 C) 567 yd3 126 yd3 1,134 yd3 59. Elaine is the manager of a small toy manufacturer. Her company produces 2,500 toys per week for shipment to retail stores. Elaine wants to know the percentage of toys her company produces that are defective. Which of the following methods would provide Elaine with a representative sample of the toys? Assign a number to each toy, randomly select 100 numbers, and test the corresponding toys. Test the first toy produced each week. C) Select the first toy produced each day of the week and test them. For each day, randomly pick 15 toys produced that day. E) Test all toys produced on Friday. 57. Which of the following figures have an area greater than 40 cm2? A triangle that has a base of 8 cm and a height of 9 cm A square that has a side length of 7 cm C) E) A rectangle that has a base of 14 cm and a height of 3 cm A parallelogram that has a base of 5 cm and a height of 6 cm A trapezoid that has 8 cm and 10 cm bases and a height of 5 cm Mathematics, Science, & Gifted Department Page 15
Day 31 Day 32 60. Leah is an administrator for a large school district. She wants to know how many hours students spend on homework each week. She asks the question to 250 randomly selected eighth grade students. The results are shown in the table. Which of the following inferences about the eighth grade students in the school district are valid? Hours Students Less than 2 44 2 to less than 4 88 4 to less than 6 90 At least 6 28 62. Sally works at a frozen yogurt shop that has about 2,500 customers per week and wants to know how many people like vanilla frozen yogurt. She asks the question to 40 randomly selected customers. She repeats this process two times. Sally finds that 14 people said they like vanilla frozen yogurt in the first sample, 18 in the second, and 12 in third. What is the difference between the highest estimate and the lowest estimate for the number of customers per week who like vanilla frozen yogurt? Show your work. C) There are more students who spend at least 4 hours per week on homework than students who spend less than 4 hours per week on homework. About 11% of students in the school district spend at least 6 hours per week on homework. About 50% of students who spend less than 4 hours per week on homework spend less than 2 hours per week. 63. The dot plot shows the heights, in inches, of the members of a school s swimming team. About 1 of every 3 students who spend at least 4 hours per week on homework spend at least 6 hours per week. 61. An electronics retailer receives a shipment of 6,000 CDs to distribute to its stores. A quality control manager inspects a random sample of 40 CDs and finds that 2 are defective. How many CDs in the shipment are likely to be defective? Show your work. The shapes of the distributions of the heights for the teams described below are similar to the shape of the distribution of the heights for the swimming team. For which of the distributions do fewer than half of the data values overlap with the distribution of the swimming team data? Soccer: Low of 60 inches, a median of 64 inches, and a high of 68 inches Gymnastics: Low of 57 inches, a median of 61 inches, and a high of 65 inches C) Basketball: Low of 66 inches, a median of 70 inches, and a high of 74 inches Volleyball: Low of 61 inches, a median of 65 inches, and a high of 69 inches E) Football: Low of 64 inches, a median of 68 inches, and a high of 72 inches Mathematics, Science, & Gifted Department Page 16
Day 33 Day 34 64. Evelyn is comparing the number of customers in the hardware store and the number of customers in the hobby store. She counts the number of customers in each store at 6 randomly selected times. The results are shown. What can Evelyn say about the numbers of customers in each store? Use stacked box plots to compare the samples. Hardware store: 5, 11, 9, 13, 11, 12 Hobby store: 7, 12, 6, 4, 8, 7 Because the median number of customers in the sample for the hardware store is greater than the median of the sample for the hobby store and the sample distributions have little overlap, it is unlikely that the median numbers of customers in the stores are the same. 65. Stephen is the produce manager at a supermarket and is comparing the number of avocados sold per day to the number of cucumbers sold per day. He takes a random sample of 26 days and displays the results as shown. Which of the following statements describe the sets of data accurately? Sample mean number of avocados sold per day: 147 Sample mean absolute deviation for number of avocados sold per day: 18 Sample mean number of cucumbers sold per day: 143 Sample mean absolute deviation for number of cucumbers sold per day: 22 The median number of customers in the sample for the hardware store is greater than the median of the sample for the hobby store, but the sample distributions have considerable overlap. So, it is not unlikely that the median numbers of customers in the stores are the same. The sample mean number of avocados sold per day is greater than the sample mean number of cucumbers sold per day. The sample mean number of avocados sold per day is less than the sample mean number of cucumbers sold per day, but the means are about the same. C) The median number of customers in the sample for the hardware store is less than the median of the sample for the hobby store, but the sample distributions have considerable overlap. So, it is not unlikely that the median numbers of customers in the stores are the same. C) There is little overlap between the sample distributions for the number of avocados sold per day and the number of cucumbers sold per day. There is considerable overlap between the sample distributions for the number of avocados sold per day and the number of cucumbers sold per day. Because the median number of customers in the sample for the hardware store is less than the median of the sample for the hobby store and the sample distributions have little overlap, it is unlikely that the median numbers of customers in the stores are the same. E) F) There is not strong evidence that the mean number of avocados sold per day is different than the mean number of cucumbers sold per day. It is likely that the mean number of avocados sold per day is different than the mean number of cucumbers sold per day. Mathematics, Science, & Gifted Department Page 17
Day 35 Day 36 Questions 66-70: Match the chance of the event with the description of the probability of the event. 71. Which of the following chance events have probabilities of occurring that are? 0 Close to 0 C) Close to 1 E) 1 66. A spinner with 8 equal sections labeled 1 through 8 landing on a number less than 9 C) E) F) Rolling a 1 on a fair number cube with sides numbered 1 through 6 Rolling an odd number on a fair number cube with sides numbered 1 through 6 A spinner with 4 equal sections labeled 1, 2, 3, and 4 landing on 1 or 4 A spinner with 4 equal sections labeled 1, 2, 3, and 4 landing on a number less than 5 Flipping a fair coin and having the coin land with the heads side facing up Flipping a fair coin and having the coin land with the tails side facing up 67. Flipping a fair coin and having the coin land with the tails side facing up 68. Picking a green ball from a bag containing 99 green balls and 1 red ball 69. Rolling a number greater than 6 on a number cube with sides numbered 1 through 6 70. Picking the 4 of hearts from a standard deck of playing cards 72. Which event is most likely to occur? An event with probability 0.1 An event with probability 0.3 C) An event with probability 0.5 An event with probability 0.7 73. Alice makes 32 of her 40 free throws during practice. Which teammate has a higher probability of making a free throw during practice? Blythe made 27 out of 36 free throws. Dawn made 45 out of 50 free throws. C) Fay made 21 out of 30 free throws. Gillian made 14 out of 25 free throws. Mathematics, Science, & Gifted Department Page 18
Day 37 Day 38 74. A jar has 5 different colors of table tennis balls. After randomly selecting a table tennis ball, each person notes the color and places the table tennis ball back into the jar. For which of the following situations would you estimate the relative frequency to be greater than 0.3? 76. Consider a set of cards where each card is printed with a letter of the English alphabet. Each letter in the alphabet has its own card. The cards are placed into a hat. What is the probability of randomly selecting a card that is printed with a vowel (a, e, i, o, u)? C) E) Anita selects a red table tennis ball 2 times after 25 attempts. Bob selects an orange table tennis ball 10 times after 30 attempts. Chase selects a yellow table tennis ball 12 times after 60 attempts. Darlene selects a green table tennis ball 6 times after 15 attempts. Felix selects a blue table tennis ball 1 time after 20 attempts. 75. What is the probability of rolling a number that is greater than 4 on a number cube? " " C) " " 1 77. There are 200 different pieces of fruit in a barrel. There are 42 apples, 82 oranges, and 76 pears. Which of the following events have a probability that is greater than 0.4? Randomly selecting an apple Randomly selecting an orange C) Randomly selecting a pear Randomly selecting an apple or an orange C) E) Randomly selecting an apple or a pear F) Randomly selecting an orange or a pear 78. An unfair coin is tossed 20 times. It lands heads up 14 times and lands tails up 6 times. What is the experimental probability for each outcome based on these results? P(heads) " ; P(tails) " P(heads) ; P(tails) C) P(heads) " ; P(tails) " P(heads) ; P(tails) Mathematics, Science, & Gifted Department Page 19
Day 39 Day 40 79. Magglio is watching a bicycle day celebration, and he records the types of bikes as they pass. Among the first 28 bicycles, Magglio counts 8 hybrid bicycles, 14 road bicycles, and 6 cruiser bicycles. Which of the following experimental probabilities are correct based on the observations? 84. A pizza stand at a movie theater has a choice of three toppings, onion (O), mushroom (M), and pepperoni (P). Nina and Russ are sharing a pizza and each of them chooses one topping. Is the sample space for the topping combinations (O, M), (O, P), (M, O), (M, P), (P, O), and (P, M)? Explain. Yes; all of the possible outcomes are shown. P(hybrid) P(hybrid) C) P(road) P(road) " E) P(cruiser) " F) P(cruiser) " Use the choices below for questions 80-83. You roll a fair number cube, and then roll the number cube again. Match each description with the associated probability. C) " " E) F) " " " 80. The sum of the number cubes is 7. 81. The sum of the number cubes is at least 9. 82. The sum of the number cubes is not a prime number. 83. The sum of the number cubes is less than 4. C) No; the possible outcomes (O, O), (M, M), and (P, P) are not shown. No; the only possible outcomes are (O, O), (M, M), and (P, P). No; the outcomes (O, M) and (M, O) are not possible. Use the choices below for questions 85-88. Match each situation with the best stimulation method. An answer choice may be used more than once. A fair coin A fair number cube C) A spinner with 7 equal sections A set of chips where of the chips are red and the rest are black E) A spinner with 4 equal sections 85. A manager of a restaurant knows that about 40% of customers order at least one appetizer. What is the probability that exactly 2 of the next 5 customers order at least one appetizer? 86. A contestant on a game show has a 1 in 6 chance of winning for each try. If the contestant has 2 tries, what is the probability that she does not win? 87. The weather forecast states there is a 25% chance of rain for each of the next 7 days. What is the probability that it will rain on at least one of those days? 88. A florist know that about 75% of her flower bulbs grow into flowers. What is the probability that at least 30 of her 60 bulbs grow into flowers. Mathematics, Science, & Gifted Department Page 20