Review for Final CE Math 1030

Transcription

1 Review for Final Please show all of your work for full credit on each problem. Circle your final answer and write it on the blank to the right of the problem. Partial credit will be awarded where work is shown, easy to follow and relevant to the problem. Name: School: Instructor/Period: 1. Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height above the water as a function of time could be modeled by the function: h(t) = 16t t where t is time in seconds and h is height in feet. This area reserved for grading. Please do not write in this area. a) How high is the cliff above the sea? b) How long did it take Jason to reach the maximum height above the water? a) Answer: possible earned 1 b) Answer: 0.5 c) What is the highest distance Jason was above the water? c) Answer: total d) When did Jason hit the water? d) Answer: Math of 13

2 2. Pamela drove her car 99 kilometers and used 9 liters of fuel. a) She wants to know how many kilometers she can drive with 12 liters of fuel. b) Pamela knows she has traveled 880 kilometers. How much fuel has she used? c) Paul drives a different model of car and can drive 30 kilometers using 2.8 liters of fuel. Whose car is more fuel efficient, Pamela s or Paul s? Explain your reasoning. Circle the correct answer: Paul s car is more fuel efficient Pamela s car is more fuel efficient Explanation: d) For a particular car with known fuel efficiency, are kilometers driven and liters of fuel used: directly proportional, inversely proportional or neither. Explain. Circle the correct answer: directly proportional inversely proportional neither Explanation: 3. You are thinking about buying a house that costs $150,000 and you plant to take out a 30-year loan with 5% interest with no down payment. The interest is compounded monthly. a) If you had $150,000 today, and instead of buying the house, you put that money in the bank for 30 years at 5% interest compounded monthly, how much money would you have at the end of 30 years? b) Okay, so you don t have $150,000 today, and you really want the house. So you take out the loan described above. What will the minimum monthly payments be? c) Over the course of 30 years, how much money will you have paid for your house? d) You have X dollars in savings that you could use as a down payment for the house. If you use your savings as a down payment, what will happen to the total amount of money you will have paid for your house over the course of 30 years: increase, decrease, stay the same? Explain. Circle the correct choice: increase decrease stay the same Explanation: 2 of 13

3 4. Assume you want to finance a home for $210,000. The bank offers you two choices. Option A: an 8% loan for 20 years or Option B: a 6% loan for 30 years. a) Use the table to the right to determine the minimum monthly payment for Option A: borrow $210,000 at 8% over 20 years. b) How much interest will you have paid over 20 years given the conditions in part a)? ANNUAL INTEREST NUMBER OF YEARS FOR THE LOAN RATE % $29.53 $22.58 $10.12 $6.06 $4.77 5% $29.97 $23.03 $10.61 $6.60 $5.37 6% $30.42 $23.49 $11.10 $7.16 $6.00 8% $31.34 $24.41 $12.13 $8.36 $ % $32.27 $25.36 $13.22 $9.65 $ % $33.21 $26.33 $14.35 $11.01 $10.29 Monthly Payments on a $1,000 loan c) Use the table above to determine the minimum monthly payment for Option B: borrow $210,000 at 6% over 30 years. d) How much interest will you have paid over 30 years given the conditions in part c)? e) Which loan option would you choose and why? 5. The yearly growth rate of a certain radioactive material is 0.61%. How long will it take for a pound of this material to decay to 0.3 pounds? a) Write an equation in the form: A = P(1 + r) n to model the reduction of radioactivity over time. b) How much radioactive material is left after 125 years? c) How long will it take for a pound of this material to decay to 0.3 pounds? 3 of 13

4 6. Each of the following represents a functional relationship between two variables. For each: i) define the two variables involved; ii) write an equation describing that function that answers the stated question iii) Identify if the function is linear, quadratic or exponential a) On the first day of each month, a homeowner decided to mow half of his lawn. Each day after that, he mowed one half of the remaining portion of the lawn not yet mowed yet. How much of the lawn did the homeowner mow on day x? i) x represents: y represents: ii) The function is: y = iii) Circle the correct description of the function: linear quadratic exponential b) A gym membership costs $40 to initially sign up and then $10 each month after that. How much would a member pay total for her membership after x months? i) x represents: y represents: ii) The function is: y = iii) Circle the correct description of the function: linear quadratic exponential 7. When the weather is cold, a shrub goes into dormancy and stops growing. As soon as the weather warms up, the shrub comes out of dormancy and begins to grow at a constant rate. Eight days after the shrub comes out of dormancy, its height has increased by 9.6cm from its dormancy height. 12 days after the shrub comes out of dormancy, the height of the plant has increased by 14.4cm from its dormancy height to 37.4cm tall. a) What is the daily growth rate of the plant? b) What is the height of the shrub in dormancy? c) How tall will the shrub be 35 days after coming out of dormancy? d) How tall is the shrub x days after coming out of dormancy? 4 of 13

5 8. The value of a trendy company can be modeled by the quadratic equation illustrated to the right. a) If the owner would like to sell the business when its value is at a maximum, when should he sell? Explain your answer. b) Is it reasonable for the owner to expect to receive $25 thousand for his business? Why or why not? c) If the owner hopes to receive at least $20,000 for his business, when should he sell? Explain your answer. d) At what point is it too late to sell the business for any kind of profit? Explain your answer. Value (thousands of dollars) e) Use a sentence or two to explain the overall trend of the model we are using for this business. Time (years) 9. When a drug such as a pain killer is introduced into the body, the kidneys work to eliminate the drug. Morphine, a powerful pain killer, has a half-life of about 2.5 hours. After 2.5 hours, half of the initial dose of Morphine has been eliminated from the body. After 5 hours, half of the remaining Morphine has been eliminated and so forth. a) A patient receives an initial dose of 20mg of Morphine at 1:00pm. Do you expect more or less than 10mg of Morphine to be left in the body at 4:00pm? Explain. Circle the correct choice: There will be more than less than 10mg left in the patient s body at 4:00. Explain: b) How much Morphine is left in the patient after 10 hours? c) When will there be 5 mg of Morphine left in the body? 10. Stanley is planning to stain his wood fence this spring. From a previous home, he knows that he needs 2 gallons of stain to cover 8ft x 50ft of fence. His new fence measures 6ft x 150ft. How many gallons of stain should Stanley buy if he must buy stain in whole gallons? 5 of 13

6 11. Rock-It is new company that is planning to sell shoes for rock climbers. The initial startup costs are graphed with the solid line below. a) What are the initial start-up costs for Rock-It? Explain your reasoning b) How much does it cost to produce a pair of shoes? Explain your reasoning. c) Write a linear equation describing the initial start-up costs for Rock-It where C is the total cost and x is the number of shoes produced. Rock-It plans to sell its shoes for $185 per pair (or $0.185 thousand dollars). The dashed line shows the profit for Rock-It where the equation for profit is P =.185x. P is the profit in thousands of dollars and x is the number of shoes sold. d) Will the company have made a profit after they sell 150 shoes? Explain. Thousands of dollars (100,29.7) Number of shoes produced (250,36.75) e) Use the graph to solve the system of equations illustrated in the graph and interpret the solution. f) Use the equations of the lines to find the intersection. Show your work. 12. A slot machine has three wheels. Each wheel has 9 symbols (4 bars, 2 lemons, 2 cherries and one bell). a) What is the probability all three wheels display a bell? b) What is the probability that exactly two wheels display lemons? c) A new slot machine was designed, like the one mentioned above, but with more symbols on each wheel. The extra symbols are all stars. Is the probability that all three wheels display a bell higher, lower, or about the same on the new slot machine compared to the slot machine described above? Explain your reasoning. Circle the correct choice: The probability the new machine will display all three bells is: higher lower about the same Explain: 6 of 13

7 13. Pandora.com surveyed a group of subscribers regarding which online music channel they use on a regular basis. The following information summarizes their answers: * 7 listened to rap, heavy metal and alternative rock * 10 listened to rap and heavy metal * 13 listened to heavy metal and alternative rock * 12 listened to rap and alternative rock * 17 listened to rap * 24 listened to heavy metal * 22 listened to alternative rock * 9 listened to none of these three channels a) Construct a Venn diagram to display the data. b) How many people were surveyed? c) How many people listened to either rap or alternative rock? d) How many listened to heavy metal only? 14. Annabelle has taken two exams. The scores on both exams were normally distributed. The Exam 1 had an average of 72 points with a standard deviation of 12 points. Exam 2 had an average of 78 points with a standard deviation of 7 points. She scored 80 points on both exams. Compared to her classmates, which exam did Anna perform better? Circle the correct answer then explain your reasoning for the answer you chose in a few sentences. You don t have to write anything by the incorrect answers. a) Relative to her classmates, Annabelle performed better on Exam 1 than Exam 2. Explanation: b) Relative to her classmates, Annabelle performed better on Exam 2 than Exam 1. Explanation: c) Relative to her classmates, Annabelle performed the same on Exam 1 and Exam 2. Explanation: 7 of 13

8 15. Use set notation to list the elements of each set. Give birth to live young Set A-Whales Breathe air Have hair Is purple Uses shampoo Run marathons a) A B b) B A c) C A d) B Have scales Internal skeletons Have fins Can swim Live in water Lay eggs Make noise from their body Have legs Set B-Fish Breathe water Set C- Frogs 16. There are 8 boys and 7 girls running for four identical council positions in student government. a) How many ways can the four positions be filled? b) What is the probability that four elected council positions were filled by girls? Would you be surprised if this happened? Explain your reasoning. c) Abby, Beth, Caitlyn and Darcy won the four positions for student government. Now they need to decide who among them serve as vice president and president. How many ways can the two offices be filled? 8 of 13

9 17. A 2017 Ford Explorer has a fair market price of $40,322. After doing a little bit of research, you find out the Explorer depreciates $14,324 in the first year. a) What percent of the fair market price has the Explorer lost in the first year due to depreciation? You decide to go ahead and purchase the Explorer for the fair market price of $40,322. The dealer has offered you two options: Option A: 48 monthly payments of $883 each Option B: 60 monthly payments of $719 each b) How much interest would you pay if you chose Option A? c) How much interest would you pay if you chose Option B? d) Which option would you chose and why? 18. The heights of NBA players that have participated in the All-Star game are normally distributed with a mean of 79 and a standard deviation of 4. Recall that a normal distribution is symmetric and follows the rule. a) About what proportion of NBA All-Star players are greater than 75 tall? b) Between what heights to we anticipate the middle 95% of All-Star players to be? c) Kyrie Irving from the Cleveland Cavaliers played in the 2017 All-Star game. He is listed at 75 tall. Is he unusually short for an All-Star player? Please use some math and a sentence or two to explain your answer. Math: Sentence: 9 of 13

10 19. The 2014 Winter Olympics in Sochi, Russia was the first time women competed in the Normal Hill Ski jump competition. Below are the jumping distances for the men and women. (For reference, the men s average distance, 97.6 meters is equivalent to about feet, over three football fields). a) Using the histograms above which gender had shortest recorded distance? Circle the correct answer: A woman man shortest recorded distance. b) About what was the shortest recorded distance in this event? c) Which gender had the shorter average distance jumped? Explain your answer. Circle the correct answer: Women Men had the shorter average distance jumped. Explain: d) Which gender had the smaller standard deviation for the distance jumped? Explain your answer. Circle the correct answer: Women Men had the smaller standard deviation on the distance jumped. Explain: 10 of 13

11 20. Use the boxplots to answer the questions below. Pay attention to the scale on the boxplots, they are not the same. Height of Men in Group A (inches) Height of Men in Group B (inches) a) Which data set has the larger median? Circle the correct statement below: Group A has the larger median. Group B has the larger median Group A and B have about the same median What is the median of the data set you chose in part a)? b) Which data set contains the shortest male? Circle the correct answer: Group A Group B has the shortest male What is the height of the shortest male from the data set you chose in part b)? c) Circle the correct statement below: Group A has the larger IQR Group B has the larger IQR Group A and B have about the same IQR Explain how you determined your answer to part c). Mathematical equations may be a useful part of your written explanation. 11 of 13

12 21. Over time it has been determined that the amount of rainfall in Seattle during the months of March and November are normally distributed. March has a mean rainfall of 1.7 with a standard deviation of 0.83 November has a mean rainfall of 5.97 with a standard deviation of of rain has been recorded at some point during both March and November. a) Is the z-score for 3.84 of rain in November positive or negative? Circle the correct answer: The z-score for 3.84 of rain in November is: positive negative b) Using words, not a mathematical equation, explain how you knew the z-score for 3.84 of rain in November was positive or negative. c) In which month is 3.84 of rainfall more remarkable? Circle the correct answer: 3.84 of rain is more remarkable during the month of March November d) Explain your answer to part c). You may use diagrams or mathematical equations to support your written explanation. 22. The following are midterm scores from Mr. Thomas class of six students: 96, 85, 65, 87, 87, 84. a) Compute the mean of the scores. b) Compute the standard deviation of the scores. c) Mrs. Lee s midterm had a mean of 85 with a standard deviation of 15. Write a sentence or two comparing the students performance in Mr. Thomas and Mrs. Lee s classes, specifically referencing the means and standard deviations. 23. Lyndon invests $1000 at 3% compounded quarterly. CallieJo sets aside $100 per month for one year in an account that earns 3%. a) How much does Lyndon have in his account at the end of 15 years? b) What is the future value of CallieJo s ordinary annuity? c) CallieJo puts the amount she has at the end of one year in an account with 3% interest that compounds quarterly. How much is in her account after 14 years? d) Compare Lyndon s investment and final balance in his account after 15 years to Calliejo s initial investment and final balance in her account after 15 years. What conclusion(s) can you make? 12 of 13

13 24. The heights of a class of 20 kindergartners range from 37 to 45 with a mean of an average (mean) height of 42. The teacher is 65 tall. a) If the mean is recalculated to include the height of the teacher, will the mean increase, decrease or remain the same? Circle your answer: When the height of the teacher is added to the data, the mean will: increase decrease remain about the same Explain your answer to part a) b) If the mode is recalculated to include the height of the teacher, will the mode increase, decrease or remain the same? Circle your answer: When the height of the teacher is added to the data, the mode will: increase decrease remain about the same Explain your answer to part b) c) If the standard deviation is recalculated to include the height of the teacher, will the standard deviation increase, decrease or remain the same? Circle your answer: When the height of the teacher is added to the data, the standard deviation will: increase decrease remain about the same Explain your answer to part c) 13 of 13