Algebra 2



Algebra IIName _______________________Series/Sequences/Stats Quiz ReviewSequence and seriesExplain the difference between an arithmetic and geometric sequence.2. Determine if the following sequences are arithmetic, geometric, or neither.(If arithmetic, determine the common difference. If geometric, determine the common ratio)a) 2, 6, 18, 54, 162 b) 1, 3, 6, 10, 15 c) ?5, ?2, 1, 4, 7 d) ?5, -1, 3, 7, 11Write a rule for the nth term of the sequence -2, 8, -32, 128, …4. Write a rule for the nth term of the sequence -2, 8, 18, 28, …5. If the fifth and eighth terms of an arithmetic sequence are -4 and -13, respectively, what are the first four terms of the sequence? 6. Write the rule for the arithmetic sequence when a14 = -73 and d = -87. Explain the difference between a sequence and a series. 8. Evaluate: 9. Find the sum. 10. Explain what must be true for an INFINITE geometric series to have a FINITE sum.11. Using the formula Sn = , find the sum of 12. What is the value of 13. Write the first 5 terms of an infinite geometric series that DOES NOT have a finite sum.Regression of various functions: Use your calculator to find the model for each of the following problems. Then, use your model to answer the following questions.The table below shows the speed, y measured in feet per second, of a space shuttle x seconds after its launch. Find the cubic model for the data.x1020304050607080y202.4463.3748.2979.31186.31421.31795.42283.5 Determine the Quadratic Model for the data set above. (round to 3 decimals)b) How fast will it be traveling 90 seconds after launch?StatisticsWays to CountExplain the difference between a permutation and a combination.Give an example of a situation that can be solved using a combination. Then, solve the problem. Give an example of a situation that can be solved using a permutation. Then, solve the problem.What is the Fundamental Counting Principle? Given an example of a problem that can be solved using this principle. Then solve the problem.From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected? Is this an example of a combination, permutation, or the Fundamental Counting Principle? Why?Solve the problem. Be sure to show your calculation or the calculator keystrokes used.An ice cream shop offers 32 flavors of ice cream, toppings of fudge, marshmallow, pineapple and strawberry, with garnishes of whipped cream and a cherry. How many different ice cream sundaes can be made? Is this an example of a combination, permutation, or the Fundamental Counting Principle? Why?Solve the problem. Be sure to show your calculation or the calculator keystrokes used.In one Austrian province, a vehicular plate number consists of 4 letters and 3 numbers. How many plate numbers are available? Is this an example of a combination, permutation, or the Fundamental Counting Principle? Why?Solve the problem. Be sure to show your calculation or the calculator keystrokes used.Normal Distribution – be sure to sketch and shade your normal curve and include your calculator command. A random survey was conducted to determine the cost of residential gas heat. Analysis of the survey results indicated a normal distribution with a mean monthly cost of gas of $125, and a standard deviation of $10. a. What percent of homes will have a monthly bill of more than $118?b. What percent homes will have a monthly bill between $118 and $130?c. Determine the percentile for a monthly bill of $140.A study of weekly salaries at High Tech Manufacturing indicated that weekly salaries are normally distributed with mean = $725 and standard deviation = $45. What salary represents the 84th percentile? What is the likelihood that an employee makes less than $650 OR more than $800? ................
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