Name: ________________________ Class: ___________________ Date: __________ ID: A GSE AA Final Exam Practice Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Nadav invests $6,000 in an account that earns 5% interest compounded continuously. What is the total amount of her investment after 8 years? Round your answer to the nearest cent. a. $14,950.95 c. $9850.95 b. $327,588.90 d. $8950.95 8x4y2 9xy2z6 ____ 2. Multiply . Assume that all expressions are defined. 3z3 4y4 a. 3 x3y2z c. 6x4yz2 2 b. 6x5z3 d. 6x5y8z9 1 Name: ________________________ ID: A ____ 3. Graph the function f(x) = 43 x5, and identify its domain and range. a. c. The domain is the set of all real numbers. The domain is the set of all real numbers. The range is also the set of real numbers. The range is also the set of real numbers. b. d. The domain is the set of all real numbers. The domain is the set of all real numbers. The range is also the set of real numbers. The range is also the set of real numbers. 2x2 48 x6 ____ 4. Subtract . Identify any x-values for which the expression is undefined. x2 16 x4 x2 2x72 a. ; The expression is undefined at x 4 and x 4. x4x4 x6 b. ; The expression is undefined at x 4 and x 4. x4 x6 c. ; The expression is undefined at x 4 and x 4. x4 x6 d. ; The expression is undefined at x 4 and x 4. x4 2 Name: ________________________ ID: A ____ 5. Suppose that a certain website claims that it averages 4.7 hours of downtime per month. (Downtime is time that the site is not available.) In a random sample of 17 months, the average downtime was 4.9 hours per month, with a standard deviation of 0.5 hours per month. What is the z-value rounded to the nearest hundredth? Is there enough evidence to reject the claim? a. The z-value is 1.65. There is enough evidence to reject the claim. b. The z-value is 2.21. There is enough evidence to reject the claim. c. The z-value is 2.21. There is not enough evidence to reject the claim. d. The z-value is 1.65. There is not enough evidence to reject the claim. 3 Name: ________________________ ID: A ____ 6. Determine if the set of rational expressions is closed under subtraction. Explain why or why not. a. The set of rational expressions is not closed under subtraction. One counterexample is shown. 3x 2x 3x 2 2x 3 3x 2x 3x 2 2x 3 66xx 66xx 6x6x6x 60x 0 0 0 If x = 0, then , which is not a rational expression, since it is undefined. 6x 6(0) 0 b. The set of rational expressions is not closed under subtraction. One counterexample is shown. 3x1 2x1 x 3x 3x 0 x Since division by zero is undefined, is not a rational expression. 0 c. The set of rational expressions is closed under subtraction. Let f(x), g(x), p(x), and q(x) be polynomial expressions where g(x) and q(x) are not equal to zero. Then f(x) p(x) f(x) q(x) p(x) g(x) g(x) q(x) g(x) q(x) q(x) g(x) gf((xx))qq((xx)) qp((xx))gg((xx)) f(x)q(x)p(x)g(x) g(x)q(x) Since the product of polynomials is a polynomial, and the difference of polynomials is a polynomial, then the difference of two rational expressions is a rational expression. d. The set of rational expressions is closed under subtraction. Let f(x), g(x), p(x), and q(x) be polynomial expressions where g(x) and q(x) are not equal to zero. Then gf((xx)) qp((xx)) gf((xx))pq((xx)) Since the difference of polynomials is a polynomial, and the quotient of polynomials is a rational expression, then the difference of two rational expressions is a rational expression. 4 Name: ________________________ ID: A ____ 7. The Soft Landing video game company is about to release a new flight simulator game. If the game is likely to sell to more than 10% of all video game buyers, the company will make 500,000 copies. If it is likely to sell to less than 10%, the company will make 200,000 copies. Soft Landing sends an e-mail survey to everyone who bought their previous flight simulator game. Of 400 people who responded to the survey, 80 said they were “very likely” to buy the new game. Based on the results of the survey, the Soft Landing company makes 500,000 copies of the game. Was this a good decision? Explain why it was a good decision, or, if not, suggest a better way to gather information to make a better information. a. This was a poor decision. The sample surveyed was biased, because it contained only people who buy flight simulator games. These people are more likely to be interested in a new flight simulator than are game buyers in general. The company could make a better decision by surveying 100 randomly-selected video game buyers at several different store locations. b. This was a good decision. Since 20% of the people surveyed are likely to buy the game, Soft Landing needed to make the greater number (500,000) of games. c. This was a poor decision. The sample surveyed was biased, because it only includes people who bought Soft Landing games. These people are more likely to buy another Soft Landing game than one from a different company. The company could make a better decision by surveying 100 randomly-selected flight simulator game buyers, not just their own customers. d. This was a good decision. Since 20% of their current flight simulator customers are likely to buy the game, Soft Landing needed to make the greater number (500,000) of games. ____ 8. A manufacturer inspects 400 personal video players and finds that 399 of them have no defects. The manufacturer sent a shipment of 800 video players to a distributor. Predict the number of players in the shipment that are likely to have no defects. a. 798 c. 780 b. 399 d. 2 ____ 9. The number of calls received by a technical support center during 18 randomly selected days is listed. Identify the outlier, and describe how it affects the mean and the standard deviation. 50 57 77 66 53 72 51 88 82 70 62 64 69 88 98 65 14 68 a. The outlier is 14. The outlier in the data set causes the mean to decrease from about 69.4 to about 66.3 and the standard deviation to increase from about 13.7 to about 18.6. b. The outlier is 88. The outlier in the data set causes the mean to increase from about 66.3 to about 69.4 and the standard deviation to decrease from about 18.6 to about 13.7. c. The outlier is 14. The outlier in the data set causes the mean to decrease from about 18.6 to about 13.7 and the standard deviation to increase from about 66.3 to about 69.4. d. The outlier is 88. The outlier in the data set causes the mean to decrease from about 18.6 to about 13.7 and the standard deviation to increase from about 66.3 to about 69.4. 5 Name: ________________________ ID: A ____ 10. The Fall Dance Committee surveys 20 eleventh and twelfth graders to see what music they would like to hear at the dance. Identify the population and sample. a. Population: All eleventh and twelfth graders at the school Sample: The 20 students who were surveyed b. Population: The 20 students who were surveyed Sample: All eleventh and twelfth graders at the school 1 ____ 11. Solve x2 x2 2 graphically. 2 a. c. x 2,4 x 2 b. d. x 2,4 x 1 ____ 12. Explain whether the situation is an experiment or an observational study. A nutritionist wants to know if taking vitamins keeps people from getting colds. She gives 100 people a vitamin supplement for 2 months, and compares the results to 100 people who do not take vitamins. a. This is an observational study. The nutritionist gathers data instead of applying a treatment. b. This is an experiment. The nutritionist gathers data instead of applying a treatment. c. This is an experiment. The nutritionist is applying a treatment (taking vitamins) instead of simply gathering data. d. This is an observational study. The nutritionist is applying a treatment (taking vitamins) instead of simply gathering data. 6 Name: ________________________ ID: A 18 ____ 13. Solve the equation x9 . x a. x 6 c. x 3 b. x 3 or x 6 d. x 3 or x 6 ____ 14. The altitude of an aircraft, h, in miles, is given by h 100logP, where P = the outside air pressure, and B 9 B = the atmospheric pressure at sea level. Let B = 31 inches of mercury (in. Hg). What is the outside air pressure at a height of 3.6 miles? Round your answer to the nearest tenth. a. 65.4 in. Hg c. –0.5 in. Hg b. 14.7 in. Hg d. 1.2 in. Hg ____ 15. The study described below is a randomized comparative experiment. Describe the treatment, the treatment group, and the control group. A group researching dental health instructs a group of 100 people to brush twice a day for at least two minutes each time. Another 100 people were told to keep their usual brushing habits. After 6 months, the people who were told to brush for two minutes twice a day were significantly less likely to have cavities than those told to brush as usual. a. Treatment: Brush for two minutes twice a day. Treatment group: The 100 people told to brush for two minutes twice a day. Control group: The 100 people told to brush as usual. b. Treatment: The 100 people told to brush for two minutes twice a day. Treatment group: Brush for two minutes twice a day. Control group: The 100 people told to brush as usual. c. Treatment: Having fewer cavities. Treatment group: The 100 people told to brush for two minutes twice a day. Control group: The 100 people told to brush as usual. d. Treatment: Brush for two minutes twice a day. Treatment group: The 100 people told to brush as usual. Control group: The 100 people told to brush for two minutes twice a day. 2x 6x ____ 16. Solve the equation . x2 7x18 x2 x2 a. x 0 or x 13 c. x 0 or x 13 b. x 2, x 9, or x 1 d. x 9 or x 1 x ____ 17. Solve 1 by using a graph and a table. x6 a. x 3 or x 6 c. x 3 or x 6 b. 3x 6 d. 3x 6 x2 x30 ____ 18. Solve 11. Check your answer. x5 a. x 6 b. x 5 c. There is no solution because the original equation is undefined at x 5. d. x 16 7 Name: ________________________ ID: A ____ 19. Using the graph of fx x as a guide, describe the transformation and graph gx 4 x3. a. Stretch f vertically by a factor of 4 and c. Compress f horizontally by a factor of 1 4 translate it left 3 units. and translate it up 3 units. b. Stretch f vertically by a factor of 4 and d. Compress f horizontally by a factor of 1 4 translate it right 3 units. and translate it down 3 units. ____ 20. The table shows the probability distribution for the number of people who contract a disease in a scientific study. Find the expected number of people who contract the disease. Round your answer to the nearest tenth. Number of People 2 3 4 5 6 Probability 0.20 0.32 0.288 0.1536 0.0384 a. 4.0 b. 3.0 c. 3.5 d. 2.5 8 Name: ________________________ ID: A ____ 21. Voters in Jackson County are going to vote on a half-percent sales tax increase to support music in local schools. According to a random survey, 40% plan to vote for the tax and 60% plan to vote against it. The survey’s margin of error is 6%. Determine whether the survey clearly projects whether the sales tax will pass. Explain your response. a. The survey clearly projects that the sales tax will pass; 60% 6% = 54% to 66% plan to vote for the tax and 40% 6% = 34% to 46% plan to vote against the tax. The intervals do not overlap, so the survey clearly projects the outcome. b. The survey clearly projects that the sales tax will not pass; 40% 6% = 34% to 46% plan to vote for the tax and 60% 6% = 54% to 66% plan to vote against the tax. The intervals do not overlap, so the survey clearly projects the outcome. c. The survey clearly projects that the sales tax will not pass; 40% 3% = 37% to 43% plan to vote for the tax and 60% 3% = 57% to 63% plan to vote against the tax. The intervals do not overlap, so the survey clearly projects the outcome. d. The survey does not clearly project whether the sales tax will pass; up to 40% +12% = 52% might vote for the tax and only 60% –12% = 48% might vote against the tax. The intervals overlap, so the survey does not clearly project the outcome. 9 Name: ________________________ ID: A x2 8x12 ____ 22. Identify holes in the graph of fx . Then graph. x2 a. There is a hole in the graph at x 6. c. There are no holes in the graph. b. There is a hole in the graph at x 2. d. There is a hole in the graph at x 2. ____ 23. A spinner has 8 equal-sized sectors, numbered 1 through 8. What is the expected value of one spin of the spinner? a. 36 c. 4 b. 5 d. 4.5 10
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