Algebra 2 Semester 2 Review


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1 Name Block Date Algebra 2 Semester 2 Review NonCalculator Consider the function f x 1 x 2. a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain and range of f (x)? d) Using anchor points, graph the function. 2. Consider the function g x x 2 1 a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain and range of g (x)? d) Using anchor points, graph the function Solve the following equation: x 4. Solve the following equation: 6x 7x 4 x 4 x 4 5. Solve the following equation: x 2 x 5 x 5 x
2 Rewrite the following expression using rational exponents: Rewrite the following expression as a radical: Simplify the following expression: 8 x Simplify the following expression: x Consider the function f x 2x. a) Describe the transformation of the graph of y x b) What is the domain and range of f (x)? c) Using anchor points, graph the function. 11. Consider the function g x x 2 4 a) Describe the transformation of the graph of y x. b) What is the domain and range of g (x)? c) Using anchor points, graph the function Solve the following equation: 4 2x Solve the following equation: 2 x Solve the following equation: x x 5
3 Evaluate the piecewise function for x = 2, x= 0, and x= 6. a. 8 if x 0 f( x) x 1 if x 5 b. 2 x x 2 if 1 x if 1 x 2 gx ( ) 10x if 2 x 5 2 x 2x if x Graph each function a. 1.5x if x 2 f( x) 2x 2 if x 2 b. 2 ( x 1) if x 1 f( x) x 1 if x Derek and his friends drove from San Francisco to Lake Tahoe to go skiing. They drove 0 minutes in the city at 0 mph and then hours on the highway at 60 mph. Using the graph, write a piecewise function for the distance d that Derek traveled.
4 Use the following functions to perform each operation. 2 g( x) x x 18 h( x) x 6 g a. ( gh)( x ) b. (g + h)(x) c. ( x) h Two spinners numbered 1 6 are spun. If all numbers are equally likely, what is the probability that the result will be two even numbers? 20. Find the probability that a point chosen at random inside the larger square shown here will also fall inside the smaller square. 6 in. 2 in Ms. Ness decided to make a bunch of flags for Flag Day using four strips of colored paper. She placed one white (W), one red (R), one black (B), and one yellow (Y) strip of paper into a bag and randomly pulls out the strips one at a time, lining them up horizontally to create a flag like the one below. Using a capital letter to represent that colored strip, create the sample space of flags made by Ms. Ness. Then, use it to find the following probabilities. a. P(of making a flag with a red strip on top and a yellow strip on bottom) b. P(of making a flag with a white strip second or third)
5 22. A bag contains 11 beads 2 blue, yellow, and 6 red. Determine whether each event is independent or dependent. Then, find the probability. a. selecting a yellow, then a blue bead with replacement. b. selecting a yellow, then a blue bead without replacement A random table in the cafeteria is chosen. Sitting at the table is 2 freshmen, 5 sophomores, 7 juniors, and 2 seniors. A student is chosen at random from the table. What is the probability of choosing a freshmen or a senior? 24. The numbers 1 20 are written on cards and placed in a bag. Find each probability. a. choosing twenty or choosing an odd number. a. choosing a number less than ten or choosing a multiple of five Use the following set of data: {, 7, 8, 2, 6, 4}. a. Find the mean, median, mode, Q1, Q, range, and IQR. b. Make a boxplot for the data and sketch it below. c. Using the rule for nonsymmetric distributions, find any outliers Determine whether each survey is likely to represent the population. EXPLAIN. a. A survey asks the members of the math club whether math classes should be required for all four years of high school.
6 b. Colorado State government sends out a survey to random Colorado City governments about the city s parking plans Classify each sample as simple random, systematic, stratified, cluster, convenience, or selfselected. a. a store owner in the mall wants to determine whether a new brand of shoes will sell in her store. She surveys random people in the mall on the weekend. b. a city councilor wants to know how residents in the city will react to a new smoking policy. He surveys residents by mailing a random sample of voters in the city. c. the director of the student theater group wants to know which of three plays will have the largest student audience. He randomly chooses 20 freshmen, 20 sophomores, 20 juniors, and 20 seniors in the hall between classes Determine whether the following situation is an experiment or an observational study. A researcher compares incomes of people who live in rural areas with incomes of people who live in large cities. 29. Explain whether the research topic is best addressed through an experiment or an observational study. Then explain how you would set up the experiment or observational study. Does reducing the fat in a particular recipe make it less appealing? Find the length of the side marked with x in each triangle below.
7 Find the exact value of each trigonometric function. Use the unit circle. 5 cos sin120 tan For each function, h x sin x and k x cos x : a. Identify the amplitude and period. b. Identify the maximum and minimum values.. Use the information above to graph each function below. 5.5 and 5.8 Calculator Solve the following inequalities using your graphing calculator to help x x x x 7 2x 1
8 A firework is launched at 20 meters per second from a 60 meter bridge. The table shows the distance, d, in meters the projectile is above the river after t seconds. Create a graph and an equation to represent the height of the firework as a function of time. y t d x 9. New members of a fitness club pay $200 to start and then $20 per month for life. Create a table and an equation that models the graph of total cost of enrollment as a function of months of participation Use constant differences or ratios to determine which parent function; linear, quadratic, or exponential, would best model the given data set. a. x y b. X y
9 41. The Fan Cost Index (FCI) tracks the cost for a family of four to attend a Major League Baseball game. The table below shows the year and the FCI for that year. Year FCI $79.41 $ $ $ $09.8 a. Write a function that models the data. b. Use your model to predict the FCI in Chapter Write a recursive and an explicit rule for the n th term of the sequence. Then find the 8 th term. a., 12, 48, 192, b. 2, 11, 20, 29, c. 4 6, 12,4,,... d. 6, 4., 2.6, 0.9, 4. Given the series 12,8,4,0,..., find the sum of the first 12 terms. 44. Given the series 0.,0.6, 1.2, , find the sum of the first 10 terms. 45. Elle is buying a graduation dress on layaway. She agrees to make a $7 down payment and increase the payment by $5 each week. What will her payment be in the 9 th week? How much money in total will Elle have paid after 9 weeks? 46. In 2002 the average tuition at a public college in the United States was $06. The average tuition increases by about 6% per year. If Joe starts college in 2002, how much is the tuition for his senior year in 2005? How much tuition does Joe pay in total for his four years of college?
10 47. Find the number of terms in the sequence 12, 7, 2, Which term is 1227 in the arithmetic sequence, 9, 15, 21, The door code to get into a topsecret laboratory is 6 digits. The first digits of the code are all odd and the last digits are all even. Digits can be used more than once. How many possible codes are there to gain access to this laboratory? 50. The principal of the high school selects 4 Merit Scholars to attend a Town Council meeting. If there are a total of 12 Merit Scholars at the school, in how many ways can the students be selected? 51. Holly wants to choose 5 different decorative tiles out of 8. If she plans to place the 5 tiles in a row, end to end, in how many different ways can she arrange them, from left to right? A bowl contains 6 blue, 75 green, and 19 yellow jelly beans. What is the probability of randomly selecting a green jelly bean? The following table shows the results of a schoolwide survey on the homecoming dance. Find the probability of each event. Homecoming Dance Location Survey Girls Boys Gymnasium a. that a student prefers the cafeteria given that they re a girl. Cafeteria 5 7 b. that a surveyed student is male and prefers the gymnasium.
11 Students and teachers at a school were polled to see if they were in favor of extending the parking lot into part of the athletic fields. The results of the poll are shown in the twoway table below. In Favor Not in Favor Students 16 2 Teachers 9 14 a. Create a table of the joint and marginal relative frequencies. b. P(not in favor)= c. P(students and in favor)= 7.5 d. P(in favor teacher)= 55. In an apartment building with 50 residents, 16 of them have cats, 28 of them are students, and 9 of the students have cats. a. Make a twoway table or a Venn diagram to represent this situation. b. Use the table and/or diagram to find the following probabilities: a. P(student)= b. P(student and has a cat)= c. P(student or has a cat)= 56. There are 8 couples in a dance competition. Each of 4 judges must pick the couple they believe should win. Suppose the judges pick at random. What is the probability that at least 2 of the judges picked the same couple?
12 a. Find the mean, median, mode, Q1, Q, range, IQR, variance, and standard deviation for: {12, 15, 18, 10, 9, 15, 16} b. Using the rule for symmetric distributions, are there any outliers in the data set? SHOW WORK! 58. Given the following table, find the expected value of the raffle prize. Raffle Prizes Value $0 $5 $20 $200 Probability In a survey of 100 town residents, 6 said they prefer the library s new hours. If you were able to survey all of the 2,000 town residents, how many would you expect to prefer the library s new hours? Determine whether the survey clearly projects the winner. Explain your response. A website had users vote for their favorite of three dog photos. 5% voted for photo 1 and 47% voted for photo. The margin of error is ± 9%. 8.7 z Area Scores on the Wechsler Adult Intelligence Scale (a standard "IQ" test) for the 20 to 4 age group are approximately normally distributed with a mean of 110 and a standard deviation of 25. Find each of the following probabilities: a. that a randomly selected adult 20 4 scores below 15. b. that a randomly selected adult 20 4 scores above 160.
13 c. that a randomly selected adult 20 4 scores between 97.5 and d. that a randomly selected adult 20 4 scores below 72.5 or above Below are the test grades for two different sections of AP Statistics on the same randomly picked chapter. 1st Class 2nd Class a. State the null hypothesis. b. Compare the results of the two groups. Does it appear that one class does significantly better in AP Stat than the other? 6. A cereal manufacturer sells boxes of cereal that list the weight as 20 oz., with standard deviation A random sample of 60 boxes was weighed and a mean of 19.9 oz. resulted. Is there enough evidence to reject the manufacturer s claim? For the triangle at the right, find sin,cos, and tan. J θ 9 K Kayla is fishing near the ferry landing near her home. She wonders how far the ferries actually travel when they cross the river. To find out, she puts a fishing pole upright on the riverbank directly across from the ferry landing. Then she walks down the bank 180 yards and measures an angle of 75 between the lines to her fishing pole and the ferry landing on the opposite bank. Find the distance, to the nearest yard, directly across the river. L
14 10.2 and Draw an angle with the given measure in standard position. Then find (a) a positive coterminal angle, (b) a negative coterminal angle, and (c) the reference angle Convert from radians to degrees or degrees to radians
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