ALGEBRA 2 FINAL EXAM STUDY GUIDE

Transcription

1 Unit: Polynomials ALGEBRA 2 FINAL EXAM STUDY GUIDE 1. (2x 4 7x 3 + 4x 7) + (2x 2 4x + 8) 2. (-4x 3 + 7x 6) (7x 4 + 3x 3 2x 4) 3. (3x 3 + 2x + 7)(x 2 4) 4. x 4 4x 3 3x x 8 (x 3) (Long AND synthetic division) Write answer as quotient + remainder/divisor 5. For the polynomial function f(x), f(2)=0 and f(-5)=0. Write f(x) in standard form. 6. Factor the following polynomial completely: f(x)= x 4 12x Where does x 4 81 cross the x axis? 8. Use the polynomial f(x)= x 3 + 9x 2 + 6x 56 to determine: a) f(-7) b) Is x+7 a factor? Why or why not?

2 9. Write an equation for the graph: 10. Write an equation for the graph: 11. Write the letters of the graphs below that have the same end behavior as f(x) = x 3 + 2x 1 A B C D E F G H 12. Write the letters of the graphs above that have the same end behavior as f(x) = x 6 + 5x 4 3x 2 + 7

3 13. For the polynomial g(x), g(-5)=0 & g(2)=0. Write a function for g(x) in standard form. 14. Write an expression to represent the area of the rectangle below. Unit: Probability and Statistics Use the Round-Off Rule (round to one decimal place past your data) on this study guide unless otherwise indicated. 1. Find the mean, median and mode of the following data: 21, 27, 20, 29, 23, 21, 21, 27, 26, The number of stamps in the collections of stamp club members are: a) Find the range b) Find the median, Q 2 c) Find Q 1 d) Find Q 3 e) Find the IQR f) If 250 was added to the data set, which of the measures above (a-e) would change the most?

4 Use the box plot to answer questions In which year were the gas prices the highest? 4.In which year were gas prices the lowest? 5. For which 2 years was the max price equal to the min price? 6. For which 2 years was the max price equal to the median? 7. What percentage of gas prices were under $1.75 in 2002? 8. What percentage of gas prices were under $1.75 in 2003? 9. What percentage of gas prices were under $1.75 in 2004? 10. What was the mean gas price in 2003? 11. In which year were gas prices least stable? Explain. 12. Find the standard deviation of this sample of data:

5 13. of this data : 14. Write 3 senten ces to describ e the distrib ution

6 Use the obstacle course information provided to answer question 16. Team R Obstacle Course Times 5:32 6:48 4:25 8:05 7:23 5:37 5:12 6:26 5:31 4:43 6:08 7:16 5:52 5:21 6:53 4:49 5:02 6:33 5:54 6:20

7 17. Draw a box plot to represent Team R s data: Use the information provided to answer questions The two-way table shows the classification of students in a mathematics class by gender and dominant hand. A student who is ambidextrous uses both hands equally well. Right-handed Left-handed Ambidextrous Male Female What is the probability that a randomly selected student in the class is female given that the student is right-handed? 19. What is the probability that a randomly selected student in the class is male or lefthanded? 20. What is the probability that a randomly selected student in the class is right-handed or ambidextrous? 21. What is the probability that a randomly selected student in the class is female? 22. What is the probability that a randomly selected student in the class is male who is right-handed? Give your answer as a percentage. 23. If you roll a fair die twice in a row, what is the probability of getting two 3 s? 24. A jar contains 10 marbles: 3 red, 3 blue, 2 green, 1 yellow and 1 black. What is the probability of drawing a blue marble, followed by a yellow marble if a) The first marble is replaced before drawing the next marble? b) The first marble is NOT replaced before drawing the second marble. Unit: Trigonometry Final Exam Review (NC = no calculator) 1. Convert: a) the angle α = 3π 5 to degree. b) the angle θ = 3100 to radians. NC

8 2. What is the degree measure of an angle whose measure is 14 radians? NC 3. If tan θ = 7 and the sine of the angle is positive, Find cosθ If Sin θ = 5 and θ is in quadrant III, what is tanθ? Graph two cycles of f(x) = 7sin ( 4π x), find the period and the amplitude Graph one cycle of f(x) = 2cos (πx), find the period and the amplitude. 7. Graph one cycle of f(x) = 5cos ( x ), find the period and the amplitude

9 10. Find the coordinates of points A, B, C and D on the unit circle below B A C D Unit: Sequences and series 1. Find the missing term or terms of the following sequences: a) 14,,54,,74 b) 10,40,,,130 c) 1,-3,,,81 2. Find the 8 th term of each of the following sequences: a) 66,50,34,18, b) 1,4,9,16,

10 UNIT : EXPONENTIAL and Logarithmic FUNCTIONS 1. Graph f(x) = e x and g(x)=ln x on the same xy- plan. How are those functions related? 2. Which of the following functions would be exponential functions? Give a rationale for OR against for each problem. a) The total amount paid for gas over x number of weeks if Sara puts $25 of gas in her car each week. b) The value of a computer after x years if it depreciates 12% each year. c) The total cost of a wedding for x people if you pay $50/person. d) The population of Jonesville after x years if the population decreases by 20 people each year. 3. Write an exponential model for the following situation: Hussein bought a house for $115,000. The value of the house appreciates by 3% each year. Write a model for the value of the house after x years. 4. Write an exponential model for the following situation: Laurie bought some office furniture. For tax purposes, the value of the furniture depreciates by 13% each year. Write a model for the value of the furniture after x years.

11 5. Joe took a job for $30,000 and gets an $800 raise each year. Nora took a job for $28,000 and gets a 3% raise each year. If this is a career choice and they are planning on staying in this job for the long term, who took the better deal? Explain. 6. The population of Berkeley can be modeled by the function P(t) = 115,000(1.013) t where t is the number of years after a) What is the population of Berkeley in 2015? b) Is Berkeley getting bigger or smaller? Explain. c) What is the rate of increase/decrease each year? 7. Convert between exponential and log a) 3 5 = 243 b) log 9 81 = 2 c) log = 3 d) log 5 50 = k