ALGEBRA 2 CP FINAL EXAM REVIEW

Transcription

1 ALGEBRA CP FINAL EXAM REVIEW

2 Algebra CP FINAL EXAM REVIEW Name CHAPTER - TRIGONOMETRY Note: always round sides to the nearest tenth and angles to the nearest degree. Find the values of the si trigonometric functions for angle θ... sin θ 4 45 cos tan csc sec cot. θ. sin cos tan csc sec Write an equation involving sin, cos, or tan that can be used to find, then solve. cot

3 Solve ΔABC by using the given measurements. 6. A = 5, a = 7. b = 5, c = B = A b = b c c = C a B 7. a = A = B = Draw an angle with the given measure in standard position Rewrite each degree measure in radians and each radian measure in degrees Find one angle with positive measure and one angle with negative measure coterminal with each angle Find the reference angle for the angle with the given measure

4 Find the eact value of each trigonometric function cot tan... 5 tan. csc Solve Δ ABC if A = 50, B = 0, and c = C = a = b = Determine whether each triangle has one, two or no solutions, then solve each triangle. 5. A = 9, a = 6, b = A = 66, a =, and b = A = 45, a = 5, and b = 8 7.

5 Solve the following triangles. 8. A 80 C 7 B a = 6, b = 0, C = Solve the following triangles completely. 0. a = 8, b = 6, c = B = 47, C =, b =. Find the eact value of each function cos. 0 sin.. 4. sin 5. cos

6 Solve each equation by finding the value of. 6. Sin ( ) 7. Arc tan Arccos 9. Arc tan Find each value. Write angle measures in radians. 40. Sin 4. Tan Find the value of each epression cos, if tan ; sin, if 6 cos ; In a sightseeing boat near the base of the Horseshoe Falls at Niagara Falls, a passenger estimates the angle of elevation to the top of the Falls to be 5. If the Horseshoe Falls are 7 feet high, what is the distance from the boat to the base of the falls? 44. Falls Boat

7 CHAPTER 4 GRAPHING SINE AND COSINE. Given, y 4sin find the following in radians: a. Amplitude a. b. Period b. c. Graph one positive and one negative period. (be sure to label graph). Given, y cos4 find the following in radians: a. Amplitude a. b. Period b. c. Graph one positive and one negative period. (be sure to label graph)

8 . Given, y cos find the following: a. Amplitude a. b. Period b. c. Phase Shift c. d. Graph one positive and one negative period. (be sure to label graph) 4. Given, y sin find the following in radians: a. Amplitude 4 a. b. Period b. c. Vertical Shift c. d. Graph one positive and one negative period. (be sure to label graph)

9 CHAPTER 8 RATIONAL EXPRESSIONS Simplify each epression. y.. 4 y m m 9m m 6m 9 m 9 4. c c c c 5 c 4c 5 4c y 5z 4 8z 6p 8p 4 p 7 p y 4p 7 p p q 4 p q 4z z 4 z z w w b d bd Determine any value(s) of that are undefined.. f 5 f.. 4.

10 Solve the following Find the product: Solve: Solve: Dave can paint a room in 6 hours. Tom can paint the same room in 4 hours. If they work together, how long will it take both of them to paint the room?.

11 Graph the following be sure to include the vertical and horizontal asymptotes.. y y Vertical Asymptote: Horizontal Asymptote: Domain: Range: 4. 6 y 6 y Vertical Asymptote: Horizontal Asymptote: Domain: Range: 5. y 4 y Vertical Asymptote: Horizontal Asymptote: Domain: Range:

12 6. y y Vertical Asymptote: Horizontal Asymptote: Domain: Range: CHAPTER SEQUENCES AND SERIES Write a rule for the nth term of the arithmetic sequence.. 8, 5,, -, -4,. d = 7, a 8 = 54. a 4 = 7, a = Find the sum of the series n n n 7 n 6. n n i 8. 5 i i 6 i i i

13 0. Joe buys a $600 computer on layaway by making a $00 down payment and then paying $5 per month. Write a rule for the total amount of money paid on the computer after n months. 0. Write a rule for the nth term of the geometric sequence.. 56, 64, 6, 4,,. r = 5, a = 00. a = 6, 6 a Find the sum of the series, if it eists. If it does not eist, write no limit eists. 9 i 4. 8 i i i 6. i 5 8 i i 7 4 i i i i i Write the first five terms of the sequence. 0. a = 4, a n = a n + 9. a = 8, a n = 5a n 0... a =, a n = n a n. a = 4, a = 7, a n = a n +a n..

14 Write a recursive rule for the sequence. 4.,, 7, 4, 5., 0, 7, 4, Find the first three iterates of the function for the given initial value. 6. f ( ) 7, 4 7. f ( ) 85, CHAPTER 0 COUNTING METHODS AND PROBABILITY 7.. A briefcase lock has rotating cylinders each containing 0 digits.. How many numerical codes are possible?. Allan is playing the role of Oliver in his school s production of Oliver Twist.. The wardrobe crew has presented Allan with 5 pairs of pants and 4 shirts that he can wear. How many possible costumes consisting of a pair of pants and a shirt does Allan have to choose from?. A Meican restaurant offers chicken, beef, or vegetarian fajitas wrapped. with either corn or flour tortillas, and topped with either mild, medium or hot salsa. How many different choices of fajitas does a customer have? 4. How many 7-digit phone numbers can be formed if the first digit cannot 4. be 0 or, and no digit can be repeated? Determine whether each situation involves a permutation of combination. Then find the number of possibilities. 5. Seating 8 students in 8 seats in the front row of the school auditorium Checking out library books from a list of 8 books for a research paper Electing 4 candidates to a municipal planning board from a field of 7 candidates The first, second and third place finishers in a race with 0 contestants. 8.

15 Evaluate P 0. 6 C. 6!. 0! 5! 5! Find the number of distinguishable permutations in the following word: a. PANAMA b. FACTORIAL c. MISSISSIPPI a. b. c. 4. Find the number of possible 5-card hands that contain the cards specified. The cards are taken from a standard 5-card deck. a. 4 kings and one other card 4 a. b. 5 hearts or 5 diamonds b. 5. Use the binomial theorem to write the binomial epression: a) 6 ; b) 4 a b ; c) 5 5 a. 5 b. 5 c.

16 6. Si representatives from a senior class of 50 students are to be chosen for the student council. In how many ways can these students be chosen to represent the senior class on the student council? 7. You have an equally likely chance of choosing any integer from through 0. Find the probability of the given event. 6. a. An even number is chosen b. A multiple of 5 is chosen 7 a. b. c. A factor of 60 is chosen d. A prime number is chosen c. 8. Let A and B be events such that P ( A), P ( B) and d. P ( Aand B). Find P ( Aor B) Let A and B be events such that P(A) = 0., P(B) = 0.48, and P(A and B) = 0.. Find the indicated probability. A P B 9 a. a. P(A or B) b. P c. b. c. 0. A card is randomly selected from a standard deck of 5 cards. Find the probability of drawing the given card. a. A red king b. A diamond c. Not a club 0 a. b. c.. Two si-sided dice are rolled. Find the probability of the given event. a. The sum is not 7 b. The sum is less than 8 or greater than a. b. Find the odds in favor of an event, given the probability of the event

17 Find the probability of an event occurring, given the odds of the event. 5. 0: 6. 4:9 7. 8: A die is rolled twice. Find the probability. a. P(5, then 6) 8 a. b. P(4, then not 6) b. 9. There are nickels, dimes and 5 quarters in a purse. Three coins are selected in succession at random. Find the probability. a. P(nickel, then dime, then quarter) if no replacement occurs. 9 a. b. P( dimes) if replacement occurs. b. c. P( nickel, then quarters) if replacement occurs. c. d. P( quarters) if no replacement occurs. d. 0. Serena is creating a painting. She wants to use more colors. She chooses randomly from 6 shades of red, 0 shades of green, 4 shades of yellow, 4 shades of purple and 6 shades of blue. What is the probability that she chooses shades of green? 0.. Becky s mother is shopping at the bakery. The owner offers Becky a cookie from a jar containing chocolate chip cookies, 8 sugar cookies and 5 oatmeal cookies. Without looking, Becky selects one, drops it back in, and then randomly selects another. What is the probability that neither selection was a chocolate chip cookie?.

18 . A die is rolled. Find each probability. a. P(5 or 6) b. P(at least a ) a. b. CHAPTER 9 CONICS Determine the conic represented by the following equations. Then, find all necessary information and graph the following equations.. 5 y 6. y 9. y 4. y 9 4

19 5. y y Write an equation given the following information. 7. Circle Center: (-, 4) and a point on the circle (-7, 5) Parabola Verte:(-, -4) Focus: 5, Parabola Verte: (, ) Directri: Ellipse Vertices: (4, ) (4, -8) Co-vertices: (, -) (7, -) 0.. Hyperbola Vertices: (-4, ) (-4, 7) Foci: (-4, ) (-4, 9).

20 Identify the vertices, foci, co-vertices, and directri from the graph if they eist.. y y V F CV d. V F CV d 4 y y 5 4. V F CV d 5. V F CV d Without graphing, identify the conic from the equation. y y y 9. y