Alg 2/Trig Honors Qtr 3 Review

Transcription

1 Alg 2/Trig Honors Qtr 3 Review Chapter 5 Exponents and Logs 1) Graph: a. y 3x b. y log3 x c. y log2(x 2) d. y 2x 1 3 2) Solve each equation. Find a common base!! a) 52n b) 42x 8x 1 c) 27x 9x 6 3) Write the equation in logarithmic form: 27 = 128 4) Write the equation in exponential form: log5125 = 3 5) Simplify: log8 x 4 a. 8 b. log8 log9 log7 343 c. log6 363x 1

2 6) Evaluate each logarithm. a) log2x = 5 b) logx64 = 3 c) log3243 = x 7) Evaluate each logarithm. Round to 3 decimal places. a) log12 63 b) log ) Use log2 = a log3 = b and log7 = c to simplify the following expressions to variables and constants a) log 42 b) log 14 c) log ) Solve each equation. Round answers to 3 decimal places if needed. a) 5(3)x b) 6log2(13 x ) 27 e) log (x + 3) + log x = 1 h) e x 5 2 f) log (5 2x) = log (3x + 1) c) 83x+5 = 59 h) ln x 6 ln x 1

3 10) Write each expression as a single logarithm. a) log312 + log36 b) log28 log24 c) 3log52 + log54 2log52 11) Radioactive gold used in imaging the structure of the liver has a half-life of 2.67 days. If we start with 50 milligrams of gold, how many milligrams will be left after 1 week? 12) You invest $5,000 into an account that pays 1.7% interest per year compounded daily. How much money will you have made on the initial amount if you keep it there for 15 years? (assuming you do not add more to the account). 13) Simplify: a) 5 36 x7 y11 c) 64 b) d) 6mn m n e) 8a 2b-3 27a b 4 3

4 Chapter 11 Probability 14. A card is drawn from a normal 52 card deck. Find: a. P(the card is a five or a six) b. P(the card is between five and ten) c. P (the card is a king or a diamond) 15. You throw a pair of dice one red, the other black a. P(the sum is at least three) b. P(the sum is between three and eleven, inclusive) c. P(the red die is a three or the black die is a four) 16. Using the letters in the word COMPUTER a. In how many ways could you pick a vowel and then a consonant? b. In how many ways could you pick a consonant or a vowel? c. In how many ways could you select a vowel and then another vowel? d. How many different four-letter words could you make using no letter more than once? e. How many different four-letter words could you make with repetition of the letters allowed? 17. How many different words can be formed using all of the letters in PROBABILITY? 18. Simplify: a) 7 C5 b) 8 P3 c) ( x 2)! x! 19. How many ways can 8 people sit around a table? 20. If six people compete for a medal at the Olympics, how many ways can three people be chosen to win the gold, silver and bronze medals?

5 21. How many ways can 12 preschoolers be arranged in a line for their class pictures, if the Smith triplets must stand next to each other? 22. Four students are selected from a home economics class of 16 students to form a committee to advise the cafeteria director about food. How many different committees can be formed? 23. How many 9-digit social security numbers are there if the first number cannot be Find the mathematical expectation and determine if the game is a fair game. You play 95 cents and draw a card at random from the normal deck of 52 cards. The payoffs are as follows: an ace - $2.95, a heart(but not an ace) - $1.25 and any other card nothing. 25. Derrick Rose had a free throw shooting average of.89 last season for the Chicago Bulls, which means that is probability of making at any one free throw is.89. Suppose that Derrick shoots only 3 free throws during the most recent game. Calculate the probability of each: he makes exactly 0, 1, 2, or 3 free throws. 26. An ordinary deck of playing cards is used to play a game in which you are dealt a 7 card hand. Find the probability that: a. you have exactly three red cards and four black cards b. you have the ace of hearts c. you have all spades 27. A well-known hamburger chain has 12 choices of items to put on their burgers. How many different burgers could be created by using three or four of the toppings?

6 28. A short multiple choice test has 5 questions. Each question has 4 choices, exactly one of which is right. Assume that you are not experienced in the subject, so you guess randomly to choose the answers. a. What is the probability of guessing any one answer right? Wrong? b. Calculate the probability of guessing 0,1,2,4, or 5 answers correct. c. You will pass the test is you get 4 answers right. What is the probability of passing? Chapter 11 Series and Sequences Write a general term for the following sequence:,,,, In a given arithmetic sequence, a3 8 and a Find: a. a22 b. S Evaluate: 6n 5 k Write this series using summation notation: Evaluate: 24 3 k k