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# Pre-Cal 40S Slides June 8, 2007

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Exam rehearsal problems for Logarithms and Exponents, Probability and Trig Identities.

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### Pre-Cal 40S Slides June 8, 2007

1. 1. Logarithms and Exponents Pre-Test
2. 2. The Department of Health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing exponentially at an annual rate of 9%. The first year that statistics were collected, 5000 cases were reported. (a) Calulate the approximate number cases reported after 7 years. (b) How many years will it take for the number of reported cases to rise to 11 000?
3. 3. Probability Pre-Test
4. 4. A certain soccer player has scored on 82% of his penalty kicks throughout his career. Given this information, the probability that he will score on exactly 4 of his next 5 penalty kicks, correct to the nearest hundredth, is: (a) 0.80 (b) 0.66 (c) 0.41 (d) 0.08
5. 5. If and P(A and B) = , where A and B are dependant events, then equals: (a) (b) (c) (d)
6. 6. Peter places 5 equal-sized tiles in a cloth bag. Each tile has a letter on it. The letters are P, E, T, E and R. The probability that Peter selects the 5 tiles, one at a time, in order such that they spell PETER, correct to the nearest hundredth, is:
7. 7. A child has 2 quarters, 2 dimes, and 3 nickels in his pocket, but he does not understand the value of any of the coins. He puts 35¢ worth of candy on the counter at a store and randomly selects two coins from his pocket. The probability that the two coins he selects will have a total value at least as high as the value of the candy is:
8. 8. It is known that 53% of graduating students are boys. Three grads are chosen at random. Given that at least two of the three grads are boys, determine the probability that all three of the grads are boys. (Answer accurate to at least 4 decimal places.)
9. 9. Trigonometric Identities Pre-Test
10. 10. The expression is equivalent to: (a) (b) (c) (d) 0
11. 11. If and , and A and B are acute angles, what is the value of ? (a) (b) (c) (d)
12. 12. Find all values of x in the interval 0 ≤ x < 2π that satisfy the equation:
13. 13. If , what is the value of:
14. 14. Prove the identity: