Logarithms and Exponents Pre-Test

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?

Probability Pre-Test

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

If and P(A and B) = , where A and B are dependant events, then
equals:
(a) (b) (c) (d)

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:

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:

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.)

Trigonometric Identities Pre-Test

The expression is equivalent to:
(a) (b) (c) (d) 0

If and , and A and B are acute angles, what is the
value of ?
(a) (b) (c) (d)

Find all values of x in the interval 0 ≤ x < 2π that satisfy the equation:

If , what is the value of:

Prove the identity: