In questions 1-4, note that ln() represents the natural logarithm (logarithm to the base e) of the expression inside of the parentheses. Below, expand each of the expressions on the right side of the equal sign into simplest algebraic form.

1) z = ln 4x 1y

2) z = ln 4(1x) y 3

3) z = ln(e 4y 2 )

4) z = ln 1 81x 2y 4w16 !

5) True or False: ln x y = ln(x) ln(y) 16)

Express the following exponential term in the form of a product of three terms. z = e 4y 2+3x 4+6w 9

7) Reduce the following expression to simplest form. z = 12 5 3

8) Reduce the following expression to simplest form. z = 86/12 14/18

9) Reduce the following expression to simplest form. z = 2 8 2 8+ 1 16

10) Let sets A and B have the following integers as elements A = {0, 14, 24, 6}, B = {0, 11, 3, 85}. Let C = A B, where is the union of the two sets. Find C.

11) Let sets A and B have the following integers as elements A = {0, 14, 24, 6}, B = {0, 11, 3, 85}. Let C = A B, where is the intersection of the two sets. Find C.

12) Let f(x) = x 2 + 3x 4 6x 3 448. Find f(4).

13) Let g(x, y) = x y + 3x2y (x+4)2 . Find g(1, 4).

14) Let y = 12 + 5 3 x. What is the change in y for a one unit change in x?

15) Let y = 2x 3. What is the value of y when x = 0? 2

For questions 16-20, use the following information. A clinical trial was conducted to test the efficacy of a new treatment for ulcer healing vs. placebo. 200 subjects were randomly assigned to either new treatment or placebo group. Subjects were followed to assess whether their ulcer healed or not. In the sample, 40% were given the new treatment, 25% had a healed ulcer, and five-sixths of the subjects in the placebo group did not have a healed ulcer. You do not need to use probability calculations for any part of this problem. Round your answers to the nearest whole number.

16) How many people did not have a healed ulcer?

17) How many subjects in the treatment group did not have a healed ulcer?

18) How many subjects in the treatment group did have a healed ulcer?

19) What proportion of subjects in the placebo group had a healed ulcer?

20) What proportion of subjects in the treatment group had a healed ulcer?

For questions 21-23, use the following information. Suppose the two year expected mortality rate from breast cancer is 40 per 100,000 individuals.

21) In a specific community of 300,000 individuals, how many deaths are expected to be attributed to breast cancer over a one year period?

22) The actual (observed) number of deaths attributed to breast cancer in the community was 40 individuals over a one year period. What would be the observed/expected ratio for these deaths? Please reduce to the simplest form. 3

23) Of the 40 individuals that died from breast cancer, it was determined that the number of deaths from individuals who were at least 50 years old was triple the number of deaths from individuals who were under 50 years old. How many individuals under 50 died from breast cancer?

For questions 24-25, use the following information. While iodine nutrition has improved worldwide due to the existence of cost-effective prevention measures such as iodization of salt, iodine deficiency remains the leading cause of preventable brain damage in childhood. Urinary iodine is the recommended indicator for evaluating the degree of iodine deficiency, and for monitoring and evaluating its correction. Based on the current recommendations produced by the World Health Organization (WHO), United Nations Children's Fund (UNICEF) and International Council for Control of Iodine Deficiency Disorders (ICCIDD), the epidemiologic criteria for assessing iodine nutrition based on median urinary iodine concentrations in school- age children are provided in the table below.

Median Iodine Iodine Intake Iodine Nutrition Status < 20 Insufficient Severe deficiency 20-49 Insufficient Moderate deficiency 50-99 Insufficient Mild deficiency 100-199 Adequate Optimal Intake 200-299 Above Requirement Slight Risk of Overdose 300 Excessive Risk of Adverse Effects The WHO Global Database on Iodine Deficiency was developed to assess the global magnitude of iodine deficiency, to evaluate the strategies for its control and to monitor each country's progress towards achieving the international community's goal of IDD elimination. The following table provides data collected on school-age children (8-12 years old) in Lesotho in 2002. Median Iodine Number of children < 20 35 20-49 42 50-99 204 100-299 402 300 305

24) What percentage of children was not iodine deficient?

25) Since iodine is essential for making thyroid hormone, hypothyroidism may develop as the body's iodine levels fall. While this is uncommon in the United States, iodine deficiency is the most common cause of hypothyroidism worldwide. Assume that 40% of those children with iodine deficiency in this sample did not have hypothyroidism. How many children in this sample had both iodine deficiency and hypothyroidism? Round up to the largest whole number.