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Complete the attached worksheet of 25 questions. Show the work for each question.
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PubH 6002: Biostatistical Applications for Public Health
Spring 1: 2024
Math Refresher
Student Name: _________________________
Instructions: This math refresher consists of 25 problems. Work individually! You may use a
calculator. You may refer to math textbooks or online materials for assistance, but you must use
your brain only. Please do not collaborate with anyone inside or outside of this class. Your
answers should reflect individual work and not group effort. You must scan and submit this
assignment in the Assignment section of MPH@GW prior to your week 2 live session. This
assignment will be graded and is worth 5% of your final course grade. Any student who answers
5 or more problems incorrectly on the refresher should review the concepts they struggled with
via an online tutorial, textbook, or other resource. Please show all your work as partial credit
may be awarded.
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1. Reduce the following expression to a single fraction or whole number: 11 × (13).
86
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2. Reduce the following expression to a single fraction or whole number: (12)⁄(18).
3. Reduce the following expression to a single fraction or whole number:
(7⁄6)⁄(2⁄3 + 11⁄36).
4. Given ( ) = 4 3 + 2 − 2 + 18. Find (3).
5. Given ℎ( , ) = 3 3 + 2 2 − 3 + 39. Find ℎ(2, −3).
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6. Given = 3 − 3 , which is the equation of a straight line. What is the y-intercept of the
line?
7. Given = 5 − 2 , which is the equation of a straight line. What is the slope of the line?
8. Let sets A and B have the following integers as elements: A = {2, 5, 6, 25}, B = {2, 3, 10,
29}. Let = ∩ , where ∩is the intersection of the two sets. Find D.
9. Let sets A and B have the following integers as elements: A = {1, 7, 16, 25}, B = {0, 7, 14,
25}. Let = ∪ , where ∪ is the union of the two sets. Find C.
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For questions 10-12, use the following information. Two genetic variants, BRCA1 and BRCA2,
are associated with increased risk of breast and ovarian cancer in women. According to the latest
estimates by the National Cancer Institute, the prevalence of BRCA1 and BRCA2 in the general
population is approximately 1 in 400 women or 0.2%. Among a group of women considered at
high risk, the prevalence of BRCA1 or BRCA2 was found to be 2%.
10. In a specific community of 120,000 women not at increased risk, how many women are
expected to have the BRCA1 or BRCA2 gene?
11. Among a group of 240,000 women at increased risk for BRCA1 or BRCA2, the actual
(observed) number of women who were found to have the BRCA1 or BRCA2 gene was
3,600. What would be the observed/expected ratio for having BRCA1 or BRCA2? Please
reduce to the simplest form.
12. Of the 3,600 at risk women found to have the BRCA1 or BRCA2 gene, it was determined
women with the BRCA1 or BRCA2 gene who were of Norwegian descent represented triple
the number of those with the BRCA1 or BRCA2 who were not of Norwegian descent.
In this sample, how many women of Norwegian descent were found to have the BRCA1 or
BRCA2 gene?
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For questions 13-16, use the following information. Research suggests that young women
diagnosed with breast cancer may have increased risk of adverse material or fetal outcomes if
they become pregnant later in life. Further, young women with the BRCA1 or BRCA2 gene that
are diagnosed with breast cancer may receive more aggressive treatments that impact fertility.
Therefore, researchers conducted a study among 4,700 women with breast cancer where 50%
had the BRCA1 or BRCA2 gene. In the sample, 8% of women with the BRCA1 or BRCA2 gene
experienced a pregnancy complication and 90% of women without the BRCA1 or BRCA2 gene
did not experience complications during pregnancy. All women in the sample were followed
throughout their pregnancy. Note that you do not need to use probability for any part of this
problem. Round your answers to the nearest whole number.
13. How many women in this study did not experience a complication during pregnancy?
14. How many women that did not have the BRCA1 or BRCA2 gene experienced a complication
during pregnancy?
15. How many women with the BRCA1 or BRCA2 gene did not experience a complication during
pregnancy?
16. How many women in this study did not have the BRCA1 or BRCA2 gene?
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For questions 17-19, 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 schoolage children are provided in the table below.
Median Urinary Iodine (g/L)
Iodine Intake
Iodine Nutrition Status
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