Semester One Final Examination 2023 SCIE1100 PDF

Semester One Examinations, 2023 SCIE1100 Venue ____________________ Seat Number __________...

Semester One Examinations, 2023 SCIE1100 Venue ____________________ Seat Number __________ Student Number |__|__|__|__|__|__|__|__| Family Name ____________________ This exam paper must not be removed from the venue First Name ____________________ School of Mathematics & Physics Semester One Examinations, 2023 SCIE1100 Advanced Theory and Practice in Science (In-Person) This paper is for St Lucia Campus students. Examination Duration: 120 minutes For Examiner Use Only Planning Time: 10 minutes Question Mark Exam Conditions: Q1 This is a Closed Book examination - specified written materials permitted Q2 Casio FX82 series or UQ approved and labelled calculator only During Planning Time - Students are encouraged to review and plan responses to the exam questions Q3 This examination paper will be released to the Library Q4a-c Materials Permitted in the Exam Venue: (No electronic aids are permitted e.g. laptops, phones) Q4d One A4 sheet of handwritten or typed notes double sided is permitted Q5 Materials to be supplied to Students: Additional exam materials (e.g. answer booklets, rough paper) will be provided upon request. Total _________ None Instructions to Students: If you believe there is missing or incorrect information impacting your ability to answer any question, please state this when writing your answer. Students may detach the last page (with formula sheet) from the question paper. Page 1 of 18 Semester One Examinations, 2023 SCIE1100 Rubric The Final Exam requires students to demonstrate the ability to: Select and implement an appropriate solution methodology. Accurately calculate quantities, evaluate information, and/or convey scientific/mathematical/ philosophical/programmatic concepts. Communicate key ideas clearly, concisely, and precisely, showing a consideration for the audience of their work through an appropriate choice of communication style and terminology. Articulately synthesise information to provide a reasoned argument that is supported by appro- priate evidence or justification. The following provides a guide as to the achievement standard expected for each of these assessment criteria. Appropriate working should be shown in all cases, where relevant. Methodology (M) Score M1 A valid approach is selected that makes progress towards addressing the requirements of the question. Note: the accuracy of the results should be assessed separately. M0 Does not meet the criteria for a 1. Accuracy (A) Score A1 The response adequately and accurately addresses the requirements of the question. A0 Does not meet the criteria for a 1. Communication (C) Score C1 The expression of the key argument is clear, and the language and approach used are appropriate for the intended audience. Units are presented where appropriate. The use of any mathematical terminology and notation is rigorous. Any graphs or diagrams are clear, appropriately detailed, and adequately labelled. Does not mislead. C0 Does not meet the criteria for a 1. Reasoning (R) Score R1 A reasoned argument is presented based on the synthesis of sensible logical deductions consistent with the information provided. R0 Does not meet the criteria for a 1. These criteria may be represented in any combination. More than one mark may be assigned to a single criterion for a given question where the indicated skill is required to be demonstrated more than once. Page 2 of 18 Semester One Examinations, 2023 SCIE1100 All questions on this exam relate to the theme of water supply and pollution. All ques- tions are self-contained which means that the required information has been provided within each question. You should attempt all questions. Your solutions will be marked on the correctness and clarity of your explanation and communication according to the rubric provided on Page 2. Include units in your answer wherever relevant. Question 1. According to the United Nations World Water Development Report 2019, global water usage has increased by approximately 1% each year since the 1980s and is expected to continue to do so until 2050. In 1980 the global water usage was around 3.1 × 1012 cubic metres. (a) Assume that the global water usage, y (m3 ), can be modelled by an exponential function of the form y = Cekt , where t represents time in years since 1980. Determine the values of the constants C and k in this model. (2 marks, A1 C1) (b) Using your model from (a), determine the doubling time for global water usage. Note: You should evaluate your answer as a numerical quantity, but if you were not able to answer part (a) you can leave your answer in terms of C and/or k as appropriate. (3 marks, M1 A1 C1) (question continued over) Page 3 of 18 Semester One Examinations, 2023 SCIE1100 (c) (Advanced ) The following plot depicts global water consumption from 1980 to 2014 on log-linear axes. Explain how this plot could be used to refine the values of C and k determined in part (a). You should describe the mathematical approaches you would use but you do not have to evaluate new values of C and k. (2 marks, M1 R1) (next question over) Page 4 of 18 Semester One Examinations, 2023 SCIE1100 Question 2. Nyabadza et al. propose a system of differential equations to model the spread of the water-borne disease cholera, which is caused by the bacteria Vibrio cholerae. A simplified version of this model is given by SI SB S 0 = µN − β1 − β2 − µS, N B+k SI SB I 0 = β1 + β2 − γI − µI, N B+k R0 = γI − µR, B 0 = αI − δB, where S(t), I(t) and R(t) represent populations of susceptible, infected and recovered individuals, respectively, B(t) represents the concentration of vibrios in contaminated water measured as the number of cells per mL, and N (t) represents the total human population. The remaining parameters in this model are all positive constants, defined as follows: Natural birth/death rate, µ (day−1 ) Effective contact rate between individuals, β1 (day−1 ) Per capita contact rate for humans and the contaminated environment, β2 (day−1 ) Half saturation constant, k (mL−1 ) Per capita recovery rate, γ (day−1 ) Per-capita shedding rate, α (mL−1 · day−1 ) Bacterial net death rate, δ (day−1 ) (a) Cholera can be spread by both human-to-human transmission or through the ingestion of contam- inated water. Explain how this is accounted for in the model. (2 marks, A2) (question continued over) Page 5 of 18 Semester One Examinations, 2023 SCIE1100 (b) Show mathematically that the total human population remains constant over time. Your answer should make reference to the system of differential equations. (2 marks, M1 A1) (c) Explain, making reference to the scientific context, why the human population remains constant over time. (1 mark, A1) (question continued over) Page 6 of 18 Semester One Examinations, 2023 SCIE1100 (d) (Advanced ) In the model, recovered individuals gain permanent immunity to cholera. Explain how you would change the model to account for immunity that wanes over time. Justify your answer making reference to the system of differential equations. (2 marks, M1 R1) (next question over) Page 7 of 18 Semester One Examinations, 2023 SCIE1100 Question 3. The gold standard test for cholera diagnosis requires laboratory facilities and takes upwards of 24 hours. If these resources are not readily available, a rapid in situ diagnostic test can be used as an alternative. Ley et al. (2012) conducted a case study in Zanzibar to examine the effectiveness of one such rapid diagnostic test. Their results can be summarised as follows: There were 622 patients who participated in the study. The rapid diagnostic test returned 402 positive results and 220 negative results. The gold standard test confirmed 203 patients had cholera and 419 patients did not have cholera. The sensitivity of the rapid test was 93.1% and the specificity of the rapid test was 49.2%. Infection is often mild or asymptomatic, but approximately 1 in 10 people with cholera experience severe symptoms which can quickly lead to death if untreated. The primary treatment for cholera is oral or intravenous hydration. Severe cases may also be administered antibiotics. (a) Create a binary classification table for the rapid diagnostic test, showing all working. (4 marks, M2 A2) (question continued over) Page 8 of 18 Semester One Examinations, 2023 SCIE1100 (b) In diagnostic testing, the positive predictive value (PPV) is the probability that a patient with a positive test result actually has the disease. Calculate the positive predictive value of the rapid diagnostic test. (1 mark, A1) (c) (Advanced ) What would be the public health implications of replacing the gold standard test with the rapid test? Write a brief paragraph for an audience of health care professionals which answers this question. (2 marks, R1 C1) (next question over) Page 9 of 18  Semester One Examinations, 2023 SCIE1100 Question 4. A model for the change in concentration of a pollutant in a lake, C (mg·L−1 ), over time t (years), is given by F F C 0 = cin − C, V V where F represents the flow rate of water into and out of the lake (L·year−1 ), V is the volume of the lake (L), and cin is the concentration of the pollutant in the water flowing into the lake (mg·L−1 ). Consider a scenario where the flow rate of water into and out of the lake varies on a seasonal basis. All other parameters will remain constant. The flow rate is greatest in the middle of January and a minimum in the middle of July, when it gets as low as 0 L·year−1. The average flow rate is 2 × 106 L·year−1. (a) Write down a model for the flow rate in the form F (t) = A sin( 2π P (t − S)) + E. You should evaluate the constants, justifying your choices. (3 marks, M1 A1 C1) Consider the following code (note that the commenting in the provided program is intentionally sparse): 1 from pylab import * 2 3 # Set time parameters 4 maxt = 30 5 stepsize = 0.1 6 7 # Gather information from user 8 initial_condition = float(input("Enter the initial concentration of pollutant:")) 9 A = float(input("Enter your value for A:")) 10 P = float(input("Enter your value for P:")) Page 10 of 18  Semester One Examinations, 2023 SCIE1100 11 S = float(input("Enter your value for S:")) 12 E = float(input("Enter your value for E:")) 13 14 times = arange(0, maxt+stepsize, stepsize) 15 times_length = size(times) 16 Cpops = zeros(int(times_length)) 17 Cpops = initial_condition 18 19 # Set remaining parameters 20 V = 5*10**6 # Volume of lake in L 21 c_in = 0 # Assume water flowing into the lake is clean (unpolluted) 22 23 # Apply numerical method 24 for i in range(0,times_length-1): 25 F = A*sin((2*pi/P)*(times[i]-S))+E 26 dC = F/V*c_in-F/V*Cpops[i] 27 Cpops[i+1] = Cpops[i] + stepsize*dC 28 29 # Output graph 30 plot(times, Cpops, "b-", linewidth=3) 31 grid(True) 32 show() (b) Line 23 of the code contains a comment referring to a numerical method. What is the numerical method that is being implemented in the code? (1 mark, A1) (c) Consider line 24 of the code. If times_length-1 was replaced with times_length, would the program still run correctly? Explain why/why not. (1 mark, A1) (question continued over) Page 11 of 18 Semester One Examinations, 2023 SCIE1100 (d) (Advanced ) In the Philosophy of Science module, we discussed a special challenge to the idea that models can be inductively inferred from data. Explain this challenge. In doing so, reference what a model is, what inductivism is and the model described in part (a). (2 marks, R2) (next question over) Page 12 of 18 Semester One Examinations, 2023 SCIE1100 Question 5. Consider the following outline of a hypothetical oil spill, similar to what might be obtained through satellite imagery or aerial photography in the event of a real spill. (a) Using any appropriate method discussed in SCIE1000, produce a rough estimate of the surface area of the oil spill giving your answer in square kilometres. (2 marks, M1 A1) (question continued over) Page 13 of 18 Semester One Examinations, 2023 SCIE1100 (b) Consider a plot depicting a model of the width of the oil spill vs. horizontal distance as shown below. Using the indicated measurements, apply the trapezoidal rule to estimate the surface area of the oil spill in square kilometres. (2 marks, M1 A1) (c) Is your answer to part (b) likely to be an overestimate or underestimate of the modelled surface area? Explain. (1 mark, R1) (question continued over) Page 14 of 18 Semester One Examinations, 2023 SCIE1100 When examining aerial images of oil spills, it is sometimes possible to estimate the thickness of the oil spill based on the colour and sheen of the oil, as summarised in the table below. Colour Thickness (µm) Silver 0.04–0.3 Rainbow 0.3–5.0 Metallic 5.0–50 Transitional Dark 50–200 Dark 200-10000 (d) (Advanced ) Suppose that the hypothetical oil spill in this question has a total volume of 360 m3. According to the table provided, what colour would you expect this oil spill to have? Record any assumptions that you make in your answer. (2 marks, M1 R1) END OF EXAMINATION Page 15 of 18 Semester One Examinations, 2023 SCIE1100 This page can be used if you need extra space to answer any of the questions. Clearly indicate the question(s) that you are answering. Ensure that you also put a note within the body of the relevant question(s) directing the marker here. (References over...) Page 16 of 18 Semester One Examinations, 2023 SCIE1100 References WWAP (UNESCO World Water Assessment Programme). (2019). The United Nations World Water Development Report 2019: Leaving No One Behind. Paris, UNESCO. Ritchie, H. and Roser, M. (2017). Water Use and Stress. Our World In Data. Retrieved April 4, 2023 from https://ourworldindata.org/water-use-stress. Nyabadza, F., Aduamah, J. M., & Mushanyu, J. (2019). Modelling cholera transmission dynamics in the presence of limited resources. BMC research notes, 12(1), 475. https://doi.org/10.1186/ s13104-019-4504-9. Ley, B., Khatib, A. M., Thriemer, K., von Seidlein, L., Deen, J., Mukhopadyay, A., Chang, N. Y., Hashim, R., Schmied, W., Busch, C. J., Reyburn, R., Wierzba, T., Clemens, J. D., Wilfing, H., Enwere, G., Aguado, T., Jiddawi, M. S., Sack, D., & Ali, S. M. (2012). Evaluation of a rapid dipstick (Crystal VC) for the diagnosis of cholera in Zanzibar and a comparison with previous studies. PloS one, 7(5), e36930. https://doi.org/10.1371/journal.pone.0036930. Centers for Disease Control and Prevention. (2022). Cholera - Vibrio cholerae infection. Retrieved March 31, 2023 from https://www.cdc.gov/cholera/. National Oceanic and Atmospheric Administration. (2016). Open water oil identification job aid for aerial observation. Retrieved April 19, 2023 from https://response.restoration.noaa.gov/ sites/default/files/OWJA_2016.pdf. (Formula sheet over...) Page 17 of 18 Semester One Examinations, 2023 SCIE1100 Formula Sheet Multiple Prefix Symbol Multiple Prefix Symbol 101 deca da 10−1 deci d Base quantity SI unit name Symbol 102 hecto h 10−2 centi c length metre m 103 kilo k 10−3 milli m mass kilogram kg 106 mega M 10−6 micro µ time second s 109 giga G 10−9 nano n electric current ampere A 1012 tera T 10−12 pico p thermodynamic temperature kelvin K amount of substance mole mol 1015 peta P 10−15 femto f luminous intensity candela cd 1018 exa E 10−18 atto a 1021 zetta Z 10−21 zepto z 1024 yotta Y 10−24 yocto y Quantity Name Symbol SI units SI base units frequency hertz Hz - s−1 force newton N - m · kg · s−2 pressure, stress pascal Pa N · m−2 m−1 · kg · s−2 energy, work, quantity of heat joule J N·m m2 · kg · s−2 power, radiant flux watt W J · s−1 m2 · kg · s−3 electric potential difference, electromotive force volt V W · A−1 m2 · kg · s−3 · A−1 ◦ Celsius temperature degree Celsius C - K function type general form linear y = mx + c Newton’s method xi+1 = xi − ff0(x i) (xi ) quadratic y = ax2 + bx + c power y = axp Trapezoid rule Atrap = (x2 − x1 )( y1 +y 2 ) 2 periodic y= A sin( 2π P (t − S)) + E exponential y = Ce kt Euler’s method ti+1 = ti + h yi+1 = yi + hyi0 surge y = atp e−bt True Status Yes No Lotka-Volterra model Test Positive A B Q0 = aQ − bP Q Test Negative C D P 0 = −cP + dP Q N =A+B+C +D A+D SIR model accuracy = N S A S 0 = −a I sensitivity = N A+C S I0 = a I − bI D N specificity = 0 B+D R = bI Page 18 of 18