LA016790_Assn9_6493MG_Ed2.doc Mathematics General LA016790 - ASSIGNMENT 9 Before doing this assignment you need to work through Chapters 6 and 12 of your textbook: New Century 12 Mathematics General 2 HSC Course, 3rd Edition Klass Bootsma, Sarah Hamper, Margaret Willard, Robert Yen (see your OLS for more details) The following topics are covered in this assignment: · Water Usage Content summary FSRe 1 Water availability and usage FSRe 2 Dams, land and catchment areas · Energy and sustainability Content summary FSRe 3 Energy and sustainability The following outcomes are addressed in this assignment: MG2H-1, MG2H-2, MG2H-3, MG2H-4, MG2H-5, MG2H-7, MG2H-9, MG2H-10 You can refer to your OLS for more details about the outcomes addressed. ASSIGNMENT 9 Before doing this assignment you need to work through Chapters 6 and 12 of your textbook. Do the questions on your own paper. Leave space for your teacher’s comments. Show all necessary working. ______________________________________________________________________ SECTION A : Water Usage 1. The table below shows the annual rainfall (to the nearest mm) of seven places around the Sydney area. SYDNEY AIRPORT AMO 123 RANDWICK BOWLING CLUB 350 AVALON (WOLLSTONECRAFT AVE) 282 SANS SOUCI (PUBLIC SCHOOL) 268 TERREY HILLS AWS 146 SYDNEY (OBSERVATORY HILL) 316 STRATHFIELD GOLF CLUB 233 (Reference: Bureau of Meteorology) a) Using the above data find the: i) mean annual rainfall ii) median annual rainfall iii) range of rainfall in these seven places iv) interquartile range of rainfall in these seven places b) Are your results from part a) representative of the greater Sydney metropolitan area? Justify your answer. (You may need to refer to a map) c) Construct a column graph illustrating the annual rainfall of each place. (On the graph, use only initial letters for place names, so Strathfield Golf Club would appear SGC) 2. In the Ambrose household there are five people. Each person has a shower each day and uses 110 L of water per shower. Water costs $2.57 per kilolitre (kL). It is decided to install a water-efficient showerhead that uses 60% less water. How much will the family save on water costs per year? 3. The aerial picture below shows two swimming pools at the University of California, San Diego. (Reference: Google earth: Canyonview Pools, La Jolla) a) The pool marked with a cross (X) is 50 m in length. Using this information, calculate a scale for the aerial photograph. b) What is the actual area of the aerial photograph? (Answer to the nearest square metre.) 4. The table below shows the full volume of some dams, in gigalitres. Dam Capacity (GL) Dartmouth 3907.95 Hume 3038 Blowering 1631.41 Copeton 1361.72 Wyangala 1220 Burrendong 1188 Burrinjuck 1026 (Reference: waterinfo.nsw.gov.au) a) How many more megalitres does Wyangala hold than Burrinjuck? b) How many times is Dartmouth dam larger than Burrinjuck dam? Write your answer correct to one decimal place. c) What percentage (correct to one decimal place) of the capacity of Dartmouth dam is the capacity of Hume dam? 5. The dimensions of a flat rectangular roof are 12m by 8m. 15mm of rain fell. Calculate how many litres of water fell on the roof. 6. The equally spaced cross-sectional areas of a water reservoir are shown. (Reference: Board of Studies Specimen Paper) Using Simpson’s rule twice, find the approximate volume of the reservoir. SECTION B: Energy and sustainability 7. Convert 2 478 000 mW to kW. 8. A rectangular room of length 6 metres has six 18 W LED lights. What is the maximum width of the room if the lamp power density requirement of 5 W/m2 is to be met? 9. Australians use their televisions more than any other household electronic goods. For purposes of establishing a TV Energy Rating, Energy Star assumes that the average television will be in operation for 10 hours per day. (Reference: http://ee.ret.gov.au/energy-efficiency/appliances-and-equipment/televisions) Above are two labels relating to the energy efficiency of two televisions. a) Determine the yearly running cost of each television if the average rate for electricity is $0.17 per kWh. b) How much money was saved by running the energy efficient model compared to the other one? (Reference: www.energymadeeasy.gov.au) 10. Refer to the electricity bill on the previous page. a) When was this electricity account issued? b) What is the due date? c) What is the amount due? d) How much would you pay if you paid the bill by 24 August 2012? e) What is the saving if you pay your bill early? f) Calculate this saving as a percentage of the full amount due. Answer correct to two decimal places. 11. A 2.0 kW solar power system in Sydney generates 7.8 kWh of power per day. The same solar power system generates 10.0 kWh of power per day in Alice Springs. Determine the percentage gain in energy generated by placing the 2.0 kW solar power system in Alice Springs rather than in Sydney. Please send your completed assignment to OTEN. See your OLS for details. 8 LA016790 Assignment 9; 6493MG Mathematics General (Pathway 2) HSC Course Ed 2 © New South Wales Technical and Further Education Commission, 2013 (TAFE NSW – WSI), Version 1, November 2013 LA016790 Assignment 9; 6493MG Mathematics General (Pathway 2) HSC Course Ed 2 7 © New South Wales Technical and Further Education Commission, 2013 (TAFE NSW – WSI), Version 1, November 2013 LA016791_Assn10_6493MG_Ed2.doc Mathematics General LA016791 - ASSIGNMENT 10 Before doing this assignment you need to work through Chapter 8 of your textbook: New Century 12 Mathematics General 2 HSC Course, 3rd Edition Klass Bootsma, Sarah Hamper, Margaret Willard, Robert Yen (see your OLS for more details) · Mathematics and Health (Focus Study) Content summary FSHe1 Body Measurements FSHe2 Medication FSHe3 Life expectancy The following outcomes are addressed in this assignment: Outcomes addressed MG2H-1, MG2H-2, MG2H-3, MG2H-5, MG2H-7, MG2H-9, MG2H-10 You can refer to your OLS for more details about the outcomes addressed. ASSIGNMENT 10 Before doing this assignment you need to work through Chapter 8 of your textbook. Do the questions on your own paper. Leave space for your teacher’s comments. Show all necessary working. ____________________________________________________________________ 1. The QE2 Cruise ship is 293.52 metres long, 32.07 metres wide and 52.1 metres high. The average adult cubit is 46 cm. (Note: a cubit is the length of the forearm from the elbow to the tip of the middle finger) (a) Convert the QE2’s length to cubits. (b) The value of a cubit has changed over the years. In ancient times a cubit was 52.9 cm. Today a cubit is 46 cm. Write the difference in these two measurements as a percentage of the ancient cubit. 2. Which graph shows a correlation of approximately r = - 0.9? (A) (B) (B) (D) 3. The dosage rate of Amoxycillin for children is 45 mg/kg per day. How much Amoxycillin is in a single dose for a child taking four doses per day and weighing 24 kg? 4. The recommended dietary intake of protein is 0.75 g/kg for adult women. Calculate the amount of salmon a 65 kg woman would need to eat for her recommended dietary intake of protein. Use 100 g of salmon = 26 grams protein. 5. Ten Year 12 students were measured with the following results: Full Height (x) 169 187 160 172 156 172 182 161 175 170 Belly button height (y) 100 107 98 107 100 104 112 97 110 110 (a) Calculate the mean and population standard deviation for both the full height(x) and the belly button height(y). Give your answers to 2 decimal places, where necessary. (b) The least squares line of best fit has a correlation coefficient of r = 0.77 (2dp). Find the equation of the least squares line of best fit. (c) Use your equation to estimate the full height of a student whose belly button height is 108 cm. 6. A patient’s intravenous tube is checked at 4 pm, exactly 2 hours after it was started. 300 mL of the 1.5 L bag has gone through during this time. (a) The bag contains 5% dextrose. How many mL of dextrose was administered between 2 and 4 pm? (b) Assuming the drip rate had not been adjusted since 2 pm, calculate the drip rate in drops per minute. Use 1 mL = 20 drops. 7. Refer to the Life Expectancy tables for the top 15 and the bottom 15 countries (2005 – 2010) in the Health and Medicine Chapter of your textbook. (Chapter 8, Section 8:07) (a) According to the table, how long would a Japanese baby girl born in 2009 be expected to live? (b) The table shows that in the top 15 countries, women tend to live longer than men by quite a few years whereas in the bottom 15 countries, the gap between male and female life expectancies is different. Name three countries where women would not be expected to live longer than men. (c) In what year would a Somalian baby boy born in 2010 be expected to die? (d) Why can’t a current Australian HSC student predict their life expectancy from this table? 8. Use Fried’s rule to calculate the correct dosage of anti-histamine for a one and a half year old infant where the adult dose is 50 mg. 9. Refer to the running rates and pulse rates data in the table in chapter 4 Section 4:10 of your textbook for this question. (a) Produce a scatter plot (for the first 15 people only) of the Pulse Before (horizontal axis) and the Pulse After (vertical axis). Graph paper is included at the end of the assignment. (b) By referring to your scatter plot comment on the correlation, if any, of this bivariate data. 10. A father taking his family on a cruise brought No More Sick tablets in case of seasickness. No More Sick Medication Use the information shown above to answer the following: (a) The 9 year old daughter gets motion sickness so he decided to give her a dose of No More Sick before they started their cruise. If they were leaving at 7:30 am, what is the latest time he can give his daughter the first dose to prevent seasickness? (b) How much No More Sick should he give her? (c) At what time should he give his daughter the next dose? (d) Meanwhile, an hour after setting sail, the father’s 1 year old son appears to be seasick. How much No More Sick should be administered to the son? Please send your completed assignment to OTEN. See your OLS for details. To be used for Question 9 (a) (Remember to attach this to your assignment)