Math2UU3*TEST2. Duration of Test: 60 minutes McMaster University, 16 October Last name (PLEASE PRINT): First name (PLEASE PRINT): Student No.

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1 Math2UU3*TEST2 Day Class Duration of Test: 60 minutes McMaster University, 16 October 2018 Dr M. Lovrić Last name (PLEASE PRINT): First name (PLEASE PRINT): This test has 8 pages. Calculators allowed: Casio fx991ms or fx991ms PLUS, or similar (i.e., two lines of display and no graphing capabilities). If some piece of information is missing, you must decide on its value. 1. Circle ONE answer, or fill in the blank. No justification is needed. (a)[2] Which of the following numbers is the largest, when converted to a decimal number? (A) (10000) 8 (B) (10000) 12 (C) (1000) 16 (D) (1; 0; 0; 0) 20 (b)[2] You are counting in base 24, starting from (22; 23; 23) 24. What is the next number? (A) (23; 23; 23) 24 (B) (22; 23; 0) 24 (C) (23; 0; 0) 24 (D) (22; 0; 0) 24 1

2 (c)[2] Given two positive numbers A and B, with A larger than B, you compute their average C =(A + B)/2. Then you are told that the weighted average of A and B is smaller than C. What can you conclude about the weights that were used? (A) The weight corresponding to A is larger than the weight corresponding to B (B) The weight corresponding to A is equal to the weight corresponding to B (C) The weight corresponding to A is smaller than the weight corresponding to B Questions (d) and (e) refer to TD Bank exchange rates (one is the buy rate, and the other is the sell rate) for Canadian Dollar, on 10 October (d)[2] Euro (EUR) is stronger than Canadian Dollar. Which statement is correct? (Note: 1/ = and 1/ = ) (A) I need $ Canadian to buy 100 EUR. (B) I need EUR to buy $ 100 Canadian. (C) I need $ Canadian to buy 100 EUR. (D) I need $ Canadian to buy 100 EUR. (e)[2] British Pound (GBP) is stronger than Canadian Dollar. If I convert $ 250 Canadian to GBP, I will receive $. pounds (work with full precision of your calculator and at the end round off to the nearest pence/ penny; there are 100 pence/pennies to the pound). 2

3 (f)[2] The average growth rate of human hair is about 1.25 centimetres per month. The average rate of growth of human nails is about 0.1 millimetres per day. (These are averages; actual growth rates depend upon age, gender, season, exercise level, diet, and hereditary factors.) (A) Human hair grows faster than human nails. (B) Human hair grows slower than human nails. (C) Human hair and human nails grow approximately at the same rate. (g)[2] In base 16, find (3F 0B) 16 +(4C7) 16. (Your answer should be a base 16 number; usual convention: A = 10,B = 11,C = 12,D = 13,E = 14,F = 15.) ( ) 16 (h)[2] A density of A kg/m 3 bas been converted to B g/cm 3. Select a correct statement. (A) A is 100 times larger than B (B) A is 1,000 times larger than B (C) A is 10,000 times larger than B (D) B is 100 times larger than A (E) B is 1,000 times larger than A (F) B is 10,000 times larger than A 3

4 2. Maya astronomers created the long calendar, which counted the number of days from what they believed was the day of the creation of the world in its current form (estimated to be some time in August 3114 BCE). They used the following units of time: one uinal is 20 days (or kins), one tun is 18 uinals, one katun is 20 tuns, and one baktun is 20 katuns. Example: they recorded their dates in the form , representing 11 baktuns, 3 katuns, 12 tuns, 16 uinals and 9 days (kins). (a)[2] In Maya calendar, today s date (16 October 2018) is recorded as How many days have expired from the creation of the world (according to Maya) until today? (b) [2] The long calendar date falls on Tuesday. What is the long calendar date for the Tuesday of the following week (i.e., a week later)? 4

5 3. (a)[3] You have A dollars. Consider the following two options: (A): A is increased by 15%, and then the new amount is further increased by 15%. (B): A is increased by 32%. Which option yields a larger value? Support you answer with a calculation. (b)[2] You are buying a book which is priced at A dollars. Consider two options: (A): A is discounted by 15%, and then 13% taxes are added to the discounted price. (B): 13% taxes are added to A, and then 15% of that new amount is taken off. Show that no matter what option is chosen, you will pay the same amount for the book. 5

6 4. In (a) and (b), work with the full precision of your calculator, and then round off as requested. For (a), use the currency exchange rates from question 1(d). (a)[2] Using $ 1000 US, buy Canadian Dollars; then, with those Canadian Dollars, buy Euro. How many Euro will you get? Round off to the nearest cent (there are 100 cents in one Euro). (b)[2] Euro is stronger than US Dollar. On Bank of America website, you found the exchange (buy and sell) rates to be and Using the appropriate exchange rate, determine how many Euro you can buy for $ 1000 US. Round off to the nearest cent (there are 100 cents in one Euro). (c)[2] You can do this one even without answering (a) and (b). Which option, (a) or (b), yields more Euro? Why? 6

7 5. According to US Geological Survey data the total volume of water in oceans, seas and bays is 1,338,000,000 cubic kilometres, and that is 96.54% of total water on Earth (the remaining water is freshwater). (a)[2] Express the total volume of water in oceans, seas and bays in litres. Use scientific notation, round off to three decimal places. (b)[3] Find the total volume of freshwater in litres. Use scientific notation, round off to one decimal place. 7

8 6. [4] In Chapman, A. D. (2009). Numbers of Living Species in Australia and the World (2nd ed.). Canberra: Australian Biological Resources Study. pp ISBN we find global estimates on the number of species (described and undescribed) by group: chordates (80,500) plants (390,800) fungi (1,500,000) invertebrates (6,755,830) You have to cut a 1 metre stick into four pieces (representing the four groups) in such a way that the length of each piece is proportional to the size of the group it represents. Find the lengths of the four pieces in millimetres (round off to the nearest millimetre; so your answer should consist of integer values, giving the lengths of the four pieces in millimetres). 8 THE END