Math2UU3*TEST2. Questions (c) and (d) refer to buy and sell rates from Bank of Montreal.

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1 Math2UU3*TEST2 Day Class Duration of Test: 60 minutes McMaster University, 24 October 2017 Name (PLEASE PRINT): Dr M. Lovrić This test has 6 pages, 40 points maximum. Calculators allowed: Casio fx991ms or fx991ms PLUS, or similar (i.e., no graphing capabilities). If some piece of information is missing, you must decide on its value. Notation: Recall that (A) n denotes number A written in base n. 1. Circle ONE answer, or fill in the blank. No justification is needed. (a)[2] Which of the numbers (32123) 8, (32123) 12, (32123) 16, and (3; 2; 1; 2; 3) 20 is the largest, when converted to a decimal number? (A) (32123) 8 (B) (32123) 12 (C) (32123) 16 (D) (3; 2; 1; 2; 3) 20 (b)[2] You are counting in base 60, starting from (48; 59; 59) 60. What is the next number? (A) (49; 59; 59) 60 (B) (48; 59; 0) 60 (C) (49; 0; 0) 60 (D) (48; 0; 0) 60 Questions (c) and (d) refer to buy and sell rates from Bank of Montreal. (c)[2] New Zealand Dollar (NZD) is weaker than Canadian dollar. correct? (Note: 1/ = and 1/ = ) (A) I need $ Canadian to buy 100 NZD. (B) I need 106 NZD to buy $ 100 Canadian. (C) I need $ 106 Canadian to buy 100 NZD. (D) I need $ Canadian to buy 100 NZD. Which statement is (d)[2] I m travelling to Netherlands. I need $. Canadian to buy 150 Euro. 1

2 (e)[2] Amount A is increased by 22%. The obtained amount is discounted by 11%, and the resulting amount is discounted again by 11%, to obtain amount B. (A) A is larger than B (B) A is smaller than B (C) A is equal to B (D) A could be larger or smaller than B, it depends on the value of A (f)[2] A is proportional to the square of some quantity B. What change (scaling) in B caused a 9-fold increase in A? (A) 2B (B) 3B (C) 9B (D) 1.73B (E) 1.41B (g)[2] Consider the following data set, and select a correct statement. (A) By extrapolation, we could estimate the population of Canada in 2008 (B) The line of regression has negative slope, i.e., slopes downward (C) In the interval from 1991 to 2016, Canadian population increased linearly (D) The smallest marginal change occurred between 2006 and 2011 (h)[2] A density of A g/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 10,000 times larger than B (C) A is 1,000,000 times larger than B (A) B is 100 times larger than A (B) B is 10,000 times larger than A (C) B is 1,000,000 times larger than A 2

3 2. (a)[2] In base 16, find (ABCD) 16 +(DC34) 16. (Your answer should be a base 16 number; usual convention: A = 10,B = 11,C = 12,D = 13,E = 14,F = 15.) (b)[2] Find (44; 59; 59) 60 + (11; 45; 11; 17) 60 ; express your answer as a base 60 number. (c)[2] You are Mayan astronomer, and figured out that today s date is (15; 17; 19; 19; 19) 20. Today is Tuesday. What date corresponds to Tuesday of the next week? Write your answer as a base 20 number. (d)[1] Convert ( ) 2 intoadecimalnumber (e)[1] Convert (18) 10 (i.e., the decimal number 18) into a base 2 number. 3

4 3. (a)[3] You are buying an item that costs A dollars, and have a coupon for 20% off. You would like to apply the coupon first, and then pay the 13% HST. However, the salesperson applies the 13% HST first, and then reduces the price by 20%. Will you end up paying more, i.e., what is the relation between the two options? Justify your answer (b)[2] You are booking a room in Vancouver s Lonsdale Quay Hotel. Hotels.com offers a room for the base price of $213. However, on top of it, you have to pay 5% GST, accommodation tax of 8%, hotel tax of 2%, and a destination tax of 1.5%. All of these taxes are applied to the base price of the room. What will your total bill be for one night? Round off to the nearest cent. 4

5 4. Current world population is about 7.48 billion people. (a)[2] Assume that all people on Earth jump into Lake Ontario at the same time. How crowded would it be, i.e., how much space (in m 2 ) would each person have? (Wikipedia: surface area of Lake Ontario is 18,960 km 2 ). Round off to two decimal places. (b)[1] According to Wikipedia article Biomass (Ecology) the average mass of a human (including children) is 50 kg. Find the total human biomass (i.e., the total mass of all humans of Earth) in kilograms. (c)[1] Assume that the density of a human is kg/cm 3 (as we are mostly water, and water has the density of kg/cm 3 ). Convert this density to kg/m 3. (d)[2] Find the total volume of the human biomass in m 3. (Recall that volume is mass divided by density.) 5

6 5. Read the following excerpt from the Globe and Mail article Eating out is the top financial indulgence for most Canadians and answer the questions on this page. (a)[1] What is the relative (to 1998) change in Canadian population between 1998 and today? Does it agree with the claim in the article? Express your answer as percent, and round off to one decimal place. (b)[2] Show how the calculation that lead to the conclusion nearly 120 percent increase was done. (c)[2] Assuming that the restaurants sales continue to increase linearly, extrapolate the given data to predict the sales in THE END