Math2UU3*TEST1 Day Class Duration of Test: 60 minutes McMaster University, 25 September 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. Multiple choice questions. Circle ONE answer, no justification is needed. (a)[2] A mathematical statement that is taken for granted (i.e., without evidence) and which is used to start building a theory, is called (A) Theorem (B) Axiom (C) Definition (D) Algorithm (b)[2] The converse of James is at risk because he has high blood pressure is (A) Since James has high blood pressure, he is at risk (B) Because he has high blood pressure, James is at risk (C) If James is at risk, then it is his high blood pressure (D) James is not at risk because he does not have high blood pressure (E) None of the above 1
(c)[2] In the scientific notation, 0.43 nanometres (possible diameter of an atom) is expressed as (A) 0.43 10 9 (B) 4.3 10 8 (C) 0.43 10 8 (D) 4.3 10 9 (E) 4.3 10 10 (d)[2] The contrapositive of Drinking coffee does not lead to dehydration is (A) Drinking coffee causes dehydration (B) Drinking coffee does not cause dehydration (C) If a person is not dehydrated then they do not drink coffee (D) If a person is dehydrated then they do not drink coffee (E) None of the above (e)[2] Which one of these hard drives has the largest capacity (i.e., can store the largest amount of data)? (A) 2.4 terabytes (B) 1,568 gigabytes (C) seven billion kilobytes (D) two thousand megabytes (E) seven hundred gigabytes 2
(f)[2] When the driving distance from Hamilton to Vancouver is expressed in metres, the resulting number has the order of magnitude equal to (Hint: think! You do not have to know what exactly, not even nearly exactly, the driving distance is.) (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 (g)[2] Consider the theorem If the last digit of a number is 2, or 3, or 7, or 8, then it is not the square of some number. What can you conclude from this theorem? (A) The number 58905625 is the square of some number (B) The number 58905625 is not the square of some number (C) The number 65712893 is the square of some number (D) The number 65712893 is not the square of some number (E) None of the above (h)[2] Which of the following experiements disproves the statement If a person takes Tylenol then their headache stops. (A) A person did not take Tylenol and their headache stopped (B) A person did not take Tylenol but their headache did not stop (C) A person took Tylenol and their headache stopped (D) A person took Tylenol but their headache did not stop 3
2. (a)[2] Consider the statement (from The reports of the death of Canadas small towns have been greatly exaggerated, Macleans, 7 Sept. 2018) If your community cannot support jobs, your town will decay. Write the contrapositive of this statement. (b)[2] Consider the statement (from Air pollution killed my daughter and now I can prove it, The Guardian, 31 August 2018) Without the unlawful levels of pollution, Ella would not have died. Rewrite this statement as an implication, by clearly identifying the cause and the effect. 3. [2] According to Statistics Canada the average undergraduate tuition in 2001 in Canada was $3,405; in 2017, it was $6,571. Find the absolute change in the undergraduate tuition from 2001 to 2017. Find the relative (relative to the 2001 tuition) change in the undergraduate tuition from 2001 to 2017. Express it as percentage, round off to the nearest integer. 4
4. (2)(a) [1] Consider the statement Every dog in Hamilton barks. State clearly what you need to do in order to prove that the given statement is false. (b)[1] Consider the statement There is a dog in Hamilton which barks or has green eyes. State clearly what you need to do in order to prove that the given statement is true. (c)[2] Consider the statement Every dog in Hamilton barks or has green eyes. State clearly what you need to do in order to prove that the given statement is false. 5
5. Canadian postal codes are of the format LdL dld, where L is a letter and d is a digit (0, 1, 2,..., 9). For instance, one of the postal codes for Mac is L8S 4K1. The first letter in a postal code is not random each of the 13 provinces and territories is assigned a single letter (for instance, postal codes in Nova Scotia start with B, and in Yukon they start with Y), except Quebec (where the postal codes start with one of the letters G, H or J), and Ontario (where they start with one of the letters K, L, M, N, or P). The first digit d is not random either: it is set to 0 for rural areas, and to any number 1, 2,..., 9 for urban areas. (a) [2] What is the largest number of urban postal codes in Canada? (b)[2] What is the largest number of rural postal codes in Quebec? 6
6. In Washington Post (11 October 2016) we read that One girl under the age of 15 gets married every 7 seconds. (a)[3] Approximately how many girls (in millions) under the age of 15 get married every year? Make explicit the assumption(s) that you made. Round off to one decimal place. (b)[2] According to UN data, the average number of marriages is 6.9 per 1000 (i.e., on average, 6.9 out of every 1000 women get married in a given year). Assuming that this average holds for all countries in the world, find the total number of women (in millions) who get married in one year. Assume that the world population (females and males together) is 7.48 billion. Round off to one decimal place. (c)[1] What percent of all marriages involved a girl under the age of 15? Use your rounded off answers from (a) and (b) to compute this. Round off your answer to the nearest integer. 7
7. You have to rank (arrange) the following liquids/fluids from the most expensive to the cheapest. You are not allowed to rank according to price only, you need to consider quantity as well. Coca Cola, 2L, $2.00 Antica Cabernet Sauvignon Red Wine, 750mL, $75.95 Correction fluid, two 20mL bottles, $4.19 Benylin Extra Strength Cough and Cold Syrup, 170mL, $12.79 (a)[1] State how you plan to do it, i.e., what will your ranking be based on. (b)[3] Do the calculations and rank the given liquids/fluids, from the most expensive to the cheapest. Round off as needed. 8 THE END