1. Quiz - Fundamental Concepts & Percentages.pdf - Haley Lo

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Name: ______________________ ( ) Class: __________ Date: __________________ Fundamental Concepts & Set Theory - QUIZ Question 1: Suppose that: [13] 𝐴 = {1, 2, 3, 6, 7} , 𝐵 = {4, 7, 12, 2, 3} , 𝐶 = {1, 3, 2, 7, 8, 9} , 𝐷 = {7, 3, 1, 2, 6} 𝜉=ℤ Fill in the symbols ∈, ∉, ⊂, ⊆, ⊃, ⊄ for the following: a) 𝐴 _____ 𝐷 b) {4, 7, 12} _____ 𝐵 c) 6 _____ 𝐶 d) {1, 2, 3, 4, 5, 6, 7, 12} _____ 𝐵 e) 7 _____ 𝐷 f) ∅ _____ 𝐶 g) 𝐴 _____ 𝜉 h) 𝐷 _____ ℝ i) 𝜉 _____ ℚ j) 30 _____ 𝜉 k) 𝐵 _____ 𝐷 l) 𝜉 _____ 𝐴 m) ℕ _____ 𝜉 Question 2: Please write down the cardinality of the following sets: [3] a) 𝐸 = {1, 4, 1, 2} 𝑛(𝐸) = ______ b) 𝐹 = {1, 2, 3, 5, 8} ∪ {6, 7, 9} 𝑛(𝐹) = ______ c) 𝐺 = {1, 2, 3, 6, 9} ∩ {7, 12, 5, 1, 6} 𝑛(𝐺) = ______ Question 3: The following questions are about set-builder notation: [6] 𝑝 a) Please write down this set into roster notation: 𝐻 = {𝑞 : 𝑝, 𝑞 ∈ ℤ, 0 ≤ 𝑝 ≤ 2, −3 ≤ 𝑞 < 0} __________________________________________________________________________________ __________________________________________________________________________________ b) Please rewrite this set into set-builder notation: 𝐾 = {Odd numbers} __________________________________________________________________________________ __________________________________________________________________________________ Question 4: Please answer the following Venn Diagram question: Question 5: The average thickness of ice in the North Pole has been decreasing due to global warming. a) In May 2000, the thickness is around 0.05% of the depth of the ocean in the North pole, which is 4000 metres in average. Find the thickness of ice in May 2000. [2] __________________________________________________________________________________ __________________________________________________________________________________ b) After 21 years, the thickness of ice is now 1.8 metres. Find the percentage change from May 2000 to May 2021. Is this a percentage increase or a decrease? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ c) What was the thickness of ice in May 1980 if the thickness is decreased by 28% from May 2021? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ Question 6: Ben has deposited $10,000 into an American savings account paying 2% per week of compound interest to his deposit. Note that there are 52 weeks in a year. a) How much will he earn if he leaves his deposit in the account for 1 year? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ b) How much will he earn if the account was compounding continuously for 1 year? [3] __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ The formula for compound interest: 𝑟 𝑛𝑡 𝐼 = 𝑃 (1 + ) 𝑛