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• MAT 212 G. DOTTI CHAPTERS 8 PRACTICE TEST # 1 Semester______________ Name___________________________________ PLEASE SHOW YOUR WORK IN ORDER TO GET CREDIT OR PARTIAL CREDIT All these problems are multiple choice type of problems. The test will have only few of those and even if a question is a multiple choice, you will still need to show your work and justify your choice. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide if the number is rational or irrational. 1) 0.12 A) Irrational B) Rational 1) 2) 38 A) Rational B) Irrational 2) 3) 1.28252626. . . A) Irrational B) Rational 3) 4) ⁻ 100 A) Irrational B) Rational 4) Simplify the radical. 5) 20 A) 4 B) 4 5 C) 2 5 D) 2 5) 6) 3 135 A) 11 B) 5 C) 5 3 3 D) 3 3 5 6) 7) 3 -64 A) ⁻4 B) 16 C) 4 D) ⁻16 7) Find the square root, rounded to hundredths. Show how you approximate the square root without your calculator. 8) 3 A) 1.71 B) 1.76 C) 1.73 D) 3 8) Find the square root, rounded to hundredths if necessary. 9) 92 A) 92 B) 9.59 C) 9.62 D) 9.57 9) Arrange the following real numbers in order from greatest to least. 10) 0.6, 0.6, 0.67, 0.667, 0.67, 0.4356 A) 0.67, 0.67, 0.667, 0.4356, 0.6, 0.6 B) 0.67, 0.667, 0.67, 0.6, 0.4356, 0.6 C) 0.67, 0.67, 0.667, 0.6, 0.4356, 0.6 D) 0.67, 0.67, 0.6, 0.667, 0.6, 0.4356 10) 1 Classify the following as true or false. 11) The product of any two distinct positive irrational numbers is irrational. A) True B) False 11) 12) The sum of any two positive irrational numbers is an irrational number. A) True B) False 12) If R is the set of real numbers, Q is the set of rational numbers, I is the set of integers, N is the set of natural numbers, and S is the set of irrational numbers, list the set(s) to which the given number belongs. If the number does not belong to any, state none. 13) 11 A) R B) Q, R C) S D) S, R 13) 14) ⁻3 A) N, I, Q, R B) Q, R C) I, Q, R D) I, R 14) Solve for x, where x is a real number. 15) 64x = 16 A) 2 3 B) 1 4 C) 3 2 D) 2 15) 16) 3⁻x = 243 A) ⁻5 B) ⁻6 C) 5 D) 1 5 16) Write an expression in terms of the given variable(s) that represents the indicated quantity. 17) The cost of having an electrician spend h hours at your house if the electrician charges $30 for coming to the house and $x per hour for labor A) 30 + hx dollars B) 30h + x dollars C) 30 + x dollars D) 30x + h dollars 17) Solve the problem. Leave the answer in exponential notation. 18) The expression 27· 64t approximates the number of bacteria after t hours. After 1 6 hr, how many bacteria are there? A) 28 B) 27 C) 2⁻13 D) 213 18) Solve the problem. 19) Find the 100th term of the following arithmetic sequence: 2, -2, -6, . . . A) -394 B) -398 C) -402 D) -390 19) 20) Find the nth term of the following arithmetic sequence: 2, -4, -10, -16, -22, . . . A) -6n + 8 B) -14 - 6n C) -6n - 8 D) 6n - 8 20) 2 21) Find the nth term of the following arithmetic sequence: π + 0.5, π + 5.5, π + 10.5, . . . A) 5n + (n - 1)π - 4.5 B) 5n + nπ + 0.5 C) 5n + π - 4.5 D) 5n + π + 0.5 21) 22) In an arithmetic sequence, find the first term if the 11th term is 18 and the difference is 2. A) 18 - 11 2 B) 18 - 10 2 C) 18 + 10 2 D) 18 + 11 2 22) 23) In a geometric sequence, find the first term if the 5th term is 625 and the ratio is 5. A) 32 2 B) 32 C) 16 D) 16 2 23) Solve the equation. 24) 32 - x = 4x + 7 A) 4 B) 5 C) 6 D) 7 24) 25) 2x + 8 = 2(x + 8) A) no solution B) 0 C) 8 D) 16 25) 26) 7(2x + 1) + 9(2x + 1) = 144 A) 5 B) 3 C) 4 D) 6 26) Solve the problem. 27) A high school graduating class is made up of 486 students. There are 186 more girls than boys. How many boys are in the class? A) 186 boys B) 150 boys C) 336 boys D) 486 boys 27) Show how you use the strategy "write an equation" to solve this problem. Here you will need to write 2 equations. In other words, translate the text of the problem into 2 equations, then combine the two equations to solve for the number of boys or girls, then answer the question. 28) A paint mixture contains 46 gallons of base for every gallon of color. In 1786 gallons of paint, how many gallons of color are there? A) 893 gallons B) 1748 gallons C) 38 gallons D) 595 gallons 28) Find or investigate the function as requested. 29) Find a function f(n) whose domain is the set of natural numbers and the output produces the terms of the sequence 3, 10, 17, 24, . . . A) 7n - 4 B) 7n + 4 C) 7n D) 4n 29) 30) Find a function f(n) whose domain is the set of natural numbers and the output produces the terms of the sequence 5, 25, 125, 625, . . . A) 5n B) n5 C) 5n D) There is no such function. 30) Determine if the following is a function or not. 31) The set of ordered pairs {(3, 8), (7, 12), (7, 13), (9, 14)} in the set of whole numbers. A) Yes B) No 31) 32) f(x) = 12 for x ∈ W. A) Yes B) No 32) 3 Solve the problem. 33) A private message agency charges 65 cents for the first ounce and 30 cents for each additional ounce or fraction of an ounce to send a message across town. How much does it cost to send a message weighing 1.5 ounces? A) 60 cents B) 95 cents C) $1.30 D) 90 cents 33) 34) The level of water in a tank after elapsed time t in minutes is given by R(t) = 6t + 1 inches. Draw a graph for this function. At what time will the water start overflowing from the tank if the depth of the tank is 79 inches? -20 -16 -12 -8 -4 4 8 12 16 20 x y 180 120 60 -60 -120 -180 -20 -16 -12 -8 -4 4 8 12 16 20 x y 180 120 60 -60 -120 -180 A) 15 minutes; t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 B) 23 minutes; t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 C) 23 minutes; t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 D) 13 minutes; t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 t -20 -16 -12 -8 -4 4 8 12 16 20 R(t) 180 120 60 -60 -120 -180 34) 4 Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. 35) "Is a team player of" A) Reflexive, symmetric and transitive; equivalence relation B) Symmetric and transitive; not an equivalence relation C) Reflexive and symmetric; not an equivalence relation D) Reflexive and transitive; not an equivalence relation 35) 36) "Is thinner than" A) Symmetric; not an equivalence relation B) Reflexive and transitive; not an equivalence relation C) Transitive; not an equivalence relation D) Symmetric and transitive; not an equivalence relation 36) 37) "Lives next door to" A) Transitive; not an equivalence relation B) Symmetric and transitive; equivalence relation C) Reflexive and symmetric; not an equivalence relation D) Symmetric; not an equivalence relation 37) Tell whether the relation is reflexive, symmetric, or transitive on the set of subsets of a nonempty set. Also tell whether the relation is an equivalence relation. 38) "Has a larger cardinal number than" A) None; not an equivalence relation B) Symmetric; not an equivalence relation C) Transitive and symmetric; not an equivalence relation D) Transitive; not an equivalence relation 38) 39) "Is the complement of" A) Symmetric and transitive; not an equivalence relation B) Symmetric; not an equivalence relation C) Reflexive; not an equivalence relation D) None; not an equivalence relation 39) 40) "Is disjoint with" A) Transitive and symmetric; not an equivalence relation B) Reflexive; not an equivalence relation C) Symmetric; not an equivalence relation D) None; not an equivalence relation 40) 5 Answer Key Testname: MAT 212 11TH ED PRACTICETEST 1 1) B 2) B 3) A 4) B 5) C 6) D 7) A 8) C 9) B 10) C 11) B 12) A 13) D 14) C 15) A 16) A 17) A 18) A 19) A 20) A 21) C 22) B 23) B 24) B 25) A 26) C 27) B 28) C 29) A 30) A 31) B 32) A 33) B 34) D 35) B 36) C 37) D 38) D 39) B 40) C 6

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