MATH 80 MOCK FINAL EXAM FORM B Instructions: the following material is presented to you for informational purposes only. No warranty or guarantee with respect to the content of the actual exam which will be based upon the homework and the material covered in class is either implied or expressed. You'll notice, for example, that this mock final is heavy on material from later in the semester, which will not be the case with respect to your real final exam (it will be much more balanced, with stuff from early and late in the class). When you work the problems that follow, please consider using your own paper. Like the problems that follow, your actual final exam will also be entirely multiple-guess (except for the bonus), and you must come equipped with a Scantron form 886-E, 886-ES, or 886-LOVAS when you sit for the actual final, as no other forms will be accepted. This mock final, however, can be submitted using a Scantron form 886 or 88, as you wish. To obtain any credit for this mock final, you must submit your answers on your Scantron form at the start of your actual final exam. Late submissions will not be scanned or recorded. Finally, for the full text of the disclaimer, please refer to the course Web page. Best of luck... Identify the sequence as arithmetic, geometric, or neither. ) an = 6 n A) Arithmetic B) Neither C) Geometric ),, 7, 9,... A) Neither B) Geometric C) Arithmetic ), 7, 9,,... A) Arithmetic B) Neither C) Geometric Find the sum of the infinite geometric series. ) -0 - - 6 -... A) 6 B) - 6 C) - 6 D) -0 Einate the parameter. ) x = t +, y = t - A) y = x +, x B) y = x +, x C) y = x -, x D) y = x -, x
Solve the problem. 6) If an earthquake has an intensity of x, then its magnitude, as computed by the Richter Scale, is given by x R(x) = log, where I is the intensity of a small, measurable earthquake. (Consider I = for this I 0 0 0 problem.) If one earthquake has a magnitude of.7 on the Richter scale and a second earthquake has a magnitude of.6 on the Richter scale, how many times more intense (to the nearest whole number) is the second earthquake than the first? A) 79 B) 99,6, C) 9 D) 7) A projectile is thrown upward so that its distance above the ground after t seconds is h = -6t + 8t. After how many seconds does it reach its maximum height? A) s B) 8 s C) s D) 7 s 8) The stadium vending company finds that sales of hot dogs average,000 hot dogs per game when the hot dogs sell for $.0 each. For each cent increase in the price, the sales per game drop by 000 hot dogs. Determine a function Rx that models the total revenue per game, where x is the number of $0. increases in the price of a hot dog. A) R x = 00x + 70x - 87,00 B) R x = -00x +,70x + 87,00 C) R x = -00x + 70x + 87,00 D) R x = -00x + 870x + 87,00 9) Rewrite the rational exponent function as a radical function, and write the domain using interval notation. f(x) = (x + 6)-/ A) ; [-, ) B) ; (-, - ) (-, ) (x + 6) (x + 6) C) ; (-, - ) (-, ) D) (x + 6) ; (-, ) (x + 6) 0) A pendulum bob swings through an arc 0 inches long on its first swing. Each swing thereafter, it swings only 60% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? A) 8 inches B) 6 inches C) 67 inches D) inches ) For the function R(x) = x + x - x - x - 6 identify any vertical asymptote(s) and/or hole(s) in the graph. A) vertical asymptote: x = -; hole at, 7 B) vertical asymptotes: x = -, x = C) vertical asymptote: x = - D) vertical asymptotes: x =, x = - ) An artifact is discovered at a certain site. If it has % of the carbon- it originally contained, what is the approximate age of the artifact to the nearest year? (carbon- decays at the rate of 0.0% annually.) A) 600 years B) 00 years C) 77 years D) 688 years
) A biologist studying the worm population in soil has found that the number of worms is related to the volume of the soil studied. This relationship can be represented by the mathematical model f(x) =.6x0. where x represents the volume of soil studied in cubic feet and f(x) represents the number of worms found in the soil. i) Evaluate f() and interpret. ii) Compute the average rate of change of the model for x = 68 and Δx = 0 and interpret. [Note that Δx gives the length of the interval over which you should compute the average rate of change.] A) i) f() =.; The worm population is about worms in cubic feet of soil. ii) From 68 cubic feet to 98 cubic feet, the average increase in the number of worms is about 0.0 worms per cubic foot. B) i) f() = 0.98; The worm population is about worms in cubic feet of soil. ii) From 68 cubic feet to 98 cubic feet, the average increase in the number of worms is about 0.0 worms per cubic foot. C) i) f() = 0.98; The worm population is about worms in cubic feet of soil. ii) From 68 cubic feet to 98 cubic feet, the average increase in the number of worms is about 6.7 worms per cubic foot. D) i) f() = 0.98; The worm population is about worms in cubic feet of soil. ii) From 68 cubic feet to 98 cubic feet, the average increase in the number of worms is about.86 worms per cubic foot. ) Determine: x x + x + x + x + 7 A) B) 7 C) 0 D) ) The growth of the population in a particular country can be modeled by P(t) = P0e0.09t where t represents time in years since 999, and P(t) represents the population of the country. If P0 =,09,000, find the population of the country in the year 007, rounded to the nearest ten-thousand. A),90,000 B) 7,0,000 C) 6,0,000 D),80,000 6) The amount of a new experimental drug present in a patientʹs bloodstream can be modeled by g(t) = 7e-0.t, t 0 where t represents the time since the drug was administered in hours and g(t) represents the amount of drug in the bloodstream, measured in milligrams. Evaluate g(9) and interpret. A) g(9) = 0. After 9 hours, there will be approximately 0. milligrams of the drug in the bloodstream. B) g(9) = 0.9 After 9 hours, there will be approximately 0.9 milligrams of the drug in the bloodstream. C) g(9) =.69 After 9 hours, there will be approximately.69 milligrams of the drug in the bloodstream. D) g(9) = 6.9 After 9 hours, there will be approximately 6.9 milligrams of the drug in the bloodstream. 7) A cake is removed from an oven at F and cools to 0 F after minutes in a room 68 F. How long will it take the cake to cool to 6 F? A) 6.7 min B) 7.7 min C) 66.06 min D).0 min
8) Determine: A) 7 x - 7x - 6x - 7 x + x - B) C) D) 9) A piece of cardboard is 0.0 in. thick. The cardboard is cut in half, with one half being placed on top of the other so that its thickness doubles for 7 times in a row. How thick would the final stack of cardboard be? Round to two decimal places. A).6 in. B). in. C) 7.6 in. D). in. 0) If Nina deposits $,000 into an account that yields 6% interest compounded quarterly, how much will be in the account after years? A) $,7.8 B) $,9.7 C) $,00.78 D) $7.8 ) The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 8x - x. What rainfall produces the maximum number of mosquitoes? A) 6 in. B) 0 in. C) in. D) 8 in. ) Identify any horizontal asymptotes for the function h(x) = 8x - x - x - 9x + 9. A) y = 0 B) y = 9 C) y = D) none ) In the formula A(t) = A0ekt, A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.7% annually. Determine the half-life of this isotope, to the nearest year. A) 86 yr B) yr C) 96 yr D) 7 yr ) The percentage of unemployed chocolate tasters in a small countryʹs labor force can be modeled by f(x) = 6.69(0.99)x, x 0 where x represents the number of years since 990. Solve the exponential equation 6.69(0.99)x =.7 and interpret. A) x 9; After 8, the number of unemployed workers in the countryʹs labor force that were chocolate tasters dropped below.7%. B) x ; After 0, the number of unemployed workers in the countryʹs labor force that were chocolate tasters dropped below.7%. C) x ; After 988, the number of unemployed workers in the countryʹs labor force that were chocolate tasters dropped below 6.69%. D) x ; After 99, the number of unemployed workers in the countryʹs labor force that were chocolate tasters dropped below 6.69%.
Solve. ) A ball is dropped from a height of.0 m. On each upward bounce the ball returns to of its previous height. Find the total vertical distance the ball travels before coming to rest. A) 8. m B).0 m C).7 m D).7 m 6) A certain radioactive isotope has a half-life of days. If one is to make a table showing the half-life decay of a sample of this isotope from grams to gram; list the time (in days, starting with t=0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column? A) Arithmetic in the first; arithmetic in the second B) Geometric in the first; geometric in the second C) Arithmetic in the first; geometric in the second D) Geometric in the first; arithmetic in the second Find the indicated roots. Write the answer in a + bi form. 7) Fourth roots of - - i A) + i, - + i, - - i, - i B) + i, - + i, - - i, - i C) + i, + i, - i, - i D) + i, + i, - i, - i 8) Square roots of - + i A) 6 - i, -6 - i B) C) + 6 i, - - 6 i - 6 i, - + 6 i D) 6 + i, - 6 - i Find the it, if it exists. 9) x x + x - x - A) Does not exist B) 9 C) 0 D) - Find the sum of the geometric series. 0) () i i= A) 9 B) C) 0 D) 6
Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f x = /x. - ) f x = x + A) Shift the graph of the reciprocal function right units, and then stretch vertically by a factor of -. B) Shift the graph of the reciprocal function left units, reflect across the x-axis, and then stretch vertically by a factor of. C) Shift the graph of the reciprocal function right units, reflect across the x-axis, and then stretch vertically by a factor of -. D) Shift the graph of the reciprocal function left units, and then stretch vertically by a factor of -. Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. ) (multiplicity ) and + i (multiplicity ) A) f x = x - 8x + 6x + 8x + B) f x = x + 8x + 6x - 8x + C) f x = x - 8x + 6x - 8x + D) f x = x - 8x + x - 8x + ), -, and - + i A) f(x) = x + 0x - 0x - 7 B) f(x) = x - x - 0x - 7 C) f(x) = x - x + 0x + 0x + 7 D) f(x) = x - x - 0x - 0x - 7 Use your grapher to determine which of the graphs matches the given polar equation. ) r = cos θ A) B) C) - - - - - r - - - D) - - - - - r - - - - - - - - r - - - - - - - - r - - - 6
Find the required part of the geometric sequence. ) Find a formula for the nth term of a geometric sequence with second term - and fifth term 80. A) an = n - - B) 7 an = - n - C) 7 an = - 7 (n - ) D) a n = - (n - ) 7 6) Find the first term of a geometric sequence with seventh term 87 and common ratio of. A) B) C) D) 9 Find the domain of the function. 7) f(x) = log9 (8 - x) A) (-8, 8) B) (-, -9) (9, ) C) [-9, 9] D) (-9, 9) Find an equivalent equation in rectangular coordinates. 8) r(cos θ - sin θ) = A) x + y = B) x + y (x - y) = C) x - y = D) x - y = 6 9) r = + cos θ A) x = 0y - B) x = - 0y C) y = - 0x D) y = 0x - Match the graph of the rational function with its equation. 0) 0 0-0 -0 0 0-0 -0 A) f(x) = x + x - x - B) f(x) = x - x - x + C) f(x) = x - x - x - D) f(x) = x + x - x + 7
) 0 8 6-0 -8-6 - - - 6 8 0 - -6-8 -0 -x A) f(x) = x + x - 0 x B) f(x) = x + x - 0 -x C) f(x) = x - x - 0 x D) f(x) = x - x - 0 0 8 6 ) -0-8 -6 - - - 6 8 0 - -6-8 -0 - A) f(x) = x + x - 0 x + B) f(x) = x + x - 0 C) f(x) = x + x - 0 x - D) f(x) = x + x - 0 Evaluate or determine that the it does not exist for each of the its (a) for the given function f and number d. ) f(x) =, for x > -, x + x - x, for x - x df(x), (b) x d+ f(x), and (c) x d f(x) d = - A) (a) Does not exist (b) (c) Does not exist B) (a) (b) Does not exist (c) C) (a) (b) Does not exist (c) Does not exist D) (a) Does not exist (b) (c) Find the average rate of change for the function over the given interval. ) y = between x = and x = 7 x - A) - 0 B) 7 C) D) 8
Find an equivalent equation in polar coordinates. ) xy = A) rsin θ = B) rsin θ cos θ = C) rsin θ = D) r sin θ cos θ = 6) x + y = 6 A) cos θ + sin θ = 6r B) sin θ + cos θ = 6r C) r( cos θ + sin θ) = 6 D) r( sin θ + cos θ) = 6 Determine the value of the it. 7) f(x) x 0 A) 0 B) - C) Does not exist D) Answer the question. 8) Write the formal notation for the principle ʺthe it of a quotient is the quotient of the itsʺ and include a statement of any restrictions on the principle. A) f(x) = g(a) f(a). B) If C) If D) = M and = M and f(x) = L, then f(x) = L, then f(x) = g(a), provided that f(a) 0. f(a) f(x) = f(x) = f(x) = M, provided that f(a) 0. L f(x) = M, provided that L 0. L Find the product or quotient. Write the answer in standard form. 9) - i - 9i A) - 06 + 6 06 i B) 6 06 + i C) 06 6 + 6 i D) - 6 6 + 6 i Write a linear factorization of the function. 0) f(x) = x + 8x + 9x + x + 60 A) f(x) = (x + )(x + )(x + i)(x - i) B) f(x) = (x + )(x + )(x + ) C) f(x) = (x + )(x + )(x + i)(x - i) D) f(x) = (x + )(x + )(x + i)(x - i) 9