Math 155 Intermediate Algebra Practice Exam on Chapters 6 & 8 Name
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1 Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 Name Find the function value, provided it eists. 1) f() = ; f(-3) Simplify by removing a factor equal to 1. ) ) m - m - m Find the vertical asymptote(s) of the graph of the given function. ) f() = Choose the correct equation of the given graph. 5) A) f() = 1-5 B) f() = + 5 C) f() = D) f() = + 5 Multiply and simplify. 6) y - 9 y - 6 y - 1 y + 3 Divide and simplify. 7) y 3-6y y - 36 y - 5y + 6 y + y - 1 Perform the indicated operation and simplify. 8) Perform the indicated operation. 9) - 3 y - y 3 y - Perform the indicated operation and simplify. 10) y + y y - 1 y + 5 1
2 Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 11) Perform the indicated operations and simplify. 1) b b b b Simplify. 13) + 3 y 3 - y 1) = 3 Find all values of a for which f(a) is the indicated value. 15) f() = ; f(a) = ) = ) A water tank can be filled in 5 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank? 18) Tom Quig traveled 0 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 0 mph due to a major accident. If the total time of travel was 8 hours, how many miles did he drive at the reduced speed? 19) A boat moves 8 km/h in still water. It travels 80 km upstream and 80 km downstream in a total time of 7 hours. What is the speed of the current? Divide. 0) ( ) ( + ) For the stated pair of functions, find the quotient function quotient function. 1) f() = , g() = - Solve the formula for the specified letter. ) 1 a + 1 b = 1 c for c f g () and give any -values that are not in the domain of the 3) L = dr D - d for d
3 Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 ) The distance D that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 1-kg object stretches a spring 69 cm, find the distance the spring is stretched when the weight is 6-kg. 5) The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 35 vibrations per second and a wavelength of 1.3 ft. Find the wavelength of another tone that has a pitch of 15 vibrations per second. 6) The weight of a body above the surface of the earth varies inversely as the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by? Determine the number of real-number solutions of the equation from the given graph. 7) = 0, given the graph of y = y ) Let f() = ( - 10). Find so that f() = 36. 9) = ) 5-3 ( ) + 6 = - 5 ( ) 31) Let f() = Find so that f() = 0. Round results to the nearest thousandth. 3) = 0 Solve the problem. 33) Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Solve the formula for the indicated letter. Assume that all variables represent nonnegative numbers. 3) rm = t - mt, for t Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; eactly one rational solution; or two different imaginary solutions. 35) v + 5v - 3 = 0 Write a quadratic equation having the given numbers as solutions. 36) - 5, + 5 Write a third-degree equation having the given numbers as solutions. 37) -, 3, 0 3
4 Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 38) (m - ) - 1(m - ) + 35 = 0 Find the -intercepts of the graph of the function. 39) f() = Graph. 0) f() = -3( + 1) + 3 y Without graphing, find the verte. 1) f() = -( + 7) - 5 Without graphing, find the line of symmetry. ) f() = 7 6 ( + ) - 1 Without graphing, find the maimum value or minimum value. 3) f() = -0.67( + 9) - 5 Without graphing, find the verte, the ais of symmetry, the maimum or minimum value, and the range. ) f( ) = 8( - 9) + 5 For each quadratic function, (a) write the function in the form f( ) = a( - h) + k, (b) find the verte, and (c) find the ais of symmetry. 5) f = Use a grapher to find the verte of the graph of each function. 6) f ( ) = Find the - and y-intercepts. If no -intercepts eist, state so. 7) f() = For each quadratic function, find (a) the maimum or minimum value and (b) the - and y-intercepts. Round answers to the nearest hundredth. 8) f ( ) =
5 Math 155 Intermediate Algebra Practice Eam on Chapters 6 & 8 9) A projectile is thrown upward so that its distance above the ground after t seconds is h = -11t + 8t. After how many seconds does it reach its maimum height? Find the quadratic function that fits the set of data points. 50) (-, -5), (-3, -7), (3, -55) Solve the problem. 51) Jane kicks a soccer ball into the air. After traveling 57 ft, it reaches a height of 3 ft. After traveling an additional 57 ft, it lands on the ground. Find a quadratic function that epresses the height h of the soccer ball as a function of the distance d that it traveled horizontally. Round numbers to four decimal places. 5
6 Answer Key Testname: 155 EXAM 6,8P 3RD 1) ) 5 3) -m ) = 5 5) C 6) y - 1 7) 8) 9) y(y - 6) (y - 6)(y - 3) y - 3 y 10) y + 3y + 13 (y - 3)(y + 5) 11) 1) 13) ( - )( + )( + 1) -5(b - 6) b(b + 5)(b - 5) y + 3 3y - 1) -5 15) 3 16) 17) min 18) 10 miles 19) 1 km/h 0) ) f g ) c = ab a + b 3) d = LD R + L () = 3 + 9; 1 ) 3.5 cm 5) 18.6 ft 6) The weight is divided by 16. 7) 0 8), 16 9) -3 ± 7 30) -3, - 31) -1 ± i 3 3).37, ) 9 hr 6
7 Answer Key Testname: 155 EXAM 6,8P 3RD 3) t = m ± m + rm 35) Two different irrational solutions 36) = 0 37) = 0 38) 9, 7 39) (3.065, 0) 0) 10 y ) (-7, -5) ) = - 3) -5 ) Verte: ( 9, 5); Ais of symmetry: = 9; Minimum: 5; Range: [5, ) 5) f = ; verte: 7, ; ais of symmetry: = 7 6) (, -0.7) 7) No -intercepts, (0, 0) 8) Minimum value: ; Intercepts: ( 3., 0), (-1.1, 0), ( 0, -9.83) 9) sec 50) f() = ) h( d) = d d 7
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