Math 55 Intermediate Algebra Practice Problems for Exam I 1 ...

Math 55 Intermediate AlgebraPractice Problems for Exam I2x11. Evaluate the expression , if possible, for the stated values of the variable.25x10x(a) x 2(b) x 22. For what values of x, if any, is the rational expression undefined?(a)4x1x23x 9(b)x 52x 253. Simplify each rational expression, if possible. If the rational expression is already in lowest terms,so indicate.(a)93x2x 9(b)2x 8x16x 4(c)3 26x18x2x 4(d)2x 6x52x 4x54. Fifteen vehicles per minute can pass through an intersection. If vehicles arrive randomly at an1average rate of x per minute, the average waiting time T in minutes is given by T for15 xx 15. (Source: N. Garber, Traffic and Highway Engineering.)a. Find T when x 10 and interpret the result.b. Complete the table.x 5 10 13 14 14.9Tc. What happens to the waiting time as the traffic rate x approaches 15 vehicles per minute?5. Perform the indicated operations. Express answers in simplest form.(a) 2x x22x 4 x(c) 2 2x 4x 4 x 92 2x x6 x 5x6(e) 2 22a 5a3 2a 5a22 2a 9 2a 5a3(b) 2y 4y5 5y5y5 y5(d) 2 2x 4 x 2x6x18 6x(f) x14 3x2x4 x4T. Henson

Math 55 Practice Problems for Exam I - Page 2 of 3(g)(i)7x3 3x13 4 3 42 2x x x xm22 2m 4 m 2m(h) 3x5xx2 x4(j) x 44x x46. Simplify the complex fraction.(a)415x8y325x12y(b) 1 12x3x2 13x6x(c) 1 1x x1xx 17. If possible, solve each of the following equations involving rational expressions. Identify anyextraneous solutions.(a) 2x3xx3 x3(c) 1 2 1 x 3x3(e) 1 612x3 x 9(g) 3 1 12 2 2x 3x x 9 x 3x(b) 1 2x 1x1 x1(d) 2 1 1 x5 6 x4(f) 1 xx1 x1(h) 1 1 1 x1 x1 48. Use the formulaH2ababfor both parts of this problem.(a) Find the value of a if H 8 and b 3 (b)Solve the formulaH2ababfor a.9. For each problem below, write and solve a rational equation. Be sure to identify explicitly whatquantity the variable represents and to answer explicitly all questions asked. Express all answers inexact, simplified rational form. Convert improper fractions to mixed number form. Do not usedecimal form.a. Two athletes jog 10 miles. One of the athletes jogs 2 miles per hour faster and finishes 10minutes ( 1 6of an hour) ahead of the other athlete. Find the average speed of each athlete.T. Henson

Math 55 Practice Problems for Exam I - Page 3 of 3b. One roofing crew can finish a 2800 square-foot roof in 12 hours, and another crew can do the jobin 10 hours. Working together, how long will it take them to do the job?c. A boat can travel 114 miles upstream in the same time that it can travel 186 miles downstream.If the speed of the current is 6 miles per hour, find the speed of the boat without a current.d. A large pump can empty a swimming pool in 100 hours, whereas a small pump can empty thepool in 160 hours. How long will it take to empty the pool if both pumps are used?10. Determine an appropriate variation model for the statement, find the constant of proportionality k,then find the value of y when x 10 . Express all answers in exact, simplified rational form. Do notuse decimal form.a. y varies directly as x; y 3 when x 5.b. y varies inversely as x; y 3 when x 5.11. Do the following: Determine whether the data represent direct variation, inverse variation, or neither. If the data represent either direct or inverse variation, find the constant of proportionality k andan equation that models the data. Use exact, simplified rational form. Graph the equation and the data when possible.(a) x 1 5 9 15y 6 30 54 90(b) x 2 6 10 14y 105 35 21 1512. Use either a proportion, direct variation, inverse variation or joint variation to solve each problembelow. Be sure to identify explicitly what quantity the variable represents and to answer explicitlyall questions asked. Express all answers in exact, simplified rational form. Convert improperfractions to mixed number form. Do not use decimal form for answers.a. The distance between Kansas City, Missouri, and Denver, Colorado, is 600 miles. On a certainwall map, this is represented by a length of 2.4 feet. On the map, how many feet would there bebetween Memphis, Tennessee, and Philadelphia, Pennsylvania, two cities that are actually 1000miles apart?b. The cost of tuition is directly proportional to the number of credits taken. If 8 credits cost $944,find the cost to take 14 credits.c. The strength of a wood beam varies inversely with its length. A beam that is 18 feet long cansupport 900 pounds. How much weight can a similar beam support if its length is 21 feet?T. Henson