Math 100 Eam 4 Review (Chapters 7-8) Name The problems included in this review involve the important concepts covered in chapters 7 and 8. Be prepared to write soltuions on the board if called upon. Find the numerical value of the rational epression for the given value of. 1) 5 2 + 8, = 3 1) 5 23 5 Objective: (7.1) Evaluate Rational Epression Find all values that make the epression undefined. b - 5 2) 5b - 20 2) 4 Objective: (7.1) Find Values for Which Epression is Undefined Write the rational epression in lowest terms. z3 + 64 3) z3-4z2 + 16z z + 4 z Objective: (7.1) Write Rational Epression in Lowest Terms II 3) Multipl or divide as indicated. Write the answer in lowest terms. 4) z 2 + 5z + 6 z2 + 7z + 12 z2 + 2z z2 + 9z + 20 z + 5 z Objective: (7.2) Multipl/Divide Rational Epressions II 4) Add or subtract. Write the answer in lowest terms. 5) 2-16 - 4 2 + 5 + 4 5) 2-3 + 16 ( - 4)( + 4)( + 1) Objective: (7.4) ^Add/Subtract Rational Epressions
Simplif the comple fraction. 6) 4 + 2 3 + 1 6 12 Objective: (7.5) Simplif Comple Fraction 6) Solve the equation. 7) - 4-5 = 3 5-8) {1} Objective: (7.6) Solve Rational Equation II 2 + 11 + 28 + 2-16 = 2 + 3-28 { 1, 0} Objective: (7.6) Solve Rational Equation II 7) 8) Solve the formula for the specified variable. 9) 4 + 6 z = 3 for z 9) z = -6 4-3 Objective: (7.6) Solve Formula for Specified Variable Solve the problem. 10) The difference of the reciprocals of two consecutive integers is 1. Find the integers. 10) 56 7 and 8 or -7 and -8 Objective: (7.7) Solve Apps: Numbers 11) Tom Quig traveled 260 mi east of St. Louis. For most of the trip he averaged 70 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 8 hr, how man miles did he drive at the reduced speed? 120 mi Objective: (7.7) Solve Apps: Distance, Rate, Time II 12) One printer can do a printing job in 2 hr. Another printer can do the same job in 14 hr. How long does it take the two printers to do the job working together? 11) 12) 1 3 4 hr Objective: (7.7) Solve Apps: Work
Find all square roots of the number. 13) 121 13) 11, -11 Objective: (8.1) Find All Square Roots of a Number Find the square root. 14) - 169 256 Not a real number Objective: (8.1) Find Square Root 14) Find the square of the radical epression. 15) 53 15) 53 Objective: (8.1) Find Square of Radical Epression Solve the problem. Give the answer to the nearest thousandth if necessar. 16) Two cars leave Springfield, Illinois at the same time. One travels north at 36 miles per hour and the other travels west at 160 miles per hour. How far apart are the after 4 hours? (Hint: Use d = rt to find the distance traveled b each car.) 16) 36 mph 160 mph 656 miles Objective: (8.1) Solve Apps: Pthagorean Theorem Find the distance between the pair of points. 17) 10, -3 and 2, -18 17) 17 Objective: (8.1) Find Distance Between Two Points Simplif the epression. 10 480 18) 2 6 18) 20 5 Objective: (8.2) Use Product and Quotient Rules to Simplif Radical (Numbers) Simplif the radical. Assume that all variables represent nonnegative real numbers. 19) 81m19n12 19) 9m9n6 m Objective: (8.2) Use Product and Quotient Rules to Simplif Radical (Variables)
Simplif the radical. 20) 3 250 20) 5 3 2 Objective: (8.2) Simplif Higher Roots (Numbers) 21) 3-64a8b5 21) -4a2b 3 a2b2 Objective: (8.2) Simplif Cube Root (Variables) Solve the problem. 22) A triangle has a base of 252 and a height of 118. What is the best estimate for its area? 22) 88 Objective: (8.2) Solve Apps: Geometr Simplif the epression b performing the indicated operations. 23) 6 3-2 50 23) -7 2 Objective: (8.3) Multipl and Combine Radicals (Numbers) 24) 2 3 486 + 3 24 10 3 2 24) 6 3 18 + 20 3 4 Objective: (8.3) Multipl and Combine Radicals (Numbers) Find the perimeter of the figure. 25) 10 2 3 3 25) 6 2 16 2 + 3 3 Objective: (8.3) Solve Apps: Perimeter Rationalize the denominator and simplif. 26) 36 11 26) 6 11 11 Objective: (8.4) Rationalize Denominator (Numbers)
Rationalize the denominator. Assume that all variables represent positive real numbers. 27) 23 13 27) 26 13 Objective: (8.4) Rationalize Denominator (Variables) Rationalize the denominator. 3 5 28) 28) 3 3 3 45 3 Objective: (8.4) Rationalize Denominator (Higher Roots) Rationalize the denominator. Write the quotient in lowest terms. 29) 10-3 10 + 3 29) 103-20 3 97 Objective: (8.5) Rationalize Binomial Denominator Solve the equation. 30) q + 3 = 5 30) {22} Objective: (8.6) Solve Equation with One Radical 31) 2 + 3 + 4 - = 4 31) 3, 11 9 Objective: (8.6) Solve Equation with Two Radicals (Quadratic) 32) 3 8a - 2 = 3 6a + 7 32) 9 2 Objective: (8.6) Solve Radical Equation with Higher Roots