M117 Review for Final Exam Revised FALL 2007 CHAPTER 7

Transcription

1 M7 Review for Final Eam Revised FALL 007 PLEASE BE ADVISED THAT THIS REVIEW IS ONLY A SAMPLING OF QUESTIONS FROM THE COURSE. ALL NOTES, HOMEWORK, EXAMS, QUIZZES, ETC. SHOULD ALSO BE REVIEWED. THERE MAY BE PROBLEM TYPES ON THE FINAL EXAM THAT DO NOT APPEAR ON THIS REVIEW. CHAPTER 7 ) Simplif -0z -z ) Simplif - + ) Simplif ) Simplif ) Perform the operation and leave in simplest form. ) Perform the operation and leave in simplest form ) Perform the operation and leave in simplest form ) Perform the operation and leave in simplest form ) Perform the operation and leave in simplest form ) Perform the operation and leave answer in simplest form. + - ) Perform the operation and leave answer in simplest form ) Perform the operation and leave in simplest form ) Perform the operation and leave in simplest form

2 ) Simplif the comple fraction. ab - b a + b ) Solve 7 - = ) Solve - = - + 7) Solve = - ) Solve n - - n n + = 0n + n + n - 0 9) Solve = + + 0) Suppose that Wend rides her biccle 0 miles in the same time that it takes Kim to ride her biccle 0 miles. If Wend rides miles per hour faster than Kim, find the rate of each. (NO EQUATION = NO CREDIT) ) If an airplane travels 00 miles in the same amount of time that a car travels 0 miles, and the speed of the plane is 0 mph more than si times the speed of the car, how fast is each moving? (NO EQUATION = NO CREDIT) ) The speed of a stream is mph. If a boat travels miles downstream in the same time that it takes to travel miles upstream, what is the speed of the boat in still water? (NO EQUATION = NO CREDIT) CHAPTERS & 9 ) Is (, ) a solution for - =? ) Given: = - + Find the - and -intercepts and one other point. Graph

3 ) Given: = - Find the - and -intercepts and one other point. Graph ) Given: - = Find the - and -intercepts and one other point. Graph ) Given the following point and slope, find the coordinates of three other points on the line. ( -, ) m = ) Find the slope of the line determined b the following pairs of points. (, -), (-, -9) 9) a. What is the slope of a vertical line? b. What is the slope of a horizontal line?

4 0) Given - = Solve for and determine the slope and -intercept. ) Find the coordinates of two points on the given line, and then use those coordinates to find the slope of the line. + = ) Given = - Determine the slope and -intercept. Graph ) Write the equation of a line that passes through the points (0, ) and (, -). ) Write the equation of a line that passes through the points (-, ) and (-, ). ) Write the equation of a line that passes through the points (-, -) and (-, ). ) Write the equation of the line that passes through the points (-, ) and (, -). 7) Write the equation of a line with slope of - and passes through the point (-, -). ) Write the equation of the line with m = - passing through the point (-, -). 9) Write the equation of the line that has an -intercept of - and a -intercept of -. 0) Write the equation of a line perpendicular to the line = - and passes through the point (, ). ) Write the equation of the line that contains the point (, ) and is parallel to the line + = 9. ) Write the equation of the line that contains the point (, ) and is perpendicular to the -ais.

5 ) A plumber charges $0 plus $0 for each hour of labor. Let n represents the number of hours of labor and c is the total cost. a. Write a linear equation modeling the scenario. b. Find the total bill if labor is hours. b. If the total bill is $0, for how man hours of labor was the customer charged? c. Graph the equation with n along the horizontal ais and c along the vertical ais. d. What does the c-intercept represent? ) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.9 as soon as ou get in the tai, to which a charge of $. per mile is added. Find a linear equation that can be used to determine the cost, C(), of an -mile tai ride, and use this equation to find the cost of a -mile tai ride. ) The cost of manufacturing a molded part is related to the quantit produced during a production run. When 00 parts are produced, the cost is $00. When 00 parts are produced, the cost is $00. Find a linear equation that models cost, C(), in terms of the number of parts produced,. ) Determine if the relation is a function: {(-9, 9), (-9, -9), (, ), (, )} 7) Determine if the relation is a function: {(-, -), (, 7), (, -), (, )} ) Determine if the relation is a function: - - 9) Determine if the relation is a function:

6 0) Determine if the relation is a function. Assume that the domain is in the left column and the range is in the right column. The number of tests in various classes: Math English Histor Biolog 7 Pscholog ) Determine the domain and range of the relation: {(9, -), (, -9), (, -), (, -)} ) Determine the domain and range. a. b ) Given f() = - +, find: a. f() b. f(-) ) Given f() = -, find: a. f(-) b. f() ) Use the graph to determine the value of the function. a. f(-) b. f(0)

7 ) Solve b graphing: - = - = ) Solve b graphing: - = = ) Solve using the substitution method: = = -0 9) Solve using the substitution method: - = 7 + = 0) Solve using the elimination b addition method: - = = -7 7

8 ) Solve using the elimination b addition method: + = - = ) Solve using the elimination b addition method: - = - = ) Suppose that the cost of tennis balls and golf balls is $7. Furthermore, suppose that at the same prices, the cost of tennis balls and 7 golf balls is $0.. Find the cost of one tennis ball and the cost of one golf ball. CHAPTER 0 ) If f() = +, find f(0). ) If f() = -, find the domain. ) Neglecting air resistance, the velocit of an object, v, in meters per second can be found after falling h meters using the formula v =.h. Find the velocit of a ball that has been dropped from a roof after falling 7 meters. Round our answer to decimal places. 7) Simplif Epress our answer in radical form. ) Simplif - 7 9) Simplif 0 70) Simplif - 7) Simplif 7) Simplif 7) Simplif ) Simplif 9-7) Simplif - - +

9 7) Simplif 9a7b 77) Simplif 7) Simplif 79) Simplif ) Simplif (- )(- ) ) Simplif 9 ) Simplif - ) Simplif ) Simplif + - ) Simplif - ) Simplif 7-7) Rationalize the denominator, then use it to solve the problem. The time T in seconds required for a pendulum of length L feet to make one swing is given b T = π L. How long is a pendulum (to nearest hundredth of a foot) if it makes one swing in seconds? Use. for π. ) Solve n - 7 = 0 9) Solve + - = 0 90) Solve n - n - = n 9) Solve + = - 9) Solve + = - + 9

10 9) Simplif 9) Simplif - 9) Simplif (-) 9) Epress in radical form 97) Simplif - 9) Simplif 9 99) Simplif ab- - CHAPTER 00) Solve - - = 0 0) Solve + = 0) Solve t = 0) Solve (t + ) = 0) Solve (9s + 7) = 9 0) Use the discriminant to determine the number and nature of the roots, then solve using the quadratic formula = 0 0) Use the discriminant to determine the number and nature of the roots, then solve using the quadratic formula. - = 07) Solve n - - n + = 0) Solve - + = 0 0

11 09) A -foot ladder resting against a house reaches a windowsill feet above the ground. How far is the foot of the ladder from the house? (to the nearest tenth of a foot) (NO EQUATION = NO CREDIT) 0) Two pipes together can fill a large tank in 0 hr. One of the pipes, used alone, takes hr longer than the other to fill the tank. How long would each pipe take to fill the tank alone? (NO EQUATION = NO CREDIT) ) A square sheet of metal has an area of 7 square inches. What is the length of each side? (NO EQUATION = NO CREDIT) ) The length of a table is inches more than its width. If the area of the table is 0 square inches, what is its length? (NO EQUATION = NO CREDIT) ) A rectangular sign must have an area of square feet. The length of the sign is feet more than the width. Find the dimensions of the sign. (NO EQUATION = NO CREDIT) ) Given the following quadratic equation: = -( + ) + a. What is the verte? b. Which wa does the parabola open? c. What is the -intercept? d. Graph

12 ) Given the following quadratic equation: = - + a. What is the verte? b. What are the -intercepts (if an)? c. What is the -intercept? d. Which wa does the parabola open? e. Graph ) Given the following quadratic equation: = a. What is the verte? b. What are the -intercepts (if an)? c. What is the -intercept? d. Which wa does the parabola open? e. Graph ) A record compan discovers that the number of CDs sold each week after release of an new album follows a parabolic pattern. The function n(t) = -00t + 000t describes the number, n, of CDs an artist sold each of t weeks after the release of the album. a. Which week had the greatest number of CDs sold? b. How man CDs sold that week?

13 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () ) 7z ) - ) ) ) - + ) ( + 9)( + 7) - 7 7) ) 7 9) - 7 0) ) ) ) ) ) + ( + )( - ) - 0 ( + )( - )( - ) - ( + )( - ) b - a b + ab ) - 7 7), 7 ) - 9) -, 0) 0 mph for Kim and mph for Wend ) Car is traveling 0mph and the plane is traveling 0mph ) mph ) es

14 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () ) intercept (0, ) intercept (-, 0) ) no -intercepts -intercept is (0,-) ) ) answers ma var. eamples (-,), (,), (,7) ) 9) a. no slope or undefined b. m = 0

15 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () 0) = - m = b = 0, - ) m = - ) m = b = (0, -) ) = - + ) = - ) = ) = ) = - - ) = - - 9) = - - 0) = - + ) = - + OR + = ) 0 + = OR = ) a. c = 0n + 0 b. $0 c. hours d. e. The initial charge, which is $

16 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () ) C() =.9 +. $.0 ) C() = - 00 ) No 7) Yes ) This relation is a function. 9) This relation is not a function. 0) Yes ) Domain: {9,,, }; range: {-, -9, -} ) a. Domain: all real numbers; range: all real numbers b. Domain: { -}; range: all real numbers ) a. f() = 0 b. f(-) = ) a. f(-) = -7 b. f() = undefined ) a. f(-) = b. f(0) = - ) (, ) ) (lines are parallel) ) (-,) 9) (, ) 0) (0, -) ) (, )

17 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () ) Infinitel man solutions ) $.0 for a tennis ball and $. for a golf ball ) ) or [, ) ). m/s 7) ) - 9) 0 70) - 7) 7) 9 7) 7 7) - 7) - 7) ab a 77) 7) 0 79) -7 0) ) 0 ) - ) + ) ) - 0 ) ) T = π L ; 7.0 ft ) 9 9), - 90) 9) - 9) 9) 9) 9) - 9) 7

18 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () 97) 9) b 99) a 00) -, 7 0) 0) ± 0) - ± 0) - 9, ) discriminant is 0, so real root 0) discriminant is, so real root s ± 07) ± 0) ±, ± 09) 7.9 feet 0) hour & 0 hours ) inches ) inches ) ( + ) ards b (- + )ards ) a. (-, ) b. down c. (0,-) d

19 Answer Ke Testname: M7 FINAL REVIEW FALL 007 () ) a. (, -) b. (, 0) and (, 0) c. (0, ) d. up ) a. (-, -) b. No -intercepts c. (0, -) d. down ) a. the 0th week b. 0,000 CDs