Review for MA Final Exam
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1 Review for MA 00 Final Eam Date Time Room Student ID Number (This will be needed on the scantron form for the eam.) Instructions for Students to get ID# a. Go to the IPFW website at ipfw.edu b. Log into My IPFW with user id and password. c. ID number is below the Welcome message on Home Page. There are 0 problems on the Final Eam. All problems are in multiple-choice format with possible answers a, b, c, d, and e. There is also more room to work the problems. No partial credit will be given. No formula sheets, notes, books or any other eternal resources may be used on the final eam. You must bring No. pencils and a calculator to the final eam with you. No Cell phones or computers allowed during the eam. This review has mied format. The following problems are provided as a review and represent many of the types of problems that you may epect on the final eam. For problems #-. Shown is the graph of function yy = ff().. (See the graph.) What is the Domain of f? ( 9, ] b) [ 9, ) ( 8, 8] [ 8,8) (, 9]. (See the graph.) What is the Range of f? ( 9, ] b) [ 9, ) ( 8, 8] [ 8,8) (8, 8]. (See the graph.) What is the -intercept? (0, ) b) (0, ) (, 0) (, 0) (, 0)
2 MA 00 Review for Final Eam Page. (See the graph.) What is the y-intercept? (0, ) b) (0, ) (, 0) (, 0) (0, ). (See the graph.) Find the value of ff(0). 9 b) 0 8. (See the graph.) Find the value of for which ff() = 0. 9 b) 0. Which of the graphs below are functions? (On the Final Eam, this will be in multiple choice format.) I II III IV I) Yes/No II) Yes/No III) Yes/No IV) Yes/No V VI VII VIII V) Yes/No VI) Yes/No VII) Yes/No VIII) Yes/N 8. Graph the inequality: < 9 ( ] [ ) b) ( ] ( ) [ ]
3 MA 00 Review for Final Eam Page 9. Solve the inequality: 9 ( + ) + < (8 ) < b) < > < > 0. Find the equation of the line from its graph. b) y = + y = + y = + y = + y = +. A company s revenue in 00 was $ million. Each year the revenue increases by $. million. Find a linear model for this situation and predict the revenue in 0. Let = 0 represent the year 00. R= +. b) R=. R=.+ $. Million $. Million $. Million R= R=.+. $.8 Million $. Million. Find the slope of the line through the points (, ) and (, ). b) Find the equation of the line through the point (,) with slope m =. y = b) y = + y = + y = + y =. Find the equation of the line through the point ( 8,) that is perpendicular to the line y =. y = + b) y = + y = + y = y = +
4 MA 00 Review for Final Eam Page. Given the graph of y = m + b, which of the following is true? y m< 0 and b> 0 b) m> 0 and b> 0 m< 0 and b< 0 m> 0 and b< 0 m= 0 and b< 0. Factor completely: 9 + ( ) b) ( ) ( )( ) + + ( ) ( + )( ) 9. Which of the following is a factor of 8? ( ) b) ( ) ( + ) ( + ) ( 8 ) 8. Factor completely: + 0 ( )( ) b) ( )( ) ( )( ) ( )( + 8) Prime 9. Factor completely: ( ) b) ( )( ) ( ) ( ) + Prime + ( )( + )
5 MA 00 Review for Final Eam Page 0. Solve for : ( + ) = 0 = 0 or = or = b) = 0 or = = = 0 or = only =. Which is the graph of yy = + +? b). Solve the system for. + y = + y = = b) = = = = For problems # &. Solve the system of equations. yy = 89 + yy =. For the system above, the value of is:. For the system above, the value of y is:
6 MA 00 Review for Final Eam Page. The graph of yy = ff() is shown. Estimate a for ff(a = 0. only b) 0 only only only only f) or g) 0 or. The graph of yy = gg() is shown. Estimate a for gg(a = 0. only b) only only or 0 only f). only g) 0 or.. Find a polynomial, with integer coefficients, having the following zeros: = and f ( ) = 8 + b) f ( ) = 0 ( ) f = =. f = 8 + ( ) f = + ( ) 0 8. Find a polynomial with integer coefficients having the following -intercepts on its graph: (,0) and (,0 ). f ( ) = + 0 b) f ( ) = 0 ( ) f = + 0 f = 0 ( ) f( ) = 0
7 MA 00 Review for Final Eam Page 9. The height of a rock that is thrown from a 0 meter cliff is given by h(tt) =.9tt + 9tt + 0, where t is time in seconds after being thrown. At what time will the rock return to a height of 0 meters? 0.9 sec b). sec. sec.8 sec never 0. The area of a rectangle lot is. square meters. The length is three more than four times the width. Find the length.. meters b). meters. meters meters. meters. Solve for : 9 = = b) 9 8 = ± = 0 or = 9 9 = 0 or = 9 =. Solve for : 9 = = 9 b) = 0 or = or = = ±. Solve for : 0 + = = or = b) = or = = 0 or = = or = = only. Solve for : + = 0. = ± 8 b) = ± = ± = ± = ± 9. Solve for : + = ± 09 = b) ± 09 = ± 09 = = ± 09 No real number solution
8 MA 00 Review for Final Eam Page 8. Solve for : ( ) = = ± b) ± = = ± = ± = +. Find the verte and y-intercept of the parabola ( ) ( ) f = + 8. verte: (, 8) b) verte: (, 8) verte: (, 8) y-int.: (, 0 ) y-int.: ( 0, ) y-int.: ( 0, 8) verte: (,8) verte: (, 8) y-int.: (., 0) y-int.: ( 0, ) 8. Given f( ) = 0, find the -intercepts.,0,, 0 ( ),0,,0 b) ( ),0,,0 ( ) 0,, 0, ( ) ( 0, ), ( 0, 0) 9. Find the verte form of the parabola shown below. ( ) y = + + b) ( ) y = ( ) y = + ( ) y = + ( ) y = +
9 MA 00 Review for Final Eam Page 9 0. For the function of the form yy = ff() = aa( h) + kk shown, determine the signs of a, h, and k. a, h, and k are all negative b) a and h are negative, k is positive a and k are negative, h is positive h and k are negative, a is positive a is negative, h and k are positive f) h is negative, a and k are positive g) k is negative, a and h are positive h) a, h, and k are all positive. For the function of the form yy = ff() = aa( h) + kk shown, determine the signs of a, h, and k. a, h, and k are all negative b) a and h are negative, k is positive a and k are negative, h is positive h and k are negative, a is positive a is negative, h and k are positive f) h is negative, a and k are positive g) k is negative, a and h are positive h) a, h, and k are all positive. The height of a rock that is thrown from a 00 foot cliff is given by ( ) ht = t + 8t+ 00 where t is time in seconds. How long will it take for the rock to hit the ground? Round to the nearest tenth of a second..0 seconds b). seconds. seconds. seconds 00 seconds. Rewrite with positive eponents: 8 0 b)
10 MA 00 Review for Final Eam Page 0. Which of the following is equivalent to 9? 9 b) 9. Which of the following is equivalent to? b). Simplify: 0aa 0 bb 0 cc aa bb 0 cc. Simplify: 8 yy yy 0 8. Simplify ( ) 8 b) 8 9. Simplify: b) 0. Simplify: 0 y y b) 0 y 0 y. y not a real number. Simplify: 9 y. y b) y y 8 y 8 y
11 MA 00 Review for Final Eam Page. Simplify. Assume all variables represent positive numbers. yy yy b) yy 8 yy 8. Use rational eponents to help write the radical epression in a simpler form. Assume all variables represent positive numbers. 9 b) 9. Use rational eponents to help write the radical epression in a simpler form. Assume all variables represent positive numbers. b). Subtract and simplify. ( ) ( + ) b)
12 MA 00 Review for Final Eam Page. Determine the domain of f ( ) = 0 all real numbers ecept and b) all real numbers ecept all real numbers ecept all real numbers ecept 0 all real numbers. Determine the domain of f ( ) = all real numbers b) all real numbers ecept and all real numbers between and all real numbers ecept 0 all real numbers 8 8. Simplify: b) Multiply and simplify: 9 b) + 0. Divide and simplify: ( ) b) ( + ) ( )( ) ( + ) +
13 MA 00 Review for Final Eam Page 9. Subtract and simplify: + ( ) ( )( + ) b) ( + ) ( )( ) + 0. Solve for : = 0 + = b) = = = =. Solve for : = + = 8 b) = = = 8 =. Solve for : + + = = or = 0 b) = or = 0 = or = 0 = or = 0 = 0 only. Assume that 0, yy 0. Simplify: 80aa bb 9 cc 8 0aa bb 9 cc b) aa bb cc aa bb cc 8 aaaaaa aa bb cc 8 0bb aa bb cc 8 bb. Solve for and then determine which interval contains the correct solution(s): =. < < b) 00 < < 00 0< < 00 < < 00 < < 0. Solve for : = = 0 b) = 990 = 00 = = 990
14 MA 00 Review for Final Eam Page 8. Graph the function and determine the intercepts for y = 9. -intercept: None b) -intercept: (9,0) -intercept: (9,0) y-intercept: (0,9) y-intercept: None y-intercept: (0,) -intercept: (9,0) -intercept: ( 9,0) y-intercept: (0, ) y-intercept: None 9. What is the domain of yy = ff() = 9? ( 9, ) b) [ 9, ) (9, ) [9, ) [0, ) f) (, 9) g) (, 9] h) (, 9) i) (, 9] j) (, ) 0. Use the Distance Formula ( ) + (yy yy ) to find the distance between the points (, ) and (, ). b)
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