Math 05 Review Eercises for the Final Eam The following are review eercises for the Math 05 final eam. These eercises are provided for ou to practice or test ourself for readiness for the final eam. There are man more problems appearing here than would be on the final. These eercises represent man of the tpes of problems ou would be epected to solve on the final, but are not meant to represent all possible tpes of problems that could appear on the final eam. Note for the final eam ou must show all our work in order to receive full credit. Scientific calculators are permitted: graphing calculators or calculators with QWERTY keboards are NOT permitted. Word problems must be done using algebraic methods to receive full credit. 1. Evaluate: 9 4 7 15 (7 18) 18 ( + 4) 6 4[7 + (1 5)] e) 5 [4 7( 8)] f) 7[ ( 5)]. Evaluate the following for = and =. + ( ) + 5 e) ( ) ( ). Simplif: ( ) ( + 5) 5( + ) ( ) ( ) ( + ) [ ( )] e) 4 [ (5 4)] - 1 -
4. Solve for : + = 5 4 7 = 7 ( + ) + 5 = + 14 5( ) = 0 ( + 6) e) 4( 5) + 6 = 19 ( 1) f) 5 ( ) ( + 4) = ( + 5) 5. Solve for and graph our solution on the real number line. 5 a > 8 5( a + ) 7a ( ) 5 15 5 ( 4) < ( + 1) 6. Perform the operations and epress our answer in simplest form with positive eponents onl. ( ) ( ) ( ) ( ) 4 ( ) ( ) 7. Perform the operations and epress our answer in simplest form with positive eponents onl. 5 10 6 4 ( ) 6 8( ) 4 ( ) ( ) 4 4 ( ) ( ) (6 ) - -
8. Perform the operations and epress our answer in simplest form with positive eponents onl. 4 15 4 5 8 4 8 16 7 1 4 1 6 7 1 + 1 6 e) 7 1 9. Perform the operations and epress our answer in simplest form with positive eponents onl. 1 0 ( ) ( ) 5 ( ) (6 ) 4 6 5 4 10. Evaluate: + ( ) + 0 11. Perform the operations and epress our answer in simplest form. ( ) ( )( + ) ( 5)( + ) ( )( ) e) ( a + 6( a f) ( )( + + ) g) ( + )(4 + ) - -
1. Perform the operations and epress our answer in simplest form. ( a + ( a a( a ( ) ( )( + ) 1. Convert the following into scientific notation and then perform the computations. Show all work to receive full credit. Epress our answer using scientific notation. (10,000)(0.0005) 0.06 (0.000)(0.06) 4,000 4 14. The mass of the earth is approimatel 5.98 10 kilograms. If one ton is 888.9 kilograms, what is the weight of the earth in tons? 15. Factor the following completel (if possible): 6 4 9 16 + 9 + 6 5 + 5 + 10 16. Use long division to find the following: ( + 6 11) ( ) + 5 10 4 5 7 + 1 1 17. Reduce to lowest terms. 9 + 9 5 5-4 -
5 10 + 5 d ( ) 18. Perform the operations and epress our answer in simplest form. e) 1 1 + 7 5 + + 6 6 + 6 4 + 8 + 6 4 + + 1 1 19. Solve for. 4 + = 5 + 1 = 5 4 5 + = 6 + = 5 4 0. The length of a rectangle is 4 more than its width, and the ratio of the length to its width is 5 to. Find the dimensions of the rectangle. (Onl algebraic solutions will receive credit.) 1. Show that the ordered pair (, 1) satisfies the equation 4 = 10.. Does ( + + ) =? Justif our answer for credit. - 5 -
. Sketch a graph of the following equations. Give the coordinates of the - and - intercepts of the graphs. 5 = 15 5 + 4 = 0 4 + 7 = 8 4. Rewrite the following as a simple fraction reduced to lowest terms. 1 1 1 1 a 1 1 a a 1 7 7 + 7 5. Epress the following in simplest radical form: 8 ( 5 5 )( 50 ) 8 50 48 75 6. Write the following in simplest radical form: 1 1 8 6 7 5-6 -
7. Solve b factoring: 8 = 0 a 11a = 1 + 1 + 4 = + 4 + 9 8. Solve using the quadratic formula: epress our answer in simplest form. 4 1 = 0 + = 8 + 1 + = 6 9. Solve the following sstems of equations: + = 0 5 + = 5 = 10 + = 0 = 16 4 = 1 0. Bob's air-conditioning service charges $50 for a service call plus $0/hr for repair time. Using t for time in hours and C for total cost, write an equation that describes how much Bob's would charge for a service call and repair. Solve eplicitl for t in terms of C using our equation in part. 1. A club bought a total of 80 orchestra and balcon tickets to an off-broadwa show for a total of $,60. Orchestra tickets cost $11 each and balcon tickets cost $8 each. How man of each tpe of tickets did the club bu? (Onl algebraic solutions will receive credit.). After driving at a certain speed for 5 hours Dave realizes that he could have covered the same distance in hours if he had driven mph faster. What distance did he travel during the 5 hour trip? (Onl algebraic solutions will receive credit.). The length of a rectangle is 7 feet more than its width. The diagonal of the rectangle is 1 feet. Find the dimensions of the rectangle. (Onl algebraic solutions will receive credit.) - 7 -
4. The graph below represents the number of students in the librar during a 4 hour period. Answer the following questions based on this graph. At what time(s) were 00 students in the librar? How man students were in the librar at 4 PM? ANSWERS: MATH 05 FINAL EXAM REVIEW EXERCISES 1. 10 1 8 10 e) -41 f) -88. 4 4-0 e) -1. 17 4 + 8 4 e) 4 4 4. = 7 / = 7 All real numbers = 4 e) = f) No Solution - 8 -
6. 4 9 6 4 10 7 6 9 8. 4 19 7 4 1 9 6 11 10 + 6 e) a 108 7 17 7. 6 9 + 6 8 10. 1/4 11. 6 18b 5 + a b ab f) 4 8 e) 1 7 6 + 9 g) 4 5 8 9. 6 9 8 + 1. 4 4b a + ab + 1. 1 10 10 9 14. 1 6.7 10 tons 15. ( + 1)( 1) ( 4)( + 4) ( + )( + 1) 5 ( + 5 + ) 16. + 9 R16 + 17 R 58 5 R 1 17. e) + 5 5 + 5 ( + 1)( 1) + 18. 7 ( 7) 8 + 1 ( + 6)( 6) + 19. 7/0-1/5 1/7 9/ 0. 6 b 10 1 5 1. ( 1) 4( ) = + 1 = 10. Let = and =. Then ( + ) = 5 = 5. But + = 9 + 4 = 1. Since ( + ) +, then ( + ) +. 4. + a 7 7 5. 4 0 10-9 -
11 6 6. 4 7 + 5 7. = 4, 7 ± a = /, 4 a = 5, 1/ 8. = ± 5 = 4 ± 14 = C 50 9. (, 6) ( 1/ 5, 1) (, 9) 0. C = 50 + 0t = t 0 1. 10 orchestra tickets and 150 balcon tickets.. 165 miles. 5 ft. b 1 ft. 4. At 11 AM, PM, and 7 PM. 150-10 -