1. Simplify each expression and write all answers without negative exponents. for variable L.

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1 MATH 0: PRACTICE FINAL Spring, 007 Chapter # :. Simplif each epression and write all answers without negative eponents. ( ab ) Ans. b 9 7a 6 Ans.. Solve each equation. 5( ) = 5 5 Ans. man solutions + 7 = ( + ) Ans. no solution ( ) = + Ans : 8 + = 6 Ans :. Solve the formula P= L+ W for variable L. Ans : L = P W. How much water must be added to 0 liters of a % alcohol solution to dilute it to an 8% solution? (Ans. 0 liters) 5. Sall has $5,000 to invest. She invests some mone at 0% interest and the rest at 9%. If her annual income from these two investments is $,0, how much does she invest at each rate? (Ans. $8,000 at 0% and $7,000 at 9% ) 6. The width of the rectangle is centimeters shorter than its length, and the perimeter of the rectangle is 6 centimeters. Find its width. (Ans: 5cm)

2 7. A car and a motorccle both leave from the same point and travel in the same direction. The car travels at the average rate of 50 mph and the motorccle at the average rate of 0 mph. How long will it take before the vehicles are 80 miles apart? (Ans: hours) 8. Adult tickets for a pla cost $5.00 and children s tickets cost $.00. For one performance, 60 tickets were sold. Receipts for the performance were $ 880. Find the number of adult tickets sold. (Ans: 0 tickets) Chapter # : 9. Graph each equation. For each equation find and intercept points and slope. a) + = 6 Ans : (, 0 ) - int; ( 0, ) - int; m = b) = 5 Ans: (5, 0 ) -int; no -int; m - undefined c) = Ans : no - int; (0, ) - int; m = 0 0. Find domain of the function. f ( ) = Ans: D= (,) (, ). The coordinates of P are (, ) and the coordinates of Q are ( 7, ). Find: a) The distance between the points P and Q; Ans : 5 b) The slope of the line PQ; Ans: c) The equation of the line PQ in point slope form and slope intercept forms. Ans : = ( + ) 5 = + d) midpoint of segment PQ. Ans: (, ). Find the equation of the line with slope of 0 and intercept of. Write the equation in slope intercept and in general forms. (Ans: = 0 +, 0 = ).. Find the slope of a line parallel to =0. (Ans: / ). Find the slope of the line perpendicular to =. (Ans: )

3 5. Tell whether the lines with given equations are parallel, perpendicular, or neither. + = 0 and =. (Ans. NO) 6. Tell whether the equation + = 5 determines to be function of. ( Ans: es ) 7. Tell whether the equation + = determines to be function of. (Ans : no ) Chapter # : 8. Solve the sstem b substitution. + = = Ans. (, ) 9. Solve the sstem b addition. + = = 5 Ans. (, ) 0. Solve the sstem of equations. Use an wa. = 9+ = Ans : no solution.. Solve the sstem of equations. Use an wa. + = 5 = 0 Ans : man solutions. Solve the sstem of equations. Use an wa. + + z = + z =6 + + z = Ans: (,, )

4 Chapter # :. Graph the solution for each inequalit. Also give the solution in interval notation. < < Ans: (, 6) 7 5 ( + ) ( ) Ans : (, ] 8. Solve each inequalit. Give the solution in interval notation and graph it. + 5 > 7 Ans : (, ) (, ) 9 < 5 Ans : (, ) 5. Solve an equation. + = 0 Ans :, 6. Graph the solution set of inequalit. Chapter # 5: 7. Find the degree of polnomial +. ( Ans: ) 8. Perform the operations. ( 5)( + 5) Ans: 5 ( + 5) ( + ) Ans: 7+ 6 ( ) + ( + 5 ) Ans: + 5

5 9. Factor completel. 8 Ans : ( ) ( + ) 8 Ans: ( )( + + 9) a+ b+ a+ b Ans: ( + ) ( a + b ) n n n + + Ans : ( + ) Ans : ( ) ( + )( + ) Ans : ( +5 ) ( + 5 ) Chapter # 6: 0: Multipl and simplif. : Ans ( 7) : Divide and simplif. 9 6 Ans : : Add and simplif: + + Ans : 5 5 : Add and simplif: Ans : 8 6 ( 8)( 8) : Subtract and simplif: + Ans : ( )( + ) 5

6 5. Simplif the comple fractions. + + Ans: 6: Solve the equation. + = Ans: + = Ans: no solution 7. Solve the equation. = Ans: The water s current is miles per hour. A boat can travel 6 miles downstream, with the current, in the same amount of time it travel miles upstream, against the current. What is the boat s average rate in still water? (Ans: 0 mph) 9. If one painter can pain a house in 8 das and another painter can paint the same house in 5 das, how long will it take them to paint the house working together? (Ans: and / das) 0. Two trains made the same 600-mile run. Since one train traveled 0mph faster than the other, it arrived hours earlier. Find the speed of each train. (50mph and 60 mph). Solve + = for variable f. Ans: p q f pq f = p + q. Do each division Ans : ( ) ( + ) Ans :

7 Chapter # 7: : Simplif. a) 5 Ans: 5 b) ( 5) Ans: c) (5 ) Ans: 5 5 : Simplif. Assume that all variables represent positive numbers. + Ans: 5: Simplif. Assume that all variables represent positive numbers. Ans: 5 6: Simplif. Assume that all variables represent positive numbers. + Ans: + 7: Simplif. Assume that all variables represent positive numbers.. Ans 8 : Simplif Ans : 9 9. Simplif the epression. ( + )( ) Ans: 6 + 7

8 50: Multipl. Assume that all variables represent positive numbers. ( )( + ) Ans. 5: Simplif. Assume that all variables represent positive numbers a b Ans. 9 a b 5: Simplif. Assume that all variables represent positive numbers. 6 z Ans: z : Simplif. Assume that all variables represent positive numbers. 7 Ans Simplif b rationalizing the denominator. :. + Ans 55. Simplif b rationalizing the denominator. Assume that all variables represent positive numbers. 5 Ans Solve: = Ans. 57. Solve each equation. + 5 = Ans : + = Ans : no solution 8

9 58: Add: ( + i) + ( i) Ans. 5 i 59: Subtract: ( + i) ( i) Ans. + i 60: Multipl. ( i)( i) Ans. 7 i 6: Divide. Ans. + i i Chapter # 8: 6. Solve each equation b using the quadratic formula or factoring. + 7 = 0 Ans : 7, + = 0 Ans: ± 5± i = 0 Ans : 8 6: Solve: Ans 5 + = 0 :,,, 6: Solve. = 0 Ans : 6 9

10 65. Solve inequalit. Give the result in interval notation and graph the solution set < 0 Ans: ( 9, ) 66. Solve each inequalit. Give each result in interval notation and graph the solution set. < 5 Ans : (, 0) (, ) 5 > 0 Ans :(,) (, ) 67. Let f() = and g() = +. Find each function. f g Ans : + f g Ans: + g f Ans : Find the inverse of the function. 5 = + 5 Ans: = 69. Is function = one to one function? Ans: no Chapter # 9: 70. Find each value. a) log 8 (Ans: ) b) log 9 (Ans: ) c) log 8 (Ans: ) 7. Find. a) log = 5 Ans : b) log = Ans: 5 c) log 6 = Ans : 0

11 7. Write the epression in terms of logarithms of,, and z. log b Ans: logb + logb logbz z 7. Write the epression as one logarithm: log + log log z Ans: log b b b b z 7. Solve each equation for : a) log + log ( 9 ) = Ans : 5, b) log + log ( ) = Ans : 7. Solve: 8 : = Ans 75. Solve an equation for. + = Ans:, Solve an equation for. log = Ans: = log 77. Find domain and range of the function. Graph the function. f ( ) = log Ans: D= (0, ); R= (, ) 78. Find domain and range of the function. Graph the function. f ( ) = Ans : D = (, ), R=(0, ) 79. An initial deposit of $,000 earns 8% interest, compounded quarterl. How much will be in the account after ears? (Ans: $68.)

12 Chapter # 0: 80. What is the graph of each equation? a ) ( + ) + ( ) = 6 Ans : circle, center(,) b) = ( + ) Ans: parabola, verte(, ) c) = ( + ) 5 Ans : parabola, verte(, 5) 8. Find equation of the circle with center in the point (, ) and radius of. Ans :( ) + ( ) = 9 8. Give the coordinates of the center and radius of the circle. Graph. ( + 5) + ( ) =. Ans: (- 5, ) center; r =. 8. Give the coordinates of the verte of the parabola a) = ( + ) Ans: (, ) b) = ( ) +5 Ans: (5,) Ans: (- 5, ) center; r =.. 8. Complete the square and write the equation in standard form. Then give the verte and graph the equation. = Ans. (, ) 85. Complete the square and write the equation in standard form. Then give the verte and graph the equation. = 6+ 5 Ans: (,). 86. Graph the function: if 0 f( ) = + if > 0

13 87. Solve each sstem on the set of real numbers: a) + = 5 = Ans: (, ), (, ), (, ), (, ) b) + = 0 = Ans : (, ), (, ) c) + = 5 + = Ans : (, ), (,) Chapter # (section.): 88. Find each sum: a) k ( Ans: 0) b k= 5 ) ( k +) ( Ans: 5) k=

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