REVIEW FOR FINAL EXAM

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1 CCDM 4N REVIEW FOR FINAL EXAM Directions: Read each question carefull. Give exact answers unless the question requests otherwise. Include correct units when appropriate.. (.8) Use the order-of-operations to simplif the following expressions: a. 4 0 (7 )( ) ( 7) ( ) ( 4 7) ( ) 4 0 ( 8). (.) Solve the following equations: a. ( x 4) x 0( x) ( x ) 6x 0( x) x x x x. (.) Translate the following problems into an algebraic equation and solve: a. Twice the difference of a number and three is equal to eight. Eight less than the product of three and a number is twent-two. Four times a number added to eight is equivalent to the opposite of four. CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

2 4. (.7) Solve the following inequalities and graph on a number line: a. ( x ) (4x 6) 0x. (.,.) Graph the following linear equations. Label at least two points on the graph. a. 4x 8 x (.) Find the slope of the line through the given points, then state whether the line is increasing, decreasing, vertical, or horizontal. Justif our answer. - 0 a. (0, -), (, ) (-, 7), (-, ) (9, -), (, -) CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

3 7. (.4) Given the linear equation x 8, answer the following. a. Rewrite the equation in slope intercept form. State the slope. State the intercept in point form. 8. (.4) Given the linear equation x 4, answer the following. a. Rewrite the equation in slope intercept form. State the slope. State the intercept in point form. 9. (.4) Write the equation of the line in slope-intercept form given the slope and the -intercept: a. m ;(0, ) m ;(0, ) 0. (.) Write the equation of the line slope-intercept form given the slope and a point that lies on the line: a. m 4;(, ) m 6;(, ). (4., 4.) Solve the following sstems of equations using substitution or elimination. a. 7x 4 4 x 6 x 7 4x. (4.4) Translate the following word problems into a sstem of equations and solve algebraicall. Include correct units in our answer. a. A restaurant manager bus 0 lb of sausage and 80 lb of hamburger for a total cost of $00. A second purchase, at the same price, includes 00 lb of sausage and 0 lb of hamburger for a cost of $480. Find the cost of the sausage and the hamburger. If David has 9 bills in his wallet worth $0, all fives and tens, how man of each bill does he have? CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

4 . (.) Simplif: a. 9n nm nm n nm 9u uv vu u vu 4. (.) Multipl and Simplif: a. ( 9)( ) (6m ) ( x 7)(x 7) ( x 4). (.,.,.7) Simplif: a. ( z 7 4 x ) ( 6 a bc 4 ) 4x z 6xz 7 0x z 8 xz 6. (.,.4) The polnomial S LW LH WH describes the surface area of a box. Find the surface area of a box with a length of 8 inches, width of 6. inches and height of 4 inches, b evaluating the polnomial. Include correct units. 7. (.8,.4) The height h (in feet) of a baseball after t seconds can be modeled b the equation h 6t 00t 4. Find the height of the baseball in four seconds. Include correct units. 8. (6. 6.) Factor Completel: a. x x 4x 6 4x 49 ab 0ab0a x 4x 4x CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

5 9. (6.6) Use factoring to solve the following equations: a. m m 6 x 9x 4 0 x 4x = 0 0. (6.6) Translate the following word problems into an equation and solve algebraicall. Include correct units in our answer. a. The length of a building is twice its width. If the floor area is 88 square feet, what are the length and width? The length of a rectangular area is 7 meters more than its width. If the area is 78 square meters, find the length and width of the rectangle.. (7.) Factor and simplif each expression: a. x x x 7x 0 x x 9 x 6. (7.) Perform the indicated operations and simplif each expression: 6 a. 0 x x 4 x 6 x x 0 x 0x. (7.) Perform the indicated operations and simplif each expression: a. x x 4 x x (7.6) Solve. a. x x 8 ( x ) ( x) CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

6 . (8.) Simplif. Assume all variables are non-negative: a. x 0x 4 8 x x 48a 7 a 7x x 6. (8.) Solve the radical equations: a. x 6 x x 4 x 7. (9.) Use the quadratic formula to solve: a. 6x x 4 0 4x 4x 0 8. (9.) For the quadratic equation below, find the vertex, -intercept, and x-intercept(s).then graph the equation, labeling all points foun a. x 4x x x CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

7 Solutions. a a. x x x x 4. a. (n ) = 8; n = 7 n 8 = ; n = 0 4n + 8 = 4; n = 4. a. x 8, graph on number line closed circle at 8, arrow pointing to the left. x 9, graph on number line open circle at 9, arrow pointing to the left.. a. graph is an increasing line passing through ( 0, 4) and (,0) graph is a decreasing line passing through ( 0,) and ( 4,0) 6. a. m ; increasing line due to positive slope m ; decreasing line due to negative slope m 0 ; horizontal line due to zero slope 7. a. 8 x 8 m 0, 8. a. x ( 0, ) 9. a. x x 0. a. 4x 7 6x 4. a. ( 4,6) ( 4,) CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

8 0x a. Equations: 00x Solution: The cost of hamburger is $.00 per poun The cost of sausage is $.0 per poun Equations: x 9 x 0 0 Solution: David has five dollar bills and 7 ten dollar bills.. a. n nm nm 6 8u uv uv 4 4. a m 4m 4 9 x 49 x 40x 6. a. 7 x 4 6 z x a b c z x 6 z 6. S 0 squareinches 7. h 48feet 8. a. ( x )( x ) ( x 7)(x 7) a ( b 7)( b ) x ( x )( x 4) 9. a. m, m x, x 4 x, x 0. a. Equation: w ( w) 88 Dimensions: width: feet, length: 4 feet Equation: w ( w 7) 78 Dimensions: width: 6 meters, length: meters. a. x x x x. a. ( )( ) x x 4. a. 6 x CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

9 4. a. x 8 x 7 6. a. 0x 8x 4a 6 x 6. a. 7 x x 9 x 48 no solution { x is extraneous} 7. a. 0 x x 8. a. vertex: (, ) -intercept: ( 0,) x-intercepts: (,0), (,0) Graph: parabolic shape opening up, containing points above. vertex: (, 9) -intercept: ( 0, 8) x-intercepts: ( 4,0),(,0) Graph: parabolic shape opening up, containing points above. CCDM 4N Final Exam Review Introductor Algebra Blitzer 6 th E Updated Fall 0

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1 Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab