CCDM 114N Final Review New Version

CCDM 114NREVIEW FOR FINAL EXAMDirections: Read each question carefully. Give exact answers unless the question requests otherwise. Includecorrect units when appropriate.1. (1.8) Use the order-of-operations to simplify the following expressions:a. 4 20 (7 2)(3 1)b. 1 2 15 (2 7)2. (3.1) Determine whether each equation is linear or nonlinear:2a. 3x 5y8b. y x 5c. y 3 6x3. (2.5) Translate the following problems into an algebraic equation and solve:a. Twice the difference of a number and three is equal to eight.b. Eight less than the product of three and a number is twenty-two.4. (2.3) Solve the following equations:a. 5(x 4) 5x10(2 x)b. 5(x 3) 6x10(3 x)c.121 3 1x xd.4 4 613x1515x13CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

5. (2.7) Solve the following inequalities and graph on a number line:a. 2(x 5) 5 21b. 3 (4x 6) 10x6. (1.1) Use d rt to solve the following problems. Include correct units in your answer.a. You and your friends decide to travel from Las Cruces to Tucson for a weekend trip this summer. If itis a 280 mile trip and your average speed is 70 miles per hour, how long will it take you to reach yourdestination?b. Suppose that you travel from Las Cruces to Albuquerque, a 230 mile trip. If you travel an averagespeed of 75 miles per hour, how long will it take you to make this trip? Round answer to the nearesttenth.7a. (3.4) Given the linear equation 3x5y8, answer the following.a. Rewrite the equation in slope – intercept form.b. State the slope.c. State the y – intercept in point form.7b. (3.4) Given the linear equation 2x4y12 , answer the following.a. Rewrite the equation in slope – intercept form.b. State the slope.c. State the y – intercept in point form.8. (3.3) Order the following linear equations from least to most steep.51a. y 5x 2 b. y x c. y x 6 d. y 4x 133Explain how you arrived at your answer.CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

9. (3.3) Find the slope of the line through the given points, then state whether the line is increasing ordecreasing.a. (0, -1), (3, 2) b. (-2, 7), (-1, 2)c. Explain how you determine whether a line is increasing or decreasing.10. (3.1, 3.2) Graph the following linear equations. Label at least two points on the graph.a. 4x 2y8b. 2x4y81010- 1 0 10- 1 0 10- 1 0- 1 011. (3.4) Write the equation of the line in slope-intercept form given the slope and the y-intercept:a. m 2;(0,3)b. m 3;(0, 2)12. (4.2, 4.3) Solve the following systems of equations using substitution or elimination.a.7x5x4yy426b.3xy5y15174xCCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

(4.4) Translate the following word problems into a system of equations and solve algebraically. Include correctunits in your answer.13. A restaurant manager buys 50 lb of sausage and 80 lb of hamburger for a total cost of $300. A secondpurchase, at the same price, includes 100 lb of sausage and 120 lb of hamburger for a cost of $480. Find thecost of the sausage and the hamburger.14. If David has 19 bills in his wallet worth $125, all fives and tens, how many of each bill does he have?15. (5.1) Simplify:a.b.16. (5.2) Multiply and Simplify:a. ( 11y 9)(15y3)b.c. ( 3x 7y)(3x7y)d.( 5x24)17. (5.1, 5.5, 5.7) Simplify:a.3( z72 4 3xy )b.2611 i jk3 42c.4x yz6xz7 32 5d.10x yz2 825xz5 218a. (1.1, 5.4) The polynomial S 2 LW 2LH2WHdescribes the surface area of a box. Find the surfacearea of a box with a length of 8 inches, width of 6.5 inches and height of 4 inches, by evaluating the polynomial.Include correct units.CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

18b. (1.8, 5.4) The height h (in feet) of a baseball after t seconds can be modeled by the equationh 16t2 100t4 . Find the height of the baseball in four seconds. Include correct units.19. (6.1 – 6.5) Factor Completely:a. 2x 2 3x4xy6yc.2 24x49y2b. 5ab 20ab105a3 2d. 2x 14x24x20. (6.6) Use factoring to solve the following equations:2a. m m 6b. 2x 2 9x4 0c. 5x 2 14x3 = 021. (7.1) Factor and simplify each expression:a.x2x25x7x10b.x2x295x622. (7.2) Perform the indicated operations and simplify each expression:a.y26y2y 15y2y 110y25b.x22x242x 16x2x2x10x302523. (7.3) Perform the indicated operations and simplify each expression:a.2xx214x2x1b.y22y3y-92y 3y24. (7.6) Solve.a.3x5x 8b.23( x2)12(3x)25. (8.2) Simplify. Assume all variables are non-negative:a. 5x 3 20xb.4 82x32xCCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

c.48a7 d.3a72x32x226. (9.5) Use the quadratic equation, y x 4x3 , to answer the following questions.a. Identify the following points of the graph ofy:10vertex =y-intercept =x-intercept(s) =a. Sketch a graph of y. Label the vertex and thex and y intercepts.- 1 0 10- 1 0227. (9.5) Use the quadratic equation, y x 2x8 , to answer the following questionsa. Identify the following points of the graph ofy:10vertex =y-intercept =x-intercept(s) =b. Sketch a graph of y. Label the vertex and thex and y intercepts.- 1 0 10- 1 0CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

28. (9.3) Use the quadratic formula to solve:a. 6x 2 3x4 0b. 4x2 4x1 029. (8.5) Solve the radical equations:a. x 1 4 3b. x 3 2 130. (6.6) Translate the following word problems into an equation and solve algebraically. Include correctunits in your answer.a. The length of a building is twice its width. If the floor area is 288 square feet, what are the lengthand width?b. The length of a rectangular area is 7 feet more than its width. If the area is 30 square feet, findthe length and width of the rectangle.CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

Solutions1. a. 12 b. 22. a. linear b. nonlinear c. linear3. a. 2(n 3) 8; n 7 b. 3n8 22; n 104. a. x 2b. x 5c.5x d. x 435. a. x 8 , graph on number line – closed circle at 8 , arrow pointing to the left.b. x 9 , graph on number line – open circle at 9, arrow pointing to the left.6. a. t 4 hours b. t 3.1hours7a. a.3 83y x b. m c.5 5580 ,51 17b. a. y x 3 b.22c. ( 0, 3)8. Equations: c, b, d, a. The larger the slope, the steeper the line.9. a. m 1; increasing b. m 5 ; decreasing c. m 0 increasing, m 0 decreasing10 a. graph is an increasing line passing through ( 0, 4)and ( 2,0)b. graph is a decreasing line passing through ( 0,2)and ( 4,0)11. a. y 2x 3 b. y 3x 212. a. ( 4,6)b. ( 4,1 )50x80y30013. Equations:100x120y480Solution: The cost of hamburger is $3.00 per pound. The cost of sausage is $1.20 per pound.x y 1914. Equations:5x10y125Solution: David has 6 ten dollar bills and 13 five dollar bills.3 23 215. a. 11n 5nm2nm26b. 8u5uv12uv416. a. 165y 2 102y27b. 36m2 24m4CCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013

c.9 y2 2x 49d. 25x2 40x1627 3 6 1272 6 2 82x17. a. x y zb. i j k c.23431213z18. a. S 220square inchesb. h 148feet5y32xyd.65z19. a. ( 2x 3)( x 2y)c. ( 2x7y)(2x7y)b. 5a ( b 7)( b 3)d. 2x( x 3)( x 4)120. a. m 2,m 3b. x , x 4c.2x3,x1521. a.xx 2b.xx3222. a.( yy 11)( y5)b.xx5423. a.6x1b.y 3y24. a. x 12b.x18725. a.210x b.68x c.34a d. 6 x26. a. vertex: ( 2, 1)y-intercept: ( 0,3)x-intercepts: ( 1,0),(3,0)b. Graph: parabolic shape opening up, containing points in part a.27. a. vertex: ( 1, 9)y-intercept: ( 0, 8)x-intercepts: ( 4,0),(2,0)b. Graph: parabolic shape opening up, containing points in part a.28. a.3 105x b.12x12229. a. x 48b. no solution { x 2 is extraneous}30. a. Equation: 2w ( w)288 Dimensions: width: 12 feet, length: 24 feetb. Equation: w (w 7) 30 Dimensions: width: 3 feet, length: 10 feetCCDM 114N – Final Exam Review Introductory Algebra – Blitzer 6 th Ed. Updated Spring 2013