MATH 081 FINAL EXAM REVIEW 1. Evaluate: 10 15 f. 4 ( ) d. 7 g. 6 56 8 4 100 5 7 h. 6 ( ) ( 5) i. e. 5( 7 16 ) j.. Perform the indicated operation: 8 5 15 1 16 d. e. 8 5 45 h. 4 8 1 i. f. g. 5(8 10) [1 ()()] (7 9) [8 4 ] 1 [1 6 ] 10 5 7 1 7 5 10 1 4 6 15 7 1 1 4 7 1 j. 9 5. Evaluate the expression: 5 4 8 7 7 6 4. Simplify the expression: 9x 4y 7 5y 6x d. (8x 4) 5. 6a 8. 9a 4. 7b 6. b 1. e. (6m 5) 7 1 1 a a f. (6 x 5) 8 4 4 5. Evaluate the expression: x y Evaluate xy if Evaluate z if 1 5 x 9and y 1. x 6, y 5, and 1 z. Evaluate 8 5 y if d. Evaluate b a c if c x c 4, x 7, and y 11. a 5, b 7, and c 1 Page 1
6. Solve the following equations: x 9 7 i. x5 x 7.. 4 9x 15 68 j. 5x 6 x x 5 k. (5 ) 14 d. z 1 l. 4( x) 8x e a 1 m. 1 7y 17 y 5( 4 y) f. 1.. 7. y n. 4 5y 7y ( y) g. x5x 6 o. h. 7x 11 p. 4 x x 5 7 6 1 y y 5 10 5 7. Write an algebraic equation for each word problem. Then solve the equation to answer the question: The difference of 9 and 5 times a number is 14. What is the number? Lisa and Bob drove 100 miles on their vacation. Lisa drove miles more than Bob drove. How many miles did each drive? Samantha is making punch with juice and soda for a large party she is catering. The recipe calls for three times as much soda as juice. Samantha needs to make a total of 4 gallons of punch. How many gallons of juice and how many gallons of soda does she need? 8. Solve each inequality, graph the solution set, and write it in interval notation: x 7 11 9x 5(5x 6) x 6 17x 15x 9. Find the indicated variable: Use the formula P L W to find P if L 10 and W 4. Use the formula F ma to find m if F 0 and a 5 Page
10. Solve the equation for the indicated variable: In the equation y mx b, solve for x. In the equation PV nrt, solve for T. In the equation N r( A s), solve for A. 11. Solve the following proportions: 6 4 n 5 n 1 5 4 5.. n 5 4 5 1. Translate each problem into a proportion and solve the problem: A solution calls for 15 ml of a drug for every 8 liters of water. How much water is needed for 4.5 ml of the drug? If.5 pounds of carriage bolts costs $.80, how much will 1.5 pounds cost? 1. Perform each unit conversion: Convert 60 inches to feet. Use the conversion fact: 1 inches = 1 foot. Convert 65 grams to milligrams. Use the conversion fact: 1000 milligrams = 1 gram. Convert 8 pounds to ounces. Use the conversion fact: 16 ounces = 1 pound. d. Convert 647 centimeters to meters. Use the conversion fact: 100 centimeters = 1 meter. 14. Convert: Write 7 8 as a percent. Write 0.65 as a percent. Write 0.00 as a percent. d. Write 9 % as a decimal. e. Write 150 % as a decimal. f. Write 84 % in simplest fraction form. g. Write 0.5 % in simplest fraction form. 15. Solve each percent problem: is 5% of what number? What percent of 50 is 7? What is 5% of 400? Page
16. Solve each application problem: An automobile company is recalling 8% of its cars sold in Baltimore. If 50 cars were sold in Baltimore, how many cars are being recalled? Alison bought a sofa for $9 and paid $14.4 in tax. What is the tax rate? Andre is paid 1.5% commission on his sales. If he wants to earn $500 in commission, what amount of sales must he make? d. A shirt costs $45 and a pair of pants costs $50. If sales tax is 6%, do I have enough to buy both with $100? Explain why or why not. e. What is the simple interest on a loan of $0,000 for 5 years if the interest rate is 8.4%? f. How much time does it take an investment of $500 to double in value if the annual simple interest rate is 5%? 17. Write the ordered pair (x, y) for each of the points shown on the graph: A A = D B B = C = E C D = E = 18. Determine if the ordered pair is a solution of the given equation: Is (,) a solution of the equation x y 7? Is (, ) a solution of the equation xy 11? Is (1, 5) a solution of the equation 5x y 10? 19. Determine the intercept of the graph of the given equation: Find the x-intercept of the graph of x y 6. Find the y-intercept of the graph of x y 6. Find the x-intercept of the graph of 1x 8y 6. Page 4
0. Find the slope of the line: passing through the points (1,10) and (,4) passing through the points (8, ) and (4, 7) passing through the points (5,) and (7,) 1. Write the equation of each graphed line:. Use the information given to write the equation of each line: Write the equation of the line that passes through the points (4,6) and (0,). Write the equation of the line that passes through the points ( 9, ) and (,4). Write the equation of the line that passes through the points ( 9, ) and ( 9,4).. Graph each line (continued on next page): y x 5 4 y x Page 5
x y 4 d. 6 x 5 y 0 4. Solve each system of equations by graphing: 1 y x 4 y x1 x y 1 y 4x Page 6