0390Test2Review

MATD 0390 INTERMEDIATE ALGEBRA Review for Test 2 Test 2 covers all cumulative material, in addition to sections 2.4-2.7, 3.1, 3.2, 3.6, 4.GR ,4.1, 4.2. Bring a non-graphing calculator and something to write with. Be prepared to show an appropriate amount of work on all test problems. 1. The value of a computer that was purchased new in 2000 is described by the graph below. Find a formula for a linear function ( ) V x that represents the value of the computer x years after 2000. Value of a computer $0 $400 $800 $1,200 $1,600 $2,000 2000 2001 2002 2003 2004 2005 2006 Value ($) 2. The population of Texas was 3.1 million in January of 1900, and 5.8 million in January of 1930. a. Find a linear function ( ) P t that gives the population in millions in the year . t b. Use the function ( ) P t to estimate the population in 1950. c. According to this function, in what year did the population reach 5.5 million? Solve graphically. You must use this method. 3. 3 6 2 2 x y x y + = ⎧ ⎨ + = ⎩ 4. 2 3 2 1 y x x y = − + ⎧ ⎨ = − − ⎩ Solve. 5. 3 2 1 5 2 x y x y + = ⎧ ⎨ + = − ⎩ 5 3 8 6. 2 1 4 2 x y x y − = ⎧ ⎨ − + = ⎩ 7. 3 4 6 2 x y x y = + ⎧ ⎨ − + = − ⎩ 8. 3 2 4 5 x y x y 7 2 − = − ⎧ ⎨ − − = ⎩ 9. Solve. Express your solution in interval notation , and graph it on a number line. a. 3 2 x − ≤ − and 5 2 8 x − < b. 2 5 13 x − < − or 3 5 14 x + > 10. Solve. Express your solution in interval notation . a. 3 5 7 x − < − ≤ b. 3 11 x − < − or 3 8 x + <

11. Solve a. 3 8 1 x − = 1 b. 5 3 3 7 x x − = − 12. Find the domain. ( ) 4 2 7 x f x x + = − 13. For the function ( ) 2 2 1 x f x x − = + 5 , find ( ) 3 f − . 14. Simplify using properties of exponents a. ( ) ( ) 5 2 2 x y xy − − b. ( ) 2 1 4 3 x y − − 15. List the degree and coefficient of each term, and state the degree of the polynomial 7 5 4 3 1.8 2 5 x x x x − − + − + 16. Simplify. ( ) 3 2 2 2 3 2 7 13 5 a b ab ab ab a b − + − − + 17. Subtract and simplify. ( ) ( ) 2 2 3 2 1 3 2 x x x x + − − − − + 18. Multiply and simplify. a. ( ) ( ) 2 2 5 3 7 x x − + b. ( ) 2 2 3 3 2 p q − c. ( )( ) 3 3 2 2 x y x y + − d. ( ) ( ) 2 3 4 3 2 x x x − + − 19. The cost, in dollars, for computer chip production is given by ( ) 9 14 C x x = + , and the revenue, also in dollars, is given by , where x represents the number of boxes of computer chips produced. The profit is defined as ( ) 2 P P R C 0.3 56 R x x x = − + = − ) . a. Find a formula for ( ) P x b. Evaluate . What does your answer mean? ( 100 P

29. Graph the linear function ( ) 1 6 3 F x x = − + and find the intercepts. 30. varies directly as the square of y x . When x is 4, is 48. Find the variation constant. y 31. varies inversely as y x . When x is 4, is 5. Find the variation constant. y 32. For a given span, the maximum weight that a wooden beam can support varies directly as the square of its height. If a beam of height 1 foot can support a maximum weight of 4 tons, what is the maximum weight that a beam of height 1.5 feet can support? 33. Hooke’s law states that the distance D a spring stretches varies directly with the weight W attached to the spring. When a weight of 40 pounds is attached, the spring stretches 5 inches. a. Express the distance that a spring stretches as a function of the weight attached. b. Find the distance that the spring stretches from a 65 pound weight attached. 34. Ohm’s law states that the amount of current that flows through a wire varies inversely as the resistance. If a current of 9 amps flows through a wire with a resistance of 2 ohms, then what current flows through a wire with a resistance of 3 ohms? 35. George drove a small motorboat for 4 hours with a 7 mph current to reach his destination. The return trip, against the same current, took 11 hours. Find the speed of George’s motorboat in still water. 36. April goes to the grocery store to create some pilaf, which is a mixture of from lentils and rice. Lentils cost $1.85 per pound and rice costs $0.75 per pound. How many pounds of each should she mix to end up with 6 pounds of pilaf that is worth $1.19 per pound? 37. There were 200 tickets sold for a volleyball game. Tickets for students were $2 each and for adults were $3 each. The total amount collected was $530. How many of each type of ticket were sold? 38. Mrs. Monroe wants to create 30 oz of ascorbic acid (vitamin C) solution of strength 9%. She has on hand some ascorbic acid solution of strengths 8% and 12%. How much of each should she use? page 4 of 6

A NSWERS : 1. ( ) 400 1800 V x x = − + 2. a. ( ) ( ) 0.09 1900 3.1 P t t = − + or ( ) 0.09 167.9 P t t = − b. 7.6 million people c. 1926 3. Solution: ( ) 2,0 −4 −3 −2 −1 1 2 3 4 −4 −3 −2 −1 1 2 3 4. Inconsistent (no solution) −4 −3 −2 −1 1 2 3 4 5 −4 −3 −2 −1 1 2 3 4 5. ( ) 3,5 − 6. (Inconsistent) ∅ 7. ( ) { } , 3 x y y x = − 4 (Dependent) 8. 39 22 , 23 23 ⎛ ⎞ − ⎜ ⎟ ⎝ ⎠ 9. a. 3 ,5 2 ⎛ ⎤ − ⎜ ⎥ ⎝ ⎦ −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 b. ( ) ( , 4 3, −∞ − ∪ +∞ ) −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 0 10. a. ( ] 2,12 b. ( ) ( ) ,5 14, −∞ ∪ +∞ 11. a. 19 , 1 3 ⎧ ⎫ − ⎨ ⎬ ⎩ ⎭ b. { } 2 12. { } 7 x x ≠ 13. ( ) 13 3 2 f − = − 14. a. 7 4 2 x y b. 2 8 9 x y 15. degree of polynomial = 7 Term Coefficient Degree 7 3 x − 3 − 7 5 1.8 x − 1.8 − 5 4 x 1 4 2 x − 2 − 1 5 5 0 16. 3 2 2 6 8 a b ab ab − + − 3 17. 2 4 5 x x + − 18. a. 3 2 6 14 15 35 x x x + − − b. 4 2 3 9 12 4 p p q − + 6 q c. 2 6 4 x y − d. 3 2 3 5 18 8 x x x + − + 19. a. ( ) 2 0.3 47 14 P x x x = − + − b. ( ) 100 1686 P = : The profit from 100 boxes of computer chips is $1686. 20. a. 3 b. 3 c. –5 page 5 of 6