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MATH 0930 Beginning Algebra Part 1 K.Rigdon Name_________________________ Practice Test for Exam 6 –3.3-3.4 Due (optional) Test Day – Monday, 2/27/2012 This practice test will give you a good idea of the type and number of problems you will see on the actual test. Working through this practice test will, therefore, provide you with a good idea of how well you know the material you will be tested over. I am providing the answers on the last sheet for you to check your answers. You have the opportunity to earn 3 extra credit points toward your test grade if you show all work for all the problems and, of course, get all the answers correct (partial points can be earned as well). If you would like to earn these extra points, you will need to turn in this packet, with your work attached (on your own notebook paper), on test day. The exam will include 6 Cumulative Review problems (like the Cumulative Review type problems assigned in Homework assignments… p210: #42-46 all & p223: #70, 71, & 73 OR like the ones you’ve been seeing in the Cumulative Review Worksheets…. Be sure to look over them You will have between 20 & 21 problems on the exam. NOTE: for the application problems on the exam, you should know how to do all of the problems from Sections 3.3 & 3.4 that were assigned or done in class – they are all possible exam questions In terms of points possible, you should expect the full (like 15-22) application problems to be worth more than the others….. And, I almost forgot….. you are allowed to use a calculator with this test!!!!! Practice Test continued on next page! PRACTICE TEST QUESTIONS….. #1-6 will be Cumulative Review problems, like it said on the front page of this Practice Test. For the following application problems, select & define a variable and other unknown (do not solve): 7) Angle A and Angle B are complementary angles. The measure of Angle B is 3 degrees less than twice the measure of Angle A. Find the measure of Angle A and Angle B. Angle A = __________ Angle B = __________ 8) The length of a rectangular road sign is 2 feet less than three times its width. Find the dimensions if the perimeter is 28 feet. Length = __________ Width = ___________ 9) A chemist working on his doctoral degree at MIT needs 12 liters of a 50% acid solution for a lab experiment. The stockroom has only 40% and 70% solutions. How much of each solution should be mixed together to form 12 liters of a 50% solution? Liters of 40% solution = __________ Liters of 70% solution = __________ Liters of 50% solution = __________ 10) A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on the level road is the entire trip was 305 miles. Rate on level road = ___________________ Rate on winding road = ____________________ For the following application problems, the unknowns have been defined. Write the appropriate equation for each problem (do not solve): 11) The perimeter of the following triangle is 35 meters. Find the length of each side. 12) The two angles below are supplementary angles. Find the measure of each angle. Practice Test page 2 13) Fred invested part of his $20,000 inheritance in a mutual funds account that pays 7% simple interest yearly and the rest in a certificate of deposit that pays 9% simple interest yearly. At the end of one year, his investments earned $1550. Find the amount he invested at each rate. Mutual funds account Certificate of deposit Principal x 20,000 - x Rate 7% 9% Interest .07x .09 (20,000 – x) 14) Planter’s Peanut Company wants to mix 20 pounds of peanuts worth $3 a pound with cashews worth $5 a pound in order to make an experimental mix worth $3.50 a pound. How many pounds of cashews should be added to the peanuts? Peanuts Cashews Experimental mix Amount x 20 - x 20 Price Rate $3 $5 $3.50 Value 3x 5 (20 – x) 3.50 ( 20) For the following application problems, be sure to define your variable (and other unknowns), write and solve an equation, and answer the question(s). 15) If the largest angle in a triangle is 5 times the measure of the smallest angle, and the middlesized angle is 20 degrees greater than twice the measure of the smallest angle. Find the three angles. 16) A pair of vertical angles is indicated in the following figure. Determine the measures of the vertical angles indicated. 17) 18) 19) 20) 21) 22) A rectangle is 8 cm longer than twice the width. If the perimeter is 88 cm, find the dimensions of the rectangle. A shoe rack (below) is to have three shelves including the top and bottom. The width of the shoe rack is to be 12 inches more than the height. Find the width and height of the shoe rack if only 96 inches of lumber is available. Community Coffee Company wants a new flavor of Cajun coffee. How many pounds of coffee worth $7 a pound should be added to 14 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound? Shirley invested some money at 9% annual simple interest and $250 more than that amount at 10% annual simple interest. If her total yearly interest was $101, how much was invested at each rate? Kathleen and Cade leave at the same time from the same point hiking in opposite directions, Kathleen walking at 4 miles per hour and Cade at 5 miles per hour. How long can they talk on their walkie-talkies if the walkie-talkies have a 20-mile radius? How many milliliters of a 25% antibiotic solution should be added to a 10 ml container of a 60% antibiotic solution in order to get a 30% antibiotic solution? Practice Test Answer Key 7) Angle A = x, Angle B = 2x – 3 11) x + (2x + 1) + (3x – 2) = 35 8) Width = x, Length = 3x – 2 12) x + (3x – 10) = 180 9) Liters of 40% solution = x, Liters of 70% solution = 12 – x, Liters of 50% solution = 12 13) .07x + .09 (20,000 – x) = 1550 14) 3x + 5 (20 – x) = 3.50 (20) 10) 15) Rate on level road = x + 20, Rate on winding road = x Define: Equation: Solve: Answer: x = measure of smallest angle 2x + 20 = measure of middle-sized angle 5x = measure of largest angle x + (2x + 20) + 5x = 180 x = 20 The angles measure 20 , 60 , and 100 . 16) Define: Equation: Solve: Answer: No definition necessary 4x – 12 = 2x + 18 x = 15 o o The angles measures are 48 and 48 . 17) Define: Equation: Solve: Answer: 18) Define: Equation: Solve: Answer: 19) Define: Equation: Solve: Answer: 20) 21) 22) Define: x = width of rectangle 2x + 8 = length of rectangle 2(x) + 2 (2x + 8) = 88 x = 12 The dimensions of the rectangle are 12 cm and 32 cm. x = height of shoe rack x + 12 = width of shoe rack 3 (x + 12) + 2 (x) = 96 x = 12 The height of the shoe rack is 12 inches and the width is 24 inches. x = pounds of $7 coffee x + 14 = pounds of coffee in mix 7x + 4(14) = 5(x + 14) x=7 7 pounds of the $7 coffee. Equation: Solve: Answer: x = amount in 9% account x + 250 = amount in 10% account .09x + .10(x + 250) = 101 x = 400 $400 at 9% and $650 at 10%. Define: Equation: x = time for each 4x + 5x = 20 Solve: x= Answer: It would take Define: 20 9 2 92 hours. x = milliliters of 25% solution x + 10 = milliliters of 30% solution Equation: .25x + .60(10) = .30(x + 10) Solve: x = 60 Answer: 60 ml of 25% solution.