MA 153 Exam 1A Spring 2008 1 1. Express the following as an inequality. The quotient of x and y is at least 18. 1.81.81. 81.8. None of the above.xAyBxyxCyDxyE≥≤≤≥ 2. Simplify. Do not leave negative exponents in your answer. ()3532412xxyy−−⎛−⎜⎝⎠⎞⎟ 52626252.483.. 48.3. None of the above.yAxyBxyCxyDxE−− 3. Simplify completely. ()()37 9210 5xyxy ()()()()()64336413 713 7.15.5 2.5 2.1.5 2Axy y5Bxy xCxy yDxy xExy xMA 153 Exam 1A Spring 2008 2 4. Simplify. 2123964ab⎛⎞⎜⎝⎠⎟ 383293864338329386128.316. 16.16.128.3aAbaBbaCbaDbaEb 5. Perform the indicated operations and express as a polynomial. ()()2225 411xxx−−−+ 2222.3 24 36. 3 16 14.3 4 36.3 4 14. None of the above.Ax xBx xCx xDx xE−+−+−+++ 6. Divide and express as a polynomial. 42 73 3103281022ab ab abab+− 73 31011 13473 31048.4 10 2.8.6 8.6 10 2.4 5Aa ab abBabCaabDa ab abEaabb+−++−+−MA 153 Exam 1A Spring 2008 3 7. Which of the following is a factor of 8225xy−? 22224.25.5.25.5. Cannot be factored.AxyBxyCxyDxyE−+−+ 8. Factor completely. Given: ()()33 2 2xyxyxxyy−=− ++ . 6361yy−−6 ()()()()()()()()()()()()()()323332342342.2224.22.28864. 2 2 8 512.28264Ay y y yBy yCy y y yDy y y yEy y y y+− +++−+− +++− +++− ++ 9. Rationalize the denominator and simplify. 35tt++ 81.59.2515.2515.521.25ttAttBttCttDtttEt+++++−−+−−−−55MA 153 Exam 1A Spring 2008 4 10. Simplify completely. ()()22244127434 4 4xx xxxx x x++ −−÷+− + − ()()()()()()( )21 4.121.122.3121 4.14. None of the above.xxAxxBxxCxxxDxxE+−++−+−−++− 11. Solve for x. Choose the answer that best describes the solution(s). 4533xxx+=−−12 . There is only one solution. It is less than 0 .. There is only one solution. It is between 0 and 10.. There is only one solution. It is greater than 10.. There is no soABCD lution for .. All real numbers are solutions except 3.xEx =12. Solve 1 wbPx+= for w. .1.1..1.Aw PxbPxBwbPbCwxxPDwbPEwbx=−−=−=−=−=MA 153 Exam 1A Spring 2008 5 13. Jacob inherited $25,000 and decided to invest the money into two accounts. One account pays 7.5% simple interest and the other account pays 4% simple interest. Let x represent the amount of money Jacob invests in the 7.5% account. Choose the equation that would solve x if the total annual interest is to be $1200. ()()(). 0.075 0.04 25,000 1200. 0.075 1200 0.04 25,000. 0.075 0.04 1200. 0.075 0.04 1200 25,000. 0.075 1200 0.04Ax xBxxCxxDxEx x+−=+= −+=x+=−+= 14. At 8:00 am, a bicyclist travels at a constant speed of 5 mph. At 10:00 am, his brother begins traveling the same path on his moped at a constant speed and reaches the bicyclist 30 minutes later. Find the speed of the moped. .30.18.21.25E. None of the above.AmphBmphCmphDmph 15. A doorway in a new building is designed to be handicapped accessible. The shape of the doorway will be a rectangle surmounted by a semicircle (see the figure). The width of the door is to be 6 feet and the height, h, has yet to be determined. If the area of the doorway is to be 32 square feet, choose the equation used to find h. Simplify your equation. . 6 36 32.6 9 329. 6 502. 6 36 509. 6 322AhBhChDhEhπππππ+=+=+=+=+=
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