Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
REVIEW GUIDE FOR MATHEMATICS PLACEMENT TEST MAT 060 – PRE-ALGEBRA MAT 072 – MATHEMATICAL LITERACY MAT 098 – INTERMEDIATE ALGEBRA DEPARTMENT OF MATHEMATICS Parkland College Office X212 Phone: 217-351-2225 www.parkland.edu/math 1 Why Mathematics Placement? Parkland College is committed to helping students achieve success in their course work. In this effort, the college has designed a mathematics placement program to aid students in selecting the most appropriate mathematics course while taking into account their widely varied mathematics backgrounds. Placement or credit in the listed prerequisite course is required prior to registering in any mathematics course. Placement scores are valid for only two years; thereafter, the student must be reassessed. Students with transfer credit in mathematics are not required to take the placement test, but can be placed on the basis of mathematics credits earned within the last five years (after a review of transcripts). How Does the Placement Test Work? Parkland uses a national test called the ACCUPLACER. The test questions are based on your responses to each question you’ve already answered. Questions increase or decrease in difficulty depending on your answers as you work through the test. ACCUPLACER tests are untimed, so you can move at a comfortable pace. It’s important to give yourself enough time to do your best and complete the test because your results are the key factor in determining the courses you can take. This is not a test to pass or fail --- it is an instrument to help select the best level for the student to have a reasonable chance of success --- not too low and not too high. What is the Purpose of this Review Guide? The purpose of this review guide is to help students know what types of questions to expect on the ACCUPLACER test. The sample questions are taken from our MAT 060, 072, and 098 courses. This review should help the student “knock the rust off” of skills that may not have been used for a while. This review is not intended to teach the material. How to Use this Guide: The student must decide what course they think is the highest level that they have already mastered, and then review that material. The student may use the answer key to determine how well they did on the sample questions. One way to review this material is to work through the chapter reviews or mastery tests at the end of each chapter of the appropriate level textbooks. 2 Pre-Algebra Review Preparation for placement out of MAT 060 into MAT 072 The purpose of the following questions is to help the student gauge their readiness on the topics taught in MAT 060. (The purpose is not to teach this material.) SIGNED NUMBERS Simplify the following problems without using your calculator. 8 9 89 1. 2. 3. 8 9 4. 5. 8 9 6. 8 0 8 9 8. 8 9 1 10. 9 9. 72 9 2 8 11. 8 9 12. 9 8 13. 72 8 14. 8 9 7. 15. 9 8 16. 9 8 17. 89 18. 09 19. 72 8 9 20. 72 8 9 21. 8 9 2 9 22. 18 4 7 2 23. 2(5) 4( 3) 8 10 24. 18 33 30 6 FRACTIONS AND MIXED NUMBERS Simplify the following problems without using your calculator. 5 1 1 5 25. 1 1 26. 6 4 4 8 1 2 3 5 22 27. 4 1 28. 5 3 11 21 25 6 3 3 7 1 29. 1 6 30. 8 4 5 5 10 42 2 1 2 1 5 31. 32. 63 4 3 2 10 3 DECIMALS Simplify the following problems without using your calculator. 33. 0.008 0.09 34. .03 35. 3.04 17 16.9 7.015 36. 14.8 12.57 37. 0.09 .5 6 .02 38. 0.03 0.0987 39. Change 40. Change 16.15 to a mixed number 41. Change 0.027 to a fraction. 42. Change 79 to a mixed number. 6 2 3 to a decimal. 8 43. Write the number for one hundred two and five thousandths. 44. Write the number for one thousand and one hundredth. 45. Round 5,525.2178 to the nearest hundred. 46. Round 5,525.2178 to the nearest thousandths. ALGEBRAIC EXPRESSIONS Write the following in symbols. 47. The quotient of 10 and x is ninety. 48. The product of 10 and x is ninety. 49. The difference of 10 and x is ninety. 50. Twice the sum of 10 and x is ninety. Simplify the following problems. 51. 8 9x 10 52. 8x 9x 53. 8 x 9 9 x 18 54. 5 3 x 4 55. 4 3 x 2 5 7 x 8 56. 3 x 2y 4 2x y 57. 8x 9x 58. 59. 61. 3 xy 5 x y 2x 3x 9 3x 4 2 2 8 60. 2 4x 8 62. x 2x y x 4 x 10 3 x 5 3 3 2 4 3 2 4 x 10 63. Find the value of the expression 7 2x when x 4 64. Evaluate the polynomial x 2 7 x 12 when x 3 . 4 EQUATIONS Solve the following problems. 65. x 13 12 66. 4 x 44 67. 3 x 7 5 68. 2 3x 5 11 69. 15 x 1 2 4 x 20 70. 5x 6 7x 4x 3 9 71. 5 x 25 3 72. 1 x 3 8 4 73. 0.2 x 8.62 13.76 74. 2x 3.3 7 x 5.2 You may use a calculator on this part, but appropriate work must be shown. GEOMETRY Perimeter, Area and Volume Problems. If necessary, round to the hundredth. 75. Use the formula P 2L 2W to find W when P 112 cm and L 22 cm . 76. Find the perimeter of a rectangle with a length of 12.2 in and a width of 8.47 in. 77. Find the area of a rectangle with a length of 12.2 in and a width of 8.47 in. 78. Find the area of a triangle whose base is 34 inches and height is 12 inches. 79. Find the area of a circle with radius 2 cm. Use 3.14 80. Find the circumference of a circle with diameter 16 miles. Use 3.14 81. Find the volume of a rectangular solid that is 5 m wide, 3 m high, and 6 m long. 82. Find the volume of a cylinder with diameter 10 in and height 10 in. Use 3.14 83. Find the length of the missing side of the right triangle. 3 mi 11 mi 84. A square lot is 85 meters on each side. How much would it cost to fence the lot if the fence costs $14 per meter? 5 RATIO, RATE AND PROPORTION PROBLEMS 85. A car travels 310 miles on 12.5 gallons of gas. Find the rate in miles per gallon. 86. Solve the proportion: 87. If Kristen is paid $202.32 for 40 hours of work, how much will she be paid for 12 hours of work? 88. The local health food store is making cereal that has nuts to cereal in a ratio of 3 to 8. If they want to make 209 oz of the mix, how many ounces of cereal will they need? 6.2 12.4 x 1.7 PERCENT PROBLEMS 89. Write 5.5 as a percent. 91. Write 93. What number is 9.2% of 1803? 94. One hundred five percent of what number is 50.715? 95. There is a 33% off sale at the jewelry store. If the regular price of a gold chain is $183, what would be the sale price of the chain? 96. If a Biology textbook costs $137.50 at the bookstore and tax is 8.5%, what is the final cost of the textbook? 97. A Kindle is priced at $219. There is a 25% discount on the Kindle and tax is 9.25%. What is the final cost of the Kindle? 3 as a percent. 5 90. Write 35% as a decimal. 92. 3 Write 1 % as a decimal. 4 MEAN, MEDIAN, MODE, AND RANGE 98. Find the mode and range of 3, 4, 5, 7, 6, 7, 4, 3, and 7. 99. Austin had bowling scores of 118, 147, 203, 156, 180, and 192 for his last six games. Find Austin’s mean and median bowling score. 100. A consumer watchdog group priced a can of tomato soup at five different grocery stores. They found the following prices: $0.89, $1.39, $1.65, $1.70 and $1.89. Find the mean and median price. Round to the nearest cent. SCIENTIFIC NOTATION 101. Write 678,000 in scientific notation. 102. Write 4.1 10 4 in standard notation 6 English Measures and Equivalents Length Weight 12 inches (in) = 1 foot (ft) 3 feet = 1 yard (yd) 5280 feet = 1 mile (mi) 16 ounces (oz) = 1 pound (lb) 2000 pounds = 1 ton (T) Liquid Volume 8 fluid ounces (oz) = 1 cup 2 cups (c) = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) Metric System Kilo Hecto Deka Base Unit Deci Centi Milli km kg kL hm hg hL dam dag daL Length Meter (m) Weight Gram (g) Volume Liter (L) dm dg dL cm cg cL mm mg mL Conversions between Systems Length Area Weight Volume 2.54 cm = 1 in 1 m = 3.3 ft 1.6 km = 1 mi 6.5 cm2 1 in2 1 m2 10.8 ft 2 28.3 g = 1 oz 1 kg = 2.2 lb 1 L = 1.06 qt 3.8 L = 1 gal The following problems involve the U.S. system conversions or conversions between systems. Convert each measurement by multiplying by the appropriate conversion factors. If necessary, round to the nearest hundredth. 103. 11 yd = __________ in 104. 2.1 gal = __________ cups 105. 275,200 oz = __________ tons 106. 61.82 lb = __________ kg 107. 4.8 km = __________ ft 108. 5.3 gal = __________ L 109. A car is traveling at a speed of 45 miles per hour. What is the car’s speed in feet per second? 110. A science fair poster is a rectangle 36 inches long and 24 inches wide. What is the area of the poster in square feet? The following problems involve the metric system. Convert each measurement. 111. 1.86 km = _______________ cm 112. 3200 m = _______________ km 7 Pre-Algebra MAT 060 Review – Answer Key 1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 72 17 72 8 64 17 9 17 1 81 55 11 23 8 38 15 3 10 5 12 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 1 Undefined 1 72 9 1 17 17 0 1 12 40 13 12 2 35 30. 4 32. 4 3 33. 35. 37. 0.00072 43.955 3.1 34. 36. 38. 0.0009 2.23 3.29 39. 13 1 6 40. 16 41. 27 1000 42. 0.375 43. 45. 102.005 5500 44. 46. 1000.01 5525.218 47. 10 90 or 10 x 90 x 48. 10 x 90 49. 10 x 90 50. 2 10 x 90 51. 53. 55. 57. 72 x 80 52. 54. 56. 58. 17 x 27 23 x 48 72x 2 3 20 17x 3x 7 5 x 10 y x15 8 59. 15x 3 y 12 60. 8x 9 y 12 61. 5x 2 x 1 62. 2 x 2 8 x 63. 15 64. 42 65. x 25 66. x 11 67. x 4 68. x 3.5 69. x 1 70. x 3 71. x 15 72. x 20 73. x 25.7 74. x 0.38 75. 34 cm 76. 41.34 in 77. 103.334 in 2 78. 204 in 2 79. 12.56 cm 2 80. 50.24 mi 81. 90 m 3 82. 785 in 3 83. 11.40 mi 84. It would cost $4760 to fence the lot. 85. 86. x 3.4 8 x 89. 24.8 miles per gallon 202.32 x , x = $60.70 40 12 550% 90. 0.35 91. 60% 92. 0.0175 93. x 165.88 94. x 48.3 95. Sale Price: $122.61 96. Final Price: $149.19 97. Final Price $179.44 98. Mode = 7, range = 4 99. Mean = 166, Median = 168 100. Mean = $1.50, Median = $1.65 101. 6.78 10 5 102. 0.00041 103. 396 inches 104. 33.6 cups 105. 8.6 tons 106. 28.1 kg 107. 15,840 ft 108. 20 L 109. 66 feet per sec 110. 6ft 2 111. 186,000 cm 112. 3.2 km 87. 88. 11 209 , x = 152 9 Beginning Algebra Review Preparation for placement out of MAT 072 into MAT 098 The purpose of the following questions is to help the student gauge their readiness on the topics taught in MAT 072. (The purpose is not to teach this material.) ALGEBRAIC EXPRESSIONS 1. 2. 3. x 2 4x 4 for x 5 xy Evaluate: for x 6 and y 2 xy Simplify the given expression: 4 y 2 y 5 6 y Evaluate: SOLVING LINEAR EQUATIONS/INEQUALITIES AND LITERAL EQUATIONS 4x 4 7x 6 7 4 4. 2 x 1 x 7 3 x 1 2 6. Solve and express the answer in interval notation: 11 5 4x 7. Solve and express the answer in interval notation: 8. 9 Solve the following formula for C: F C 32 5 5. 13 1 2 5 x x 1 2 3 6 RULES OF EXPONENTS AND OPERATIONS ON POLYNOMIALS Simplify the following and write all answers using positive exponents. 2 30c 18d 12 9. 10. 3a 2 b5 12c 6 d 4 9 y 13 3 3 11. 12. 2a 2b 4 4 3y 2 13. 5 15. 2x 2 y 4 2 3 xy 17. 5x 19. 3x 7 2 2 1 14. 1 6 1 4 16. 3 0 5 3 18. 2 x 3 4 x 5 20. (8 x 2 5 y 2 ) 3 x 2 2 xy y 2 3 x 1 2 x 2 3 x 7 0 10 GRAPHS 21. Complete the table and graph the line. y 3 x 6 x y 8 y x 8 -8 -8 22. Complete the table and graph the line. y 1 x 1 6 x y 8 y x 8 -8 -8 23. From the graph of the line, find the slope. 8 y x 8 -8 -8 24. Graph the inequality y 3 x 5 8 y x 8 -8 -8 11 25. If the slope of the line L1 is 2 , find the slope of L2 so that L2 is perpendicular to L1. 26. If the slope of the line L1 is 2 , find the slope of L2 so that L2 is parallel to L1. 27. Write the equation of the line through the points 2,1 and 2,3 . Write the answer in slope-intercept form. 28. Given the line 2 x 3 y 6 , find the slope, x-intercept, and y-intercept. 29. Determine which of the following ordered pairs are a solution to 5 x 3 y 30 . a. (5,3) b. 5, 3 c. 3, 5 30. Write an inequality to represent the shaded portion of the graph below: 8 y x 8 -8 -8 LINEAR SYSTEMS 31. Solve: 6 x 4y 42 10 x 8y 26 32. The total receipts for a concert were $650. Adult tickets cost $3, and children’s tickets cost $2. Seventy-five more adult tickets were sold than children’s tickets. How many of each type were sold? 33. How many gallons of a 60% acidic solution must be added to 15 gallons of a 30% solution to obtain a 51% solution? 34. You and a friend started jogging at the same location but headed in opposite directions. After 45 minutes, you were 12 miles apart. If your rate was 6 mph faster than that of your friend, what was your rate? 12 Beginning Algebra Review – Answer Key 1. 7 2. 3. 8 y 60 4. 5. x6 6. 1 2 x 7 4, 7. ( 1, ) 8. C 9. 9a 4 b10 10. 11. y 3 12. 13. 15. 1 25 27 8x 3 y 18 14. 5 F 32 9 5c12d 8 2 6 a 8b12 23 6 16. 4 8 x 2 2 x 15 24 x 4 16 x 3 y 7 x 2 y 2 10 xy 3 5y 4 17. 7x 2 4x 8 18. 19. 9 x 2 42 x 49 20. 22. 21. 8 23. m 25. 1 2 2 3 24. y x 8 -8 -8 27. 29. 1 x2 2 a and c y 31. 5, 3 33. 35 gallons 26. –2 28. m 30. 2 , x-int = 3,0 , y-int = 0, 2 3 y x 2 32. 85 children’s & 160 adult tickets 34. 11 miles per hour 13 Intermediate Algebra Review Preparation for placement out of MAT 098 into 105/107/108/124 The purpose of the following questions is to help the student gauge their readiness on the topics taught in MAT 098. (The purpose is not to teach this material.) FUNCTION NOTATION Determine the domain of each function. x2 f x 1. 2 x 12 2. f x 3 4x FACTORING POLYNOMIALS AND SOLVING EQUATIONS BY FACTORING Completely factor each polynomial. 3. 3 x x 5 y 2y x 5 y 4. 24 x 5 y 7 8 x 8 y 3 12x 2 y 9 5. 2 xm 3 ym 2 xn 3 yn 6. x 2 3 x 18 7. x 2 3 x 28 8. x 2 8 xy 16y 2 9. 144 x 4 25 10. 2 x 2 7 x 30 11. 5 x 2 20y 2 12. 6 x 3 33 x 2 42 x 13. 27 x 3 64 14. 2 x 3 12 3 x 8 x 2 16. x 1 Solve algebraically 15. x 12 x 1 40 2 37 3 x RATIONAL EXPONENTS, RADICAL EXPRESSIONS, COMPLEX NUMBERS, AND QUADRATIC EQUATIONS Simplify the following. 17. 8 19. 2 21. 3 2i 5 i 22. i 99 23. 7 3 2i 24. 4 18. 3 2 5 3 2 2 5 3 4 81x 5 y 4 3 3 4 3 20. 7 2 1 3a 4 k 2 3 1 6a 2k 4 3 14 x 2 4 x 9 x 1 25. Solve: 26. Write the quadratic formula 27. Find the solutions to the nearest tenth: 5 x 2 7 x 2 0 28. Find the exact solutions: 3 x 2 2 x 1 0 29. Calculate the distance between the points 4,3 and 2, 3 . 30. Solve the inequality. Write the answer in interval notation: x 2 15 8 x RATIONAL EXPRESSIONS AND RATIONAL EQUATIONS Simplify the following. 31. 3 x2 x2 3 32. 15 x 2 15 y 2 5x3 y 2 5x 2y 3 11x 3 11y 3 4 x 3 4 x 2 y 4 xy 2 33. x 2 x 3 8 x 2 2x 4 x 3 x2 9 x 3 34. 12 x 2 x 1 1 8 x 2 6 x 1 1 36. 15 x 4 x 3 x 5x x 5 x Solve for x. 35. 4 3 8 0 x 7 x 10 x 2 x 5 2 2 Solve the following applications. 37. A boat completes a trip from Riverton to Clear Creek and back each weekday. The distance one way is 60 miles, and the speed of the current in the river is 4 miles per hour. If the round trip takes 8 hours, determine the speed of the boat in still water. 38. A window washer can wash the windows on one side of a building in 112 working hours. With an assistant he can do the job in 63 hours. How many hours would the assistant need to do the job alone? Answer the following. 39. If y is directly proportional to the square of x, and y is 37.5 when x is 5, find y when x is 12. 40. If y varies inversely as x, and y is 36 when x is 22, find y when x is 33. 15 Intermediate Algebra MAT 098 Review – Answer Key 4. 6. x 6 x 3 7. x 5 y 3 x 2 y m n 2 x 3 y x 7 x 4 3 , 4 2 3 4 x y 6 x 3 y 4 2x 6 3y 6 8. 9. 12x x 4y 10. 11. 5 x 2 y x 2 y 1. 3. 5. , 6 6, 2 5 12 x 2 5 2. 12. 2 2 x 5 x 6 3 x 2 x 7 x 2 13. 3x 4 9x 2 12x 16 14. 2x 15. x 7, x 4 16. x 9, x 4 18. 27x 5 y 20. 7 2 17. 19. 1 16 67 2 3 x 4 3 17 7i 21 14 i 13 13 22. i 24. 18a 4 k 2 25. x4 26. 27. x 1.6, x 0.2 28. 29. 6 2 30. 31. 1 32. 12 11xy 2 33. x2 x 2 34. 3x x2 35. 37. x 1 The speed of the boat in still water is 16 mi/h 36. 38. No solution The assistant would need 144 hours to do the job alone 39. y 216 40. y 24 21. 23. 3 b b 2 4ac 2a 1 i 2 x 3 , 3 5, x 16 Center for Academic Success D 120 The Center for Academic Success (CAS) in D120 is Parkland College’s one-stop learning center. CAS provides many learning and student development support services to empower students to achieve their academic goals. Preparation for Parkland’s assessment tests for entering students is highly recommended. Assessment results determine course placements; low assessment scores may result in several semesters in pre-college or developmental academic skill courses. Help in reviewing math skills is available in CAS for prospective students as well as current students who wish to re-assess. We invite you to use any of the following services. FREE WALK-IN TUTORING HELP: CAS has tutoring services for currently enrolled Parkland students as well as prospective students preparing for assessment tests. Tutoring services are intended to help students complete assignments and review for tests. They are not instructional sessions to teach new material. Math Faculty Tutoring (MFT): Experienced math faculty provide free tutoring services for students enrolled in pre-college math courses at Parkland. Students preparing to take the Parkland math assessment may use MFT services to ask questions as they work through the Mathematics Department’s Math Placement Review Guide. Math Faculty Tutoring is available in the fall and spring semesters Mondays through Fridays, 10:00 a.m. to 1:00 p.m. Peer Tutoring: Trained student tutors provide free walk-in tutoring services for currently enrolled Parkland students. Students preparing for math assessment may use Peer Tutoring services to ask questions as they review with the Math Placement Review Guide. Math Faculty Tutoring is available Mondays through Thursdays, 9:00 a.m. to 9:00 p.m., Fridays, 9:00 a.m. to 5:00 p.m. FOR-CREDIT TUTORIALS: Students who need extended instruction to learn and/or review math knowledge and skills are invited to enroll for CAS one-credit hour tutorials. Supplemental Tutorials: A one-credit hour tutorial lasts 8 weeks. Interested students will take a diagnostic to ascertain level of math ability. The tutorial consists of a weekly onehour conference with an instructor in a small group setting. Students complete an additional hour or more of homework in CAS each week. A letter grade is assigned to each tutorial taken. For more information about CAS and its services, call 217/353-2005 or visit www.parkland.edu/cas. 17