Mathematics exam 7

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– DATA ANALYSIS, STATISTICS, AND PROBABILITY – C alculating Interest Example Kai invests $4,000 for nine months. Her invest- ment will pay 8%. How much money will she Interest is a fee paid for the use of someone else’s money. have at the end of nine months? If you put money in a savings account, you receive inter- Step 1: Write the rate as a decimal. 8% = 0.08 est from the bank. If you take out a loan, you pay inter- Step 2: Express the time as a fraction est to the lender. The amount of money you invest or by writing the length of time in months borrow is called the principal. The amount you repay is over 12 (the number of months in a year). the amount of the principal plus the interest. 9 months = 192 = 3 year The formula for simple interest is found on the for- 4 Step 3: Multiply. I = prt mula sheet in the GED. Simple interest is a percent of the = $4,000 × 0.08 × 3 principal multiplied by the length of the loan: 4 = $180 Interest = principal × rate × time Kai will earn $180 in interest. Sometimes, it may be easier to use the letters of each P robability as variables: Probability is expressed as a fraction and measures the I = prt likelihood that a speciﬁc event will occur. To ﬁnd the probability of a speciﬁc outcome, use this formula: Example Michelle borrows $2,500 from her uncle for Number of speciﬁc outcomes Probability of an event = three years at 6% simple interest. How much Total number of possible outcomes interest will she pay on the loan? Step 1: Write the interest as a Example decimal. 6% = 0.06 If a bag contains 5 blue marbles, 3 red marbles, Step 2: Substitute the known and 6 green marbles, ﬁnd the probability of values in the formula I = prt selecting a red marble: = $2,500 × 0.06 × 3 and multiply. Probability of an event = = $450 Number of speciﬁc outcomes Total number of possible outcomes Michelle will pay $450 in interest. 3 = 5+3+6 Some problems will ask you to ﬁnd the amount that Therefore, the probability of selecting a red marble is 134 . will be paid back from a loan. This adds an additional step to problems of interest. In the previous example, Michelle will owe $450 in interest at the end of three Helpful Hints about Probability years. However, it is important to remember that she will If an event is certain to occur, the probability is 1. ■ pay back the $450 in interest as well as the principal, If an event is certain not to occur (impossible), ■ $2,500. Therefore, she will pay her uncle $2,500 + $450 the probability is 0. = $2,950. If you know the probability of all other events ■ In a simple interest problem, the rate is an annual, or occurring, you can ﬁnd the probability of the yearly, rate. Therefore, the time must also be expressed in remaining event by adding the known probabili- years. ties together and subtracting their total from 1. 420
– DATA ANALYSIS, STATISTICS, AND PROBABILITY – G raphs and Tables Broken-line graphs ■ Broken-line graphs illustrate a measurable change over time. If a line is slanted up, it repre- The GED exam will test your ability to analyze graphs sents an increase whereas a line sloping down and tables. Read each graph or table very carefully before represents a decrease. A ﬂat line indicates no reading the question. This will help you to process the change as time elapses. information that is presented. It is extremely important to read all of the information presented, paying special attention to headings and units of measure. Here is an se De Unit of Measure overview of the types of graphs you will encounter: rea cre Inc ase D se ec rea re Circle graphs or pie charts ■ a Inc se This type of graph is representative of a whole No Change and is usually divided into percentages. Each sec- tion of the chart represents a portion of the whole, and all of these sections added together will equal 100% of the whole. Change in Time S cientific Notation 25% Scientiﬁc notation is a method used by scientists to con- 40% vert very large or very small numbers to more manage- able ones. You will have to make a few conversions to scientiﬁc notation on the GED. Expressing answers in 35% scientiﬁc notation involves moving the decimal point and multiplying by a power of ten. Example Bar graphs ■ A space satellite travels 46,000,000 miles from Bar graphs compare similar things with differ- Earth. What is the number in scientiﬁc notation? ent length bars representing different values. Be sure to read all labels and legends, looking care- Step 1: Starting at the decimal point to the right fully at the base and sides of the graph to see what of the last zero, move the decimal point until the bars are measuring and how much they are only one digit remains to its left increasing or decreasing. 46,000,000 becomes 4.6. Comparison of Roadwork Funds Step 2: Count the number of places the decimal of New York and California was moved left (in this example, the decimal 2001–2005 Money Spent on New Roadwork 90 point was moved 7 places), and express it as a 80 power of 10: in Millions of Dollars 70 107 60 Step 3: Express the full answer in scientiﬁc nota- 50 KEY 40 tion by multiplying the reduced answer from New York 30 Step 1 by 107: California 20 4.6 × 107 10 0 2001 2002 2003 2004 2005 Year 421
– DATA ANALYSIS, STATISTICS, AND PROBABILITY – Example later. Do the easy problems ﬁrst. The GED is not An amoeba is .000056 inch long. What is its arranged with increasingly difﬁcult questions. length in scientiﬁc notation? The difﬁcult questions appear alongside the easier questions. Therefore, it is important to skip Step 1: Move the decimal point to the right until difﬁcult problems and come back to them. there is one digit other than zero to the left of Plugging in. ■ the decimal. There will be times when you should use the .000056 becomes 5.6 answer choices to ﬁnd the correct answer. This Step 2: Count the number of places moved to can be done when you have a problem that gives the right—5. However, because the value of the you a formula or equation. Plug in answers when number is being increased as it is expressed in you feel it will be quicker than solving the prob- scientiﬁc notation, it is written as a negative lem another way, and when you have enough exponent. information to do so. 10−5 Eliminating. ■ Step 3: Express the full answer in scientiﬁc Eliminate choices you know are wrong so that notation: you can spend more time considering choices .0000056 becomes 5.6 × 10−5 that might be right. It may sound like a simple strategy, but it can make a big difference. Making educated guesses. ■ G eneral Strategies for Math It’s important to remember you are not penal- Questions ized for a wrong answer. If you don’t know the answer to a question and you are approaching the Skipping and returning. time limit, simply use the last few minutes to ■ If you are unsure of what you are being asked make an educated guess to the remaining ques- to ﬁnd, if you don’t know how to solve a problem, tions. If you can eliminate some of the answer or if you will take a long time to ﬁnd the correct choices, you will improve your odds of getting answer, skip the question and come back to it it right. 422
GED CHAPTER 45 Mathematics Practice Questions NOW IT’S time to put all that you have learned about mathematics and problem solving into practice. In the following section, you will find 100 multiple-choice questions like those you will find on the GED Mathematics Test. D irections Read the following questions carefully and choose the best answer for each question. Some questions may refer to a ﬁgure, table, or graph. Be sure to answer every question; you will not be penalized for incorrect answers. Do not spend too much time on any one question so you can be sure to complete the questions in the allotted time. Record your answers on the answer sheet provided on the following page. Make sure you mark the answer in the circle that corresponds to the question. Note: On the GED, you are not permitted to write in the test booklet. Make any notes or calculations on a sep- arate piece of paper. 423
– LEARNINGEXPRESS ANSWER SHEET – A nswer Sheet 1. a b c d e 31. a b c d e 61. a b c d e 2. a b c d e 32. a b c d e 62. a b c d e 3. a b c d e 33. a b c d e 63. a b c d e 4. a b c d e 34. a b c d e 66. a b c d e 5. a b c d e 35. a b c d e 67. a b c d e 6. a b c d e 36. a b c d e 68. a b c d e 7. a b c d e 37. a b c d e 69. a b c d e 8. a b c d e 38. a b c d e 72. a b c d e 9. a b c d e 39. a b c d e 73. a b c d e 10. a b c d e 40. a b c d e 74. a b c d e 11. a b c d e 41. a b c d e 76. a b c d e 12. a b c d e 42. a b c d e 79. a b c d e 13. a b c d e 43. a b c d e 80. a b c d e 14. a b c d e 44. a b c d e 81. a b c d e 15. a b c d e 45. a b c d e 82. a b c d e 16. a b c d e 46. a b c d e 84. a b c d e 17. a b c d e 47. a b c d e 85. a b c d e 18. a b c d e 48. a b c d e 86. a b c d e 19. a b c d e 49. a b c d e 88. a b c d e 20. a b c d e 50. a b c d e 89. a b c d e 21. a b c d e 51. a b c d e 90. a b c d e 22. a b c d e 52. a b c d e 91. a b c d e 23. a b c d e 53. a b c d e 93. a b c d e 24. a b c d e 54. a b c d e 94. a b c d e 25. a b c d e 55. a b c d e 95. a b c d e 26. a b c d e 56. a b c d e 96. a b c d e 27. a b c d e 57. a b c d e 97. a b c d e 28. a b c d e 58. a b c d e 98. a b c d e 29. a b c d e 59. a b c d e 99. a b c d e 30. a b c d e 60. a b c d e 100. a b c d e For questions 64, 65, 70, 71, 75, 77, 78, 83, 87, and 92, see the answer grids that follow each question. 425