86. e. Similar triangles have the same angle measures. Congruent triangles have the same angle meas- ures and the same side lengths. From the given information, you cannot know if the side lengths are the same, so you can conclude only that the triangles are similar. 87. (1,1). Plot the points given in the problem and com- pete the parallelogram. Remember that in a par- allelogram, both pairs of opposite sides are equal and parallel. 88. e. The median time is the middle time. There is no way of knowing how far behind the median the slowest runner was. 89. b. The steepest rise on the graph was from April 23 to April 30. The symbol indicates that it was in the Midwest. 90. d. The prices for the West Coast have been rising steadily by 2 or 3 cents each week. On May 7, the price on the West Coast is a little beneath $1.80. If it rises 2 or 3 cents, it should be at about $1.82 by the following week. The question gives no reason to expect a sudden decline in price or a sharp increase. 91. b. Add the times and multiply by 9 cents: 19 + 24 + 8 = 51 minutes; 51 × .09 = $4.59. 92. 56. Let x represents the amount that Christian put in and 2x − 20 represents Maggie’s contribution. Solve the equation. x + 2x − 20 = 94 3x = 114 x = 38 Christian put in $38 and Maggie put in 94 − 38 = $56. 93. d. The number of games played is the total of the wins and losses, (20 + 15 = 35). Write the ratio and simplify. ᎏ 2 3 0 5 ᎏ = ᎏ 4 7 ᎏ . 94. b. Use the Pythagorean theorem: 25 2 + 9 2 = c 2 : c = ͙25 2 + 9 ෆ 2 ෆ = ͙625 + ෆ 81 ෆ = ͙706 ෆ 95. b. Use the order of operations. −3 × 5 2 + 2(4 − 18) + 3 3 −3 × 25 + 2(−14) + 27 −75 + (−28) + 27 −76 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 6 7 8 9 0 • / 1 2 3 4 5 7 8 9 0 • 56 1 2 −3 4 −5 −6 0 1 −2 3 4 5 6 −1 2 3 −4 5 −6 −1 −2−3−4 −5 6 – GED MATHEMATICS PRACTICE QUESTIONS– 455 96. e. ᭝ABC is a right triangle, but you have no way of knowing which angle is a right angle, so elimi- nate choice a. Regardless of the type of triangle, the sum of the measure of the interior angles of triangle must be 180°. 97. c. You can try each combination of sides in the Pythagorean theorem. Only 6, 8, and 10 will work. 6 2 + 8 2 = 10 2 , 36 + 64 = 100, 100 = 100. 98. b. A four-sided figure with only one pair of paral- lel sides is a trapezoid. 99. e. A closet is the shape of a rectangular solid. To find the volume, multiply. V = lwh. 7(4)(8) = 224 cubic feet. 100. e.Use the Pythagorean theorem. If a 2 + b 2 = c 2 and c is the hypotenuse, then b 2 = c 2 − a 2 or x 2 = 15 2 − 6 2 . – GED MATHEMATICS PRACTICE QUESTIONS– 456 Glossary of Terms: Mathematics base a number used as a repeated factor in an expo- nential expression. In 8 5 , 8 is the base number. base 10 see decimal numbers binary system one of the simplest numbering sys- tems. The base of the binary system is 2, which means that only the digits 0 and 1 can appear in a binary rep- resentation of any number. circumference the distance around the outside of a circle composite number any integer that can be divided evenly by a number other than itself and 1. All num- bers are either prime or composite. counting numbers all whole numbers, with the exception of 0 decimal a number in the base 10 number system. Each place value in a decimal number is worth ten times the place value of the digit to its right. denominator the bottom number in a fraction. The denominator of ᎏ 1 2 ᎏ is 2. diameter a chord that passes through the center of a circle and has endpoints on the circle difference the result of subtracting one number from another divisible by capable of being evenly divided by a given number, without a remainder dividend the number in a division problem that is being divided. In 32 ÷ 4 = 8, 32 is the dividend. even number a counting number that is divisible by 2 expanded notation a method of writing numbers as the sum of their units (hundreds, tens, ones, etc.). The expanded notation for 378 is 300 + 70 + 8. exponent a number that indicates an operation of repeated multiplication. For instance, 3 4 indicates that the number 3 should be multiplied by itself 4 times. factor one of two or more numbers or variables that are being multiplied together fractal a geometric figure that is self-similar; that is, any smaller piece of the figure will have roughly the same shape as the whole improper fraction a fraction whose numerator is the same size as or larger than its denominator. Improper fractions are equal to or greater than 1. integer all of the whole numbers and negative num- bers. Examples are −3, −2, −1, 0, 1, 2, and 3. Note that integers d o not include fractions or decimals. multiple of a multiple of a number has that number as one of its factors. 35 is a multiple of 7; it is also a multiple of 5. negative number a real number whose value is less than zero numerator the top number in a fraction. The numerator of ᎏ 1 4 ᎏ is 1. odd number a counting number that is not evenly divisible by 2 percent a ratio or fraction whose denominator is assumed to be 100, expressed using the % sign. 98% is equal to ᎏ 1 9 0 8 0 ᎏ . perimeter the distance around the outside of a polygon polygon a closed two-dimensional shape made up of three or more line segments that are joined together positive number a real number whose value is greater than zero prime number a real number that is divisible by only two positive factors: 1 and itself product the result when two numbers are multiplied together proper fraction a fraction whose denominator is larger than its numerator. Proper fractions are equal to less than 1. proportion a relationship between two equivalent sets of fractions in the form ᎏ a b ᎏ = ᎏ d c ᎏ quotient the result when one number is divided into another radical the symbol used to signify a root operation radius any line segment from the center of the circle to a point on the circle. The radius of a circle is equal to half its diameter. ratio the relationship between two things, expressed as a proportion real numbers include fractions and decimals in addition to integers reciprocal one of two numbers that, when multi- plied together, give a product of 1. For instance, since ᎏ 3 2 ᎏ × ᎏ 2 3 ᎏ is equal to 1, ᎏ 3 2 ᎏ is the reciprocal of ᎏ 2 3 ᎏ . remainder the amount left over after a division problem using whole numbers. Divisible numbers always have a remainder of zero. – GED MATHEMATICS PRACTICE QUESTIONS– 457 root (square root) one or two (or more) equal fac- tors of a number. The square root of 36 is 6, because 6 × 6 = 36.The cube root of 27 is 3 because 3 × 3× 3 = 27. simplify terms to combine like terms and reduce an equation to its most basic form variable a letter, often x, used to represent an unknown number value in a problem whole numbers 0, 1, 2, 3, and so on. They do not include negatives, fractions, or decimals. – GED MATHEMATICS PRACTICE QUESTIONS– 458 459 APPENDIX A Online Resources GED Test Preparation www.acenet.edu/calec/ged—The official GED site. www.LearningExpressFreeOffer.com—Offers FREE online GED practice exams. GED Math www.LearningExpressFreeOffer.com—Offers FREE online GED Math practice exams. www.algebrahelp.com—Offers online algebra help. www.cne.gmu.edu/modules/dau/algebra/algebra_frm.html—Offers a review of basic algebraic concepts as well as practice problems and their solutions. www.ies.co.jp/math/products/geo1/menu.html—Offers a review of basic geometric concepts, principals, and formulas. www.math.rice.edu/~lanius/geom/index.html—Offers a variety of geometry exercises. http://cite.telecampus.com/GED/math.html—Offers a list of formulas commonly used on the GED Mathematics section. www.webmath.com—Offers the answer and an analysis of any math question typed into the system. GED Science www.learnatest.com—Offers online GED Science practice exams. www.scicentral.com—Offers a wide variety of science articles. www.pbs.org/wgbh/aso—Offers a history of science and biographies of famous scientists. highered.mcgrawhill.com/sites/0809222302—Offers practice GED Science questions and answers. GED Social Studies www.learnatest.com—Offers online GED Social Studies practice exams. www.historycentral.com/index.html—Offers history reading selections from 5,500 B.C. to the present. www.historychannel.com—Offers a wide variety of history materials and information. www.nationalgeographic.com/resources/ngo/maps— Offers an assortment of downloadable maps. www.tourolaw.edu/patch/supremecourtcases.asp— Offers summaries of landmark Supreme Court cases. www.constitutioncenter.org—Offers basic facts about the U.S. Constitution. www.founding.com/home.htm—A guide to the Declaration of Independence. GED Language Arts www.LearningExpressFreeOffer.com—Offers FREE online GED Language Arts practice tests. www.utexas.edu/cee/dec/scoring/hints.html—Offers strategies for the GED essay. www.ket.org/ged2002/writing—Offers practice multiple-choice and essay questions to help you prepare for the GED Language Arts section. http://writing.richmond.edu/writersweb—Explores all aspects of the writing process. Test-Taking Skills www.d.umn.edu/student/loon/acad/strat/test_take .html—Offers general test-taking strategies. www.studygs.net/tstprp.htm—Offers six test-taking strategies. www.muskingum.edu/~cal/database/general/testtaking .html—Offers a wide variety of test-taking and learning strategies. www.bucks.edu/~specpop/tests.htm—Offers test- taking strategies. www.testtakingtips.com—Offers ways to improve your test-taking skills. www.mtsu.edu/~studskl/teststrat.html—Offers survival strategies for taking tests. www.brazosport.cc.tx.us/~lac/objtest.htm—Offers tips for improving your objective test-taking skills. www.uno.edu/~counserv/cserv_selfhelp_testanxiety .htm—Offers test-taking strategies for people who experience test anxiety. – APPENDIX A: ONLINE RESOURCES– 460 . is the hypotenuse, then b 2 = c 2 − a 2 or x 2 = 15 2 − 6 2 . – GED MATHEMATICS PRACTICE QUESTIONS– 456 Glossary of Terms: Mathematics base a number used as a repeated factor in an expo- nential. 27 −76 1 2 3 4 5 6 7 8 9 • 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 5 6 7 8 9 0 • / 1 2 3 4 6 7 8 9 0 • / 1 2 3 4 5 7 8 9 0 • 56 1 2 −3 4 −5 −6 0 1 −2 3 4 5 6 −1 2 3 −4 5 −6 −1 −2−3−4 −5 6 – GED MATHEMATICS PRACTICE QUESTIONS– 455 96. e. ᭝ABC is a right triangle, but you have no way of knowing. division problem using whole numbers. Divisible numbers always have a remainder of zero. – GED MATHEMATICS PRACTICE QUESTIONS– 457 root (square root) one or two (or more) equal fac- tors of a