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33Math NotesWe’ll discuss many of the concepts in this chapter in depth later. But for now, we need a brief review ofthese concepts for many of the problems that follow.1.To compare two fractions, cross-multiply.The larger product will be on the same side as thelarger fraction.Example:Given56vs.67.Cross-multiplying gives57vs.66, or 35 vs. 36.Now 36 is largerthan 35, so67is larger than56.2.Taking the square root of a fraction between 0 and 1 makes it larger.Example:14=12and12is greater than14.Caution:This is not true for fractions greater than 1.For example,94=32.But32<94.3.Squaring a fraction between 0 and 1 makes it smaller.Example:122=14and14is less than12.4.ax2ax()2.In fact,a2x2=ax()2.Example:322=34=12.But32()2=62=36.This mistake is often seen in the following form:-x2= -x()2.To see more clearly why this is wrong, write-x2= -1()x2, which is negative.But-x()2= -x()-x()=x2, which is positive.Example:-52= -1()52= -1()25= -25.But-5()2= -5()-5()=55=25.5.1ab1ab.In fact,1ab=1aband1ab=ba.Example:123=1213=16.But123=132=32.6.–(a+b)a+b.In fact, –(a+b) = –ab.Example:–(2 + 3) = –5.But –2 + 3 = 1.Example:–(2 +x) = –2 –x.7.Memorize the following factoring formulas—they occur frequently on the GRE.A.x2-y2=x+y()x-y()B.x2±2xy+y2=x±y()2C.a(b+c) =ab+acKolby, Jeff, and Derrick Vaughn. GRE Math Bible, Nova Press, 2008. ProQuest Ebook Central, .Created from gmu on 2018-01-28 05:42:58.Copyright © 2008. Nova Press. All rights reserved.
34GRE Math Bible8.Know these rules for radicals:A.xy=xyB.xy=xy9.Pythagorean Theorem(For right triangles only):abcc2=a2+b2Example:What is the area of the triangle to the right?5h
Since the triangle is a right triangle, the Pythagorean Theorem applies:h2+32=52, wherehis the heightof the triangle.Solving forhyieldsh= 4.Hence, the area of the triangle is12base()height()=12(3)(4)=6.The answer is (A).10.When parallel lines are cut by a transversal, three important angle relationships are formed:Alternate interiorangles are equal.aaCorresponding anglesare equal.ccInterior angles on the same side of thetransversal are supplementary.aba+b=180˚11.In a triangle, an exterior angle is equal to the sum of its remote interior angles and thereforegreater than either of them.eabe=a+bande>aande>b12.A central angle has by definition the same measure as its intercepted arc.60˚60˚Kolby, Jeff, and Derrick Vaughn. GRE Math Bible, Nova Press, 2008. ProQuest Ebook Central, .Created from gmu on 2018-01-28 05:42:58.Copyright © 2008. Nova Press. All rights reserved.
Math Notes3513.An inscribed angle has one-half the measure of its intercepted arc.

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Term
Fall
Professor
LawrenceWhite
Tags
Prime number, Nova press, Derrick Vaughn
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