Course Hero Logo

Created from gmu on 2018 01 28 054258 copyright 2008

Course Hero uses AI to attempt to automatically extract content from documents to surface to you and others so you can study better, e.g., in search results, to enrich docs, and more. This preview shows page 20 - 24 out of 88 pages.

Created from gmu on 2018-01-28 05:42:58.Copyright © 2008. Nova Press. All rights reserved.
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.

Upload your study docs or become a

Course Hero member to access this document

Upload your study docs or become a

Course Hero member to access this document

End of preview. Want to read all 88 pages?

Upload your study docs or become a

Course Hero member to access this document

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

Newly uploaded documents

Show More

Newly uploaded documents

Show More

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture