Math-Book-GMAT-Club

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ChordA line that links two points on a circle or curve.• A diameter is a chord that contains the center of the circle.• Below is a formula for the length of a chord if you know the radius and the perpendicular distance from thechord to the circle center. This is a simple application of Pythagoras' Theorem., where is the radius of the circle, is the perpendicular distance from the chordto the circle center.• In a circle, a radius perpendicular to a chord bisects the chord. Converse: In a circle, a radius that bisects achord is perpendicular to the chord, or In a circle, the perpendicular bisector of a chord passes through the centerof the circle.‐ 75 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Angles in a circleAn inscribed angle is an angle ABC formed by points A, B, and C on the circle's circumference.• Given two points A and C, lines from them to a third point B form the inscribed angle ∠ABC. Notice that theinscribed angle is constant. It only depends on the position of A and C.• If you know the lengthof the minor arc and radius, the inscribed angle is:A central angle is an angle AOC with endpoints A and C located on a circle's circumference and vertex O locatedat the circle's center. A central angle in a circle determines an arc AC.• The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central‐ 76 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
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For the latest version of the GMAT
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Number TheoryDefinitionNumber Theor
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• 1 (and ‐1) are divisors of ev
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other digits: 21‐(9+8+6+9)=‐11,
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Sum of n first positive integers:Su
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Converting Decimals to Fractions•
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Operations involving the same bases
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PERCENTDefinitionA percentage is a
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Absolute ValueDefinitionThe absolut
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satisfied (‐15 is not within (‐
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FactorialsDefinitionThe factorial o
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AlgebraScopeManipulation of various
Page 26 and 27: There is a common misconception tha
Page 28 and 29: RemaindersDefinitionIf and are posi
Page 30 and 31: A. 2B. 4C. 8D. 20E. 45divided by yi
Page 32 and 33: Example #10 (hard)When positive int
Page 34 and 35: Word Problems OverviewThe Following
Page 36 and 37: Key words: less than (implies subtr
Page 38 and 39: Distance/Speed/Time Word ProblemsWh
Page 40 and 41: In the next section we will learn h
Page 42 and 43: Time(3) = Time(1) + Time(2) ‐‐
Page 44 and 45: 3*x = 5*(x ‐ 20) ‐‐> x = 50 m
Page 46 and 47: Work Word ProblemsWhat is a ‘Work
Page 48 and 49: Example 3:Working together, printer
Page 50 and 51: Advanced Overlapping Sets ProblemsS
Page 52 and 53: the writing club. If 6 students sig
Page 54 and 55: two of the courses and 1 employee h
Page 56 and 57: Consider this problem to be an over
Page 58 and 59: Median The median of a triangle is
Page 60 and 61: • The midsegment is always parall
Page 62 and 63: Equilateral triangle all sides have
Page 64 and 65: • A right triangle where the angl
Page 66 and 67: Then the triangles ABC, CHB and CHA
Page 68 and 69: Quadrilateral A polygon with four '
Page 70 and 71: Squares A 4‐sided regular polygon
Page 72 and 73: • Area ‐ The usual way to calcu
Page 74 and 75: • A circle is the shape with the
Page 78 and 79: angle.• An inscribed angle is exa
Page 80 and 81: chords.‐ This becomes the theorem
Page 82 and 83: Coordinate GeometryDefinitionCoordi
Page 84 and 85: As you can see, the distance formul
Page 86 and 87: Lines in Coordinate GeometryIn Eucl
Page 88 and 89: The equation of a straight line tha
Page 90 and 91: Positive slopeHere, y increases as
Page 92 and 93: A horizontal line has a slope of ze
Page 94 and 95: Solution: We first find the slope o
Page 96 and 97: To answer, we must find the slope o
Page 98 and 99: Example #2Q: Find the point of inte
Page 100 and 101: ParabolaA parabola is the graph ass
Page 102 and 103: Standard DeviationDefinitionStandar
Page 104 and 105: Standard deviation of is . Decrease
Page 106 and 107: ProbabilityDefinitionA number expre
Page 108 and 109: Therefore, the probability of getti
Page 110 and 111: 2) Reversal combinatorial approach:
Page 112 and 113: Combinations & PermutationsDefiniti
Page 114 and 115: 1. The total number of arrangements
Page 116 and 117: is the first termDefining Propertie
Page 118 and 119: Solution(1) a1=8, does not tell us
Page 120 and 121: CuboidA cube is the 3‐D generaliz
Page 122 and 123: ConeA cone is a 3‐D object obtain
Page 124 and 125: Volume =Surface Area w/o base =Surf
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(2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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