Math-Book-GMAT-Club

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ParabolaA parabola is the graph associated with a quadratic function, i.e. a function of the form .The general or standard form of a quadratic function is, or in functionform, , where is the independent variable, is the dependent variable, and , ,and are constants. The larger the absolute value of , the steeper (or thinner) the parabola is, since the value of y isincreased more quickly. If is positive, the parabola opens upward, if negative, the parabola opens downward.x‐intercepts: The x‐intercepts, if any, are also called the roots of the function. The x‐intercepts are the solutionsto the equationand can be calculated by the formula:andExpressionis called discriminant:If discriminant is positive parabola has two intercepts with x‐axis;If discriminant is negative parabola has no intercepts with x‐axis;If discriminant is zero parabola has one intercept with x‐axis (tangent point).y‐intercept: Given , the y‐intercept is , as y intercept means the value of y when x=0.Vertex: The vertex represents the maximum (or minimum) value of the function, and is very important incalculus.‐ 99 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
The vertex of the parabola is located at point .Note: typically just is calculated and plugged in for x to find y.Practice from the GMAT Official Guide:The Official Guide, 12th Edition: DT #39; PS #9; PS #25; PS #39; PS #88; PS #194; PS #205; PS #210; PS #212; PS#229; DS #69; DS #75; DS #93; DS #94; DS #108; DS #121; DS #149; DS #164;The Official Guide, Quantitative 2th Edition: PS #21; PS #85; PS #102; PS #123; DS #22;The Official Guide, 11th Edition: DT #39; PS #7; PS #23; PS #36; PS #89; PS #199; PS #222; PS #227; PS #229; PS#248; DS #15; DS #78; DS #85; DS #124‐ 100 ‐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
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There is a common misconception tha
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RemaindersDefinitionIf and are posi
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A. 2B. 4C. 8D. 20E. 45divided by yi
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Example #10 (hard)When positive int
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Word Problems OverviewThe Following
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Key words: less than (implies subtr
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Distance/Speed/Time Word ProblemsWh
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In the next section we will learn h
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Time(3) = Time(1) + Time(2) ‐‐
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3*x = 5*(x ‐ 20) ‐‐> x = 50 m
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Work Word ProblemsWhat is a ‘Work
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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 76 and 77: ChordA line that links two points o
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 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
Page 126: (2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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