Math-Book-GMAT-Club

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• A circle is the shape with the largest area for a given length of perimeter (has the highest area to length ratiowhen compared to other geometric figures such as triangles or rectangles)• All circles are similar• To form a unique circle, it needs to have 3 points which are not on the same line.Circumference, Perimeter of a circleGiven a radiusformula:of a circle, the circumference can be calculated using theIf you know the diameterformula:If you know the areaformula:of a circle, the circumference can be found using theof a circle, the circumference can be found using theArea enclosed by a circleGiven the radiusof a circle, the area can be calculated using the formula:If you know the diameterof a circle, the area can be found using the formula:If you know the circumferenceof a circle, the area can be found using the formula:SemicircleHalf a circle or a closed shape consisting of half a circle and a diameter of that circle.‐ 73 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
• The area of a semicircle is half the area of the circle from which it is made:• The perimeter of a semicircle is not half the perimeter of a circle. From the figure above, you can see that theperimeter is the curved part, which is half the circle, plus the diameter line across the bottom. So, the formula forthe perimeter of a semicircle is:• The angle inscribed in a semicircle is always 90°.• Any diameter of a circle subtends a right angle to any point on the circle. No matter where the point is, thetriangle formed with diameter is always a right triangle.‐ 74 ‐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
Page 24 and 25: 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 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 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
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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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