Math-Book-GMAT-Club

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angle.• An inscribed angle is exactly half the corresponding central angle. Hence, all inscribed angles that subtend thesame arc are equal. Angles inscribed on the arc are supplementary. In particular, every inscribed angle thatsubtends a diameter is a right angle (since the central angle is 180 degrees).Arcs and SectorsA portion of the circumference of a circle.• Major and Minor Arcs Given two points on a circle, the minor arc is the shortest arc linking them. The major arc‐ 77 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
is the longest. On the GMAT, we usually assume the minor (shortest) arc.• Arc Length The formula the arc measure is:, where C is the central angle of the arc in degrees.Recall that is the circumference of the whole circle, so the formula simply reduces this by the ratio of thearc angle to a full angle (360). By transposing the above formula, you solve for the radius, central angle, or arclength if you know any two of them.• Sector is the area enclosed by two radii of a circle and their intercepted arc. A pie‐shaped part of a circle.• Area of a sector is given by the formula:, where: C is the central angle in degrees. Whatthis formula is doing is taking the area of the whole circle, and then taking a fraction of that depending on thecentral angle of the sector. So for example, if the central angle was 90°, then the sector would have an area equalto one quarter of the whole circle.Power of a Point TheoremGiven circle O, point P not on the circle, and a line through P intersecting the circle in two points. The product ofthe length from P to the first point of intersection and the length from P to the second point of intersection isconstant for any choice of a line through P that intersects the circle. This constant is called the "power of pointP".If P is outside the circle:secants.‐ This becomes the theorem we know as the theorem of intersectingIf P is inside the circle:‐ 78 ‐GMAT Club Math Bookpart of GMAT ToolKit iPhone App
Page 2 and 3:
For the latest version of the GMAT
Page 4 and 5:
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 76 and 77: ChordA line that links two points o
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
Page 126: (2) : Sum of sides = . Not sufficie
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Math-Book-GMAT-Club

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