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NUMBER AND QUANTITY - ACT

ACT FORMULA SHEETMATHan = a1 + c(n 1)an = a1(c)n 1 NUMBER AND QUANTITYS equencesLogarithmsRatesSequence with a constant of c:arithmetic sequence:geometric sequence:distance = speed timevariation: QUANTITY = rate timelogab = c ac = bSTATISTICS AND PROBABILITYP ercentsStatisticspercent = part / whole 100%% symbol = divide by 100a% of b = a/100 b = a b/100percent change = change / originalaverage (mean) = sum of terms / NUMBER of termsmedian = middle NUMBER (or average of 2 middle numbers)mode = most common numberrange = biggest smallestProbability and Counting Techniquesprobability = NUMBER of desired terms / total NUMBER of termsP(event happens) + P(event doesn t happen) = 1P(A and B) = P(A) P(B)

ACT FORMULA SHEET MATH an = a1 + c(n – 1) an = a1(c)n – 1 NUMBER AND QUANTITY Sequences Logarithms Rates Sequence with a constant of c: arithmetic sequence: geometric sequence: distance = speed × time variation: quantity = rate × time log a b = c ˜ ac = b STATISTICS AND PROBABILITY Percents Statistics percent = part / whole × 100% ...

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Transcription of NUMBER AND QUANTITY - ACT

1 ACT FORMULA SHEETMATHan = a1 + c(n 1)an = a1(c)n 1 NUMBER AND QUANTITYS equencesLogarithmsRatesSequence with a constant of c:arithmetic sequence:geometric sequence:distance = speed timevariation: QUANTITY = rate timelogab = c ac = bSTATISTICS AND PROBABILITYP ercentsStatisticspercent = part / whole 100%% symbol = divide by 100a% of b = a/100 b = a b/100percent change = change / originalaverage (mean) = sum of terms / NUMBER of termsmedian = middle NUMBER (or average of 2 middle numbers)mode = most common numberrange = biggest smallestProbability and Counting Techniquesprobability = NUMBER of desired terms / total NUMBER of termsP(event happens) + P(event doesn t happen) = 1P(A and B) = P(A) P(B)

2 GEOMETRYALGEBRAL inear Graphsslope-intercept formula: y = mx +bm = slope = (y1 y2) / (x1 x2)QuadraticsFOIL (First, Outer, Inner, Last): (a + b)(c + d) = ac + ad + bc + bddiscriminant: b 4acIf .. b = y-intercept = (0,b)distance formula: [(y1 y2) + (x1 x2) ]midpoint formula: midpoint = [(x1 + x2)/2, (y1 + y2)/2]quadratic formula: X= -b + b2 - 4ac2a discriminant > 0 2 real solutions discriminant = 0 1 real solution discriminant < 0 no real solutions Oyx(xy(xyvertical angles are congruent45 : 45 : 90 triangle ratio: x : x : x 230 : 60 : 90 triangle ratio: x : x 3 : 2xangles of a triangle add to 180 area of a triangle = base heightPythagorean theorem.))

3 A + b = c Trianglessupplementary angles add to 180 complementary angles add to 90 Lines and AnglesFUNCTIONSF unction Notationfog(x) = f(g(x))note: this is different from fg(x), which is f(x) g(x)Trigonometry on the Coordinate Plane radians = 180 Triangles and TrigonometrySOH-CAH-TOA:sin(x) = opposite / hypotenusecos(x) = adjacent / hypotenusetan(x) = opposite / adjacentsin (x) + cos (x) = 1sin(x) = cos(90 x)cos(x) = sin(90 x)Sine (sin)Cosine (cos)Tangent (tan)oppositehypotenuse354534adjacenthyp otenuseoppositeadjacentB534 CAarea of a rectangle = length widtharea of a parallelogram = base heightPolygonstrapezoid area = average of bases height = (b1 + b2)/2 hperimeter = sum of sidessum of angles in n-sided figure = (n 2)

4 180 x45 45 x 2xarea of circle = r circumference of circle = 2 rdiameter of circle = 2rradius = r(x h) + (y k) = r center of circle = (h, k)Vertex form for a parabola:y = a(x h) + kvertex = (h, k)axis of symmetry: x = hCircles and Parabolascircle arc length = central angle / 360 circumferencecircle sector area = central angle / 360 areavolume of rectangular prism: V = lwhvolume of right cylinder: V = r h3D Figuressurface area of rectangular prism: 2(length width + length height + width height)O(h, k)yxy = a(x h)2 + kx = h0(h,k)rxy(x-h)2+(y-k)2=r2


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