Transcription of NUMBER AND QUANTITY - ACT
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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)GEOMETRYALGEBRAL inear Graphsslope-intercept formula: y = mx +bm = slope = (y1 y2) / (x1 x2)QuadraticsFOIL (First, Outer, Inner, Last).
discriminant: b² – 4ac If . . . b = y-intercept = (0,b) distance formula: √[(y1 – y2)² + (x1 – x2)²] midpoint formula: midpoint = [(x1 + x2)/2, (y1 + y2)/2] quadratic formula: X= -b +√b2 - 4ac 2a • discriminant > 0 2 ˜ real solutions • discriminant = 0 1 ˜ real solution • ˜discriminant < 0 no real solutions O y x (x y
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