SAT MATH CHECKLIST: Facts and Formulas - Ivy Global

SAT MATH CHECKLIST:Facts and FormulasNumbers and ArithmeticSum of consecutive integersn + n + 1 + n + 2 …Sum of the consecutive integers from 1to an integer n(n + 1) × n 2Adding or multiplying even or oddintegerseven + even = evenodd + odd = evenodd + even = oddeven ⨯ even = evenodd ⨯ odd = oddodd ⨯ even = evenCross-multiplicationIf a b = c d, then ad = bc.Percent increase or percent decreasecange in amountoriginal amount × 100%Exponent rulesa 1 = aa 0 = 1a −m = 1a ma m a n = a m+na m= am−nan (a m ) n = a mna m b m = (ab) ma mb m = ( a b )ma m nn = a mAbsolute valueIf x = 4, then x = 4 or x = −4If x < 4, then − 4 < x < 4If x > 4, then x < −4 or x > 4Ivy Global

Algebra and FunctionsDifference of squaresa 2 − b 2 = (a + b)(a − b)Properties of inequalitiesThe inequality is reversed by taking the negative of both sides taking the reciprocal of both sides multiplying or dividing both sides by a negativenumberRatesdistance = rate × timeDomain of a functionThe set of all the “input” numbers for which the functionstill worksRange of a functionThe set of all the “output” numbersFormula for slopem = riserun = y 2 − y 1x 2 − x 1Facts about slopeHorizontal lines have slopes of zero.Vertical lines have undefined slopes.Non-vertical parallel lines have equal slopes.Non-vertical perpendicular lines have slopeswhose product is -1.Linear functionsy = mx + bQuadratic functionsy = ax 2 + bx + cTranslation of y = f(x), a unitsvertically and b units horizontallyy − a = f(x − b)Ivy Global

GeometryAngle sumsThe sum of any number of angles that form astraight line is 180°.The sum of any number of angles around a point is360°.Two angles that add to 90° are calledcomplementary angles.Two angles that add to 180° are calledsupplementary angles.Sum of the interior angles of a polygonwith n sides180°(n − 2)Vertical anglesa = d and b = cTransversalsa = d = e = b = c = f = gc + e = 180° and d + f = 180°Exterior angle of a triangled = a + bIvy Global

Classification of trianglesPythagorean Theorem a 2 + b 2 = c 2Special right trianglesTriangle inequalityThe sum of the lengths of two sides of a triangle is alwaysgreater than the length of the third sideArea of a triangleA = 1 2 bArea of a parallelogram or rectangleA = bArea of a trapezoidA = 1 (a + b)2Area and circumference of a circleA = πr 2C = πd = 2πrIvy Global

Arc length (L) and area (A)L2πr = x°360°Aπr 2 = x°360°Volume and surface area of arectangular solidV = lwSA = 2lw + 2w + 2lDiagonal of a rectangular solid d 2 = l 2 + w 2 + 2Volume and surface area of a rightcylinderV = πr 2 SA = 2πr 2 + 2πrDistance formula d = (x 2 − x 1 ) 2 + (y 2 − y 1 ) 2Midpoint formula ( x 1 + x 2, y 1 + y 2)2 2Ivy Global

Data Analysis and StatisticsCounting principleIf there are m ways to complete the first and n ways tocomplete the second, then there are m × n ways tocomplete the two of themProbabilitynumber of favorable outcomesnumber of possible outcomesAverageaverage = sumnIvy Global