Download Act Formula Sheet and more Cheat Sheet Mathematics in PDF only on Docsity! 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 logab = c — ac = b STATISTICS AND PROBABILITY Percents Statistics percent = part / whole × 100% % symbol = divide by 100 a% of b = a/100 × b = a × b/100 percent change = change / original average (mean) = sum of terms / number of terms median = middle number (or average of 2 middle numbers) mode = most common number range = biggest – smallest Probability and Counting Techniques probability = number of desired terms / total number of terms P(event happens) + P(event doesn’t happen) = 1 P(A and B) = P(A) × P(B) GEOMETRY ALGEBRA Linear Graphs slope-intercept formula: y = mx +b m = slope = (y1 – y2) / (x1 – x2) Quadratics FOIL (First, Outer, Inner, Last): (a + b)(c + d) = ac + ad + bc + bd 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 (x y vertical angles are congruent 45 : 45 : 90 triangle ratio: x : x : x√2 30 : 60 : 90 triangle ratio: x : x√3 : 2x angles of a triangle add to 180° area of a triangle = ½ × base × height Pythagorean theorem: a² + b² = c² Triangles supplementary angles add to 180° complementary angles add to 90° Lines and Angles FUNCTIONS Function Notation fog(x) = f(g(x)) note: this is different from fg(x), which is f(x) × g(x) Trigonometry on the Coordinate Plane π radians = 180°
