SAT Formul a Shee t Heart of Algebra Lines General Standard Form: Ax + By = C Midpoint: M = (____ 1 2 2 , ____ 1 2 2 ) Point-Slope Form: (y - y1) = m(x - x1) Distance: d = √( x2 - x1 ) 2 + (y2 - y1 ) 2 Slope-Intercept Form: y = mx + b Average Velocity: Vavg = __________ total distance total time x + x y + y ______________ y - y Slope of a Line: m = ____ x2 - x1 2 1 Problem Solving and Data Analysis Growth and Decay Statistics and Probability General Form: A = P (1 ± r) t Arithmetic Mean: _____________ Number of Terms Continuous Growth/Decay: A = Pert Percent Change: _______ New - Old × 100% Old Sum of the Terms Compounding Growth/Decay: A = P (1 ± __ nr ) nt Exclusive OR: P(A or B) = P(A) + P(B) - P(A & B) ( ) Conditional Probability: P (A | B)= ______ P PA & B ( B) Passport to Advanced Math Quadratics (ax2 + bx + c) Equations of Circles ______ –b ± √ b 2 - 4ac ________ Quadratic Formula: x = 2a Vertex of Parabola: x = __ –b 2a Equation of a circle with center (h, k) and radius r: (x - h) 2 + (y - k) 2= r 2 Additional Topics in Math The Circle Area: A = πr2 A Circumference: C = 2πr θ Arc length (in degrees): L (A, B)= ____ 36 0 o ∙ 2πr θ 2 Sector Area (in degrees): A OB = ____ 36 0 o ∙ π r O θ B 1 Areas Volumes Parallelogram: A = bh Cube: V = s3 1 2 Trapezoid: A = __ (b 1 + b 2)h Rectangular Prism: V = lwh 1 2 Triangle: A = _ bh Cylinder: V = πr 2h 1 Regular Polygon: A = _ aPor A = ________ n s___ 2 4tan( 180˚ ) n 2 Cube: SA = 6s Sphere: V = _ 43 πr 3 Angles Angles and Parallel Lines 2 Sum of Interior Angles: = 180(n - 2)˚ 180(n - 2)˚ Each Interior Angle: = _______ n Sum of Exterior Angles: = 360˚ 360˚ Each Exterior Angles: = ___ n Special Right Triangles Trigonometry: c os(90° - x)= sin x Trig Ratios Pythagorean Identities opposite sin x = _________ hypotenuse sin 2x + cos 2x = 1 adjacent cos x = _________ hypotenuse tan 2x + 1 = sec 2x opposite sin x _________ tan x = ____ cos x = hypotenuse 1 + cot 2x = csc 2x hypotenuse 1 csc x = ____ sin x = _________ opposite hypotenuse 1 sec x = ____ cos x = _________ adjacent adjacent 1 cot x = ____ tan x = ____ cos x = _______ opposite sin x 2
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