Download Quantitative Reasoning Formulas: Trigonometry, Statistics, and Geometry and more Exams Nursing in PDF only on Docsity! DAT Quantitative Reasoning Formulas questions and answers 30-60-90 Triangle - x-x(√3)-2x 45-45-90 Triangle - 1-1-(√2) Midpoint formula - (x₁+x₂)/2, (y₁+y₂)/2 avg the X and Y values Distance formula - d = √(x₂ - x₁)² + (y₂ - y₁)² standard deviation (variance) - √(∑(x-xavg)²/n) Standard deviation = √variance Law of Sines - sin(A)/a = sin(B)/b = sin(C)/c Sin and Cos Relationships - sin(θ) = cos(90°-θ) cos(θ) = sin(90°-θ) DAT Quantitative Reasoning Formulas questions and answers sin(-θ) = -sin(θ) cos(-θ) = cos(θ) sin²(θ) + cos²(θ) = 1 Cosecant (csc) - 1/sin = hypotenuse/opposite Cotangent (cot) - 1/tan = adjacent/opposite Secant (sec) - 1/cos = hypotenuse/adjacent Basic Trigonometric Functions - cos = x, sin = y, tan = y/x, cot = x/y Foci Formula - a²−b²=c² where x²/a² + y²/b² = 1 and c = distance from origin to foci DAT Quantitative Reasoning Formulas questions and answers Number of diagonals = (1/2) n(n-3)∙ n = number of sides S = length from center to a corner volume of sphere - (4/3)πr³ Combined Work - 1/t₁ + 1/t₂ + 1/t₃ ... = 1/total Combinatrics - n!/(a! b! c! ...)∙ ∙ ∙ The number of ways n things can be ordered when a of them are identical, b of them are identical, c of them are identical, etc. ex) TENNESSEE 9!/(2! x 2! x 4!) Angles of a Circle - Inscribed angle of a circle = 1/2 intercepting arc Central angle of a circle = intercepting arc DAT Quantitative Reasoning Formulas questions and answers External angle = (1/2)(difference of intercepting angles) Inscribed angle = angle formed by two chords in a circle which have a common end point that forms the vertex of the inscribed angle Unit Circle - (x²)(y²) - = (xy)² (x²)(x³) - = x²⁺³ x²/y² - = (x/y)² x²/x³ - = x²⁻³ x⁻² - =1/x² area of circle - πr² DAT Quantitative Reasoning Formulas questions and answers area of sphere - 4πr² (surface area) area of cylinder - 2πrh+2πr² area of ellipse - πab area of quadrilateral - bh area of triangle - ½bh area of equilateral triangle - (s²√3)/4 volume of cylinder - πr²h log(X) + log(Y) = - log(X Y)∙ log(X) - log(Y) = - log(X/Y) DAT Quantitative Reasoning Formulas questions and answers n ---- if interest is compounded quarterly (every 3 months, then the length of one year is 4 periods.) Probability two events occur: MULTIPLY 16 total disks = 4 blue 12 green , two disk removed.. what is the probability the first is blue and second is green - (1) ⁴/₁₆ = ¹/₄ (2) only 15 disks left --> ¹²/₁₅ = ⁴/₅ multiply (1)x(2) 1/4 × 4/5= 4/20 = 1/5 Probability that one out of two events occur: bag w/ 20 tiles, 11 marked with #'s (1-11) and 9 marked with letters A-I .. what is the P(even #) or P(vowel) - ADD (5/20) + (3/20) = 8/20 = 2/5 DAT Quantitative Reasoning Formulas questions and answers Probability that at least one out of 2 events occur - P(A) + P(B) - P(A&B) Cos(60°) - = 1/2 Cos(45°) - = √2 / 2 Cos(30°) - = √3 / 2 Sin(60°) - √3 / 2 Sin(45°) - √2 / 2 Sin(30°) - 1/2 Tan(60°) - = √3 Tan(45°) - =1 DAT Quantitative Reasoning Formulas questions and answers Tan(30°) - =1/ √3 probability that multiple events occur : Multiply - P(1) x P(2) x P(3) sin x = (π-x) - speed - distance/time sin(2x) = - 2sin(x)cos(x) r³/² - = (²√r)³ circumference - 2 x pi x r standard equation of circle - (x-h)² + (y-k)² = r² 1 + cot²(θ) = - csc² (θ)
