Cheatography

# Quantitative Methods Midterm Cheat Sheet by rockcollector2

### Fraction Rules

 Common Denomi­nators a/b + c/d = ad + bc/bd Multip­lic­ation a/b * c/d = ac/bd Reciprocal 1/(a/b) = b/a

### Lines

 Given point (c,d) and slope m, the unique line that satisfies this is the set of all points (x,y) such that m = y-d/x-c slope is change in y/change in x Parallel, Perpen­dicular y=2x+4 and y=2x+3 are parallel y=2x+4 and 2y=4x+8 are same line y=2x+4 and y = 1/2x+6 meet perpen­dic­ularly Parallel lines never meet, same slope Perpen­dicular lines meet once at right angles and slopes are negative recipr­ocals

 f(x) = ax2 + bx + c Zeros given by the quadratic formula: -b +/- sqrt(b2 - 4ac)/2a Coordinate point (-b/2a,( -b2 +4ac)/4a)

### Geometric Equations

 Circles: Circum­ference 2(pi)r Area (pi)r2 Cylinders: Surface area 2(pi)r x h + 2(pi)r2 Volume: (pi)r2h Sphere: Surface area 4(pi)r2 Volume 4/3(pi)r3

### Geometric Formulas

 SOHCAHTOA SOH = sin(x) = a/c CAH = cos(x) = b/c TOA = tan(x) = a/b 180 degrees = (pi)rad Divide arclength by radius to get radian measure Special Angles Degree Radian Cosine Sine Tangent 0 0 1 0 0 30 (pi)/6 sqrt3/2 1/2 1/sqrt3 45 (pi)/4 1/sqrt(2) 1/sqrt(2) 1 60 (pi)/3 1/2 sqrt(3)/2 sqrt(3) 90 (pi) 0 1 undefined

### Theory of Geometric Series

 S = p + pr + pr2 + pr3 + ... + prn Sr = p + pr + pr2 + pr3 + ... + prn + prn+1 S - Sr = p - pr^n+1 S = p-prn+1/1-r

### Negative Exponents

 a-m = 1/am 1/a-m = am

### Multip­lic­ation and Scientific Notation

 Multip­lic­ation and Division: - Convert into scientific notation - Add/su­btract exponents - Multip­ly/­divide coeffi­cients - Convert to scientific notation - 2.3E4 x 9.5E7/­1.6E10 = 2.3x9.5­/1.6E­(4+­7-10)

### Absolute Values

 Absolute Values often generate "­and­" and "­or" situat­ions. Examples: |x|<1: -11: x>1 or x<-1 |2x+3|> 1: 2x+3>1 or -(2x+3­)>1 x>-1 or x<-2

### Expone­ntial Rules

 exp(a)­exp(b) = exp(a+b) [exp(a)]^b = exp(ab) exp(-a) = 1/exp(a) Domain: all real numbers Range: all positive numbers

### Pythag­orean Theorem

 a2 + b2 = c2

### Unit Circle ### Secant, Cosecant, Cotangent

 Secant: 1/cos(x) Cosecant = 1/sin(x) Cotangent = 1/tan(x) = cos(x)­/sin(x)

### Trigon­ometric Identities

 cos2x + sin2x = 1 tan-1x = arctan x cot(x) = 1/tan x e10 = cos x + isin x

### Basic Facts

 Total human popula­tion: 7 billion USA popula­tion: 300 million Distance from NY to LA: 2500 miles Distance to the moon: 2.4E5 miles Distance to the Sun: 1E8 miles Distance around the equator: 2.5E4 miles Area of the US: 4E6 square miles Surface area of the Earth: 2E8 square miles

### Distance Between Points

 The distance between two points on the plane is based on the Pythag­orean Theorem |A-B| = sqrt((­Xa-Xb)2 +(Ya - Yb)2) A=(Xa,Ya) B=(Xb,Yb)

### Function Variables

 Domain = valid inputs to function Range = what can the function produce Zeros or Roots = where is f(x)=0 Inters­ections = Where is f(x) = g(x) Local maximum is largest value around itself Local minimum is smallest value around itself Global is largest overall

### Logarithms

 Logarithms are the functional inverses of the expone­ntial y = b^x is equivalent to logb(y) = x log(mn) = log(m) + log(n) log(m^n) = nlog(m) log(1/m) = -log(m) loga(m) = logb(m­)/l­ogb(a) exp(a)­exp(b) = exp(ab) exp(-a) = 1/exp(a) e2.3 = 10, e12 = e2.3*5.2 = (e2.3)5.2 = 105.2 = 2E5

### Sine

 Sine is the y component as theta spins Domain is all real numbers Range -1

### Cosine

 Cosine is the x component as theta spins Domain is all real numbers Range is -1

### Tangent

 Tangent is the slope of the line with angle theta Domain is all real numbers except pi/2 + kpi Range is all real numbers No max or min. asymptotes at undefined points Zeros at kpi Period is pi