Math - need to know

stats

• know your basic distributions - normal, etc
• know how to find characterstics of data:
  • Average (\(\mu\)), median, mode
  • Beyond basics - variance, standard deviation
  • \(\text{z-score} = \frac{\text{observation or raw mark} - \text{mean}}{\text{standard devisation} \delta}\)
  • Note: Confidence scores - 95% of the data/observations fall within 2 standard deviations of of the mean
  • Correlation coefficient
  • weak positive strong positive
  • careful of algebra

Trig identities

• Unit circle: \(\cos^2 + \sin^2 = 1\)
• Unit circle trig ratios
• Derived identities
• Calculate amplitude, period, wave stuff:
  • \(y = A\sin(B(x + C)) + D\)
  • Amplitude is \(A\)
  • Period is \(\frac{2 \pi}{B}\)
  • Phase shift is \(D\) (positive to left)
  • Vertical shift is \(D\)
• Formulas involving \(\sin, \cos, \tan\):

Differentiation

• Chain, Product, Quotient rule
• Trig Differentiation
• Exponential Differentiation
  • \(ln(a)a^x\) (remember to use chain if needed)
  • \(\log e^x = \frac{1}{x}\)
• know how to convert ln to log, log to ln

Functions

• Know your functions
  • domain
  • range
  • roots
  • y-intercept
  • discriminant (\(\triangle\))
  • points of inflection
  • min and max (derivative at 0)
  • find tangent at any point x, and normal
• What does discriminant tell you about roots?
• Describe as even/odd, oncave up/concave down, increasing/ decreasing
• Transforming functions:
  • Add to y to go high
  • add to x to go left
• Know how to find asymptotes:
  • start by reducing any common factors
  • solve for 0 in denom to get vertical asymptotes
  • For horizontal:
    • If the degree of the denominator greater than degree of the numerator, there is a horizontal asymptote at y = 0.
    • If the degree of the denominator less degree of the numerator by one, we get a slant asymptote, no bounds.
    • If the degree of the denominator = degree of the numerator, there is a horizontal asymptote at \(y = \frac{a_n}{b_n}\) where \(a_n\) and \(b_n\) are leading coeffiecents of numerator and denominator