C3

C3

1. functions

   • modulus
     • graph
       • |f(x)|
         • draw normally, flip up the negatives. always label
       • f(|x|)
         • ignore left side, draw over it with the reflection of the right side
     • solve simultaneous modulus equations
   • domain / range
     • mapping diagrams
     • one to one, one to many
   • inverse function
     • calc by reversing subject (make x the subject, not f(x))
     • reverses domain / range
     • mirrors in y=x
   • combining functions
   • graphs
     • transforming them
       • outside y, inside x
       • y truths, x lies
       • x / stretch and squish, + - shift
     • sketching
       • axis crossing points
         • cross x axis, y=0
         • cross y axis, x = 0
       • asymptotes
       • turning points
         • \(\frac{dy}{dx}=0\)

2. e / ln

   • graphs
     • e, asymptote y=0, crosses (0,1)
     • ln, asymptote x=0, crosses (1,0)
     • all kinds of e^x powers
       • incl. e^-x
   • y = e^x, dy/dx = e^x
     • can be to any power of it too
   • ln = log to the base e
     • essentially the inverse to e^x
   • also called exponential functions
   • solve equations!

3. trigonometry

   • Trig Identities
     • \[cos^{2}A + sin^{2}A \equiv 1\]
     • \[sec ^{2}A \equiv 1 + tan^{2}A\]
     • \[cosec^{2}A \equiv 1 + cot^{2}A\]
     • prove them
   • CAST diagrams
   • sin, cos, tan, cosec, sec, cot
     • graphs of all
     • when are they 0? 1? asymptote?
     • the inverses are 1/whatever
   • the trig triangles
   • simplify equations / expressions
   • degree / radian conversions
   • triples

4. algebra

   • algebraic fractions
     • cancelling down
     • +, -, x, /
   • division of expressions
   • logs, powers
   • do u remember surds
   • inequalities

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