2017 - 2018 (pch and bc)

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PCH Outline

Known Functions (Review)

• Linear
  
• Quadratic
  
• Polynomial
  
• Rational
  
• Radical
  
• Absolute Value
  
• Step Functions (floor, ceiling, round)
  
• Exponential
  
• Logarithmic
  

Functions (as a concept)

• Domain/Range
  
• Inverse
  
• Even/Odd
  
• Transformations (easy)
  
  • horizontal shift/stretch/reflect
    
  • vertical shift/stretch/reflect
    
• Transformations (hard)
  
  • composition, as in y = f(|x|) or y = (f(x))^2, y = f(int(x)) or y = int(f(x)), etc
    
• Idea of multivariable functions - z = f(x, y) or f(t) = (x(t), y(t))
  

Trigonometry

• Right triangle definitions (for all 6 functions)
  
• Unit circle definitions (for all 6 functions - degrees and radians)
  
• Graphing trig functions (focus on sin x, cos x)
  
• Inverse trig functions
  
• Solving trig equations
  
• Pythagorean Identities
  
• Sum/Difference Identities
  
• Double Angle Identities
  
• Law of Sines/Law of Cosines
  

Vectors/Vector Functions

• Definitions
  
• Vector arithmetic (add, subtract, mult by scalar, dot product)
  
• Definition of magnitude, unit vectors
  
• Angle between vectors (Law of Cosines in vector form)
  
• Applications (groundspeed, forces)
  
• Projections (?)
  
• Vector Functions as parametric equations
  
• Motion in the plane with constant velocity
  
• Parametric equations for circles, ellipses, lines
  
• Finding/describing intersection between parametric graphs
  

Polar Functions

• Definition of polar coordinates (r, θ)
  
• Idea of multiple representations for a given polar point
  
• Converting points from polar to rectangular and rectangular to polar
  
• Converting (some) functions from polar to rectangular and rectangular to polar
  
• Polar equations and graphs of circles (centered at origin, or center along an axis)
  
• Polar equations and graphs of limaçons/cardioids, roses, lines
  

Complex Numbers

• Add/subtract/multiply/divide
  
• Represent in trig form x + iy = r(cos θ + i sin θ)
  
• Multiply/divide numbers in trig form
  
• Powers of complex numbers in trig form
  
• Roots of complex numbers in trig form
  

3D Space

• Drawing points in (x, y, z)
  
• Distance formula, midpoint formula
  
• Equation of sphere
  
• Equation of plane
  
• Equation of line
  
• Vectors in space, including cross product
  

Sequences/Sums review

• Arithmetic sequences and sums
  
• Geometric sequences and sums
  

Counting/Probability

• Use of factorial
  
• Use of permutations
  
• Distinguishable permutations (?)
  
• Use of combinations
  
• Definition of sample space
  
• Binomial distribution
  

Calculus Intro

• Informal definition of limit (including the idea that a limit might not exist)
  
• Evaluate limit by table
  
• Evaluate limit by graph
  
• Evaluate limit with algebra
  
  • factor and cancel
    
  • multiply by conjugate
    
  • simplify complex fraction
    
• Formal definition of the derivative
  
• Evaluate derivatives using the definition
  
• Shortcut derivative rules
  
  • constant
    
  • constant multiple
    
  • sum/difference
    
  • power
    
• Basic applications
  
  • equation of tangent line to graph
    
  • ID horizontal tangents
    
  • position/velocity
    
• Antiderivatives (using the same rules as derivatives)