The common final exam is constructed using the following principles.
Problems primarily reflect the assigned homework problems.
Easy, Moderate and Hard homework problems will be represented.
Problems will cover:
- Each of the derivative rules.
- Each function: polynomial, rational, root, exp(x), ln(x), sin(x), cos(x), tan(x), sec(x).
Multiple problems use the chain rule.
At least two problems include graphing in some form.
At least one problem will cover:
- limit definition of derivative
- tangent lines
- implicit differentiation
- applied related rates
- applied optimization
- optimization on an interval
- discontinuities and asymptotes
- one of MVT, IVT or Rolle's Theorem
- l'Hopital's rule
- Newton's method (1 step)
- FTC Part I
- FTC Part II
Often the exam includes:
- An inverse trig function
- A hyperbolic function
- The absolute value function
- Linear approximation
- Average of a function
- Area as an integral
- Distance as anti-derivative of velocity
- Approximating an integral from data or a graph
- Midpoint Rule
- Other problems from the homework