How the Calculus I Common Final is Constructed
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