MAT 280: Exams


Exam outlines serve as a guide as to what you can expect to see on exams.

  • In terms of definitions and theorems, I will only ask you to state the Fundamental Theorem of Calculus and the limit definition of the derivative.
  • There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, definite integrals, areas of bounded regions, etc…)
  • Find the limit of a function using general properties of limits and basic rules of limits.
  • Determine if \(f(x)\) is continuous at \(c\).
  • Find the derivative of a function using general properties of derivatives and basic rules of differentiation.
  • Find the antiderivative of a function using general properties of antiderivatives and basic rules of integration.
  • Find the absolute extrema of \(f(x)\) on a closed interval \([a,b]\).
  • Find the relative extrema.
  • Find the average value of a function on \([a,b]\)
  • Find a \(c\) that satisfies the Mean Value Theorem for Integrals
  • Sketch the graph of a function using calculus techniques.
  • Determine the intervals on which \(f(x)\) is concave up or concave down.
  • Find an equation of the tangent line.
  • Find inflection points.
  • Find horizontal and vertical asymptotes.
  • Exam 3 Solutions
  • State the definition of an antiderivative
  • State the Fundamental Theorem of Calculus
  • State the definition of average value of a function
  • There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, definite integrals, areas of bounded regions, etc…)
  • Find the indefinite integral of a function (There are at least a couple of these)
  • Evaluate a definite integral (There are at least a couple of these, one of which will involve an absolute value).
  • Find the average value of a function on an interval
  • Take the derivate of a function defined as an integral.
  • Find an indefinite integral using u-sub. One of these will be such that the old variable will not completely cancel after making the substitution.
  • Sketch and find the area of a region bounded by the graphs of some equations (There will be at least two of these).
  • Exam 2 Solutions
  • State the Extreme Value Theorem
  • State the Rolle’s Theorem
  • State the Mean Value Theorem
  • There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, intervals of increase/decrease/constant, absolute max/min, relative max/min, etc…)
  • Find the absolute extrema of \(f(x)\) on a closed interval \([a,b]\).
  • Find the relative extrema.
  • Determine the intervals on which \(f(x)\) is increasing, decreasing, or constant.
  • Determine the intervals on which \(f(x)\) is concave up or concave down.
  • Find inflection points.
  • Find horizontal and vertical asymptotes.
  • Sketch the graph of a function (2 problems) one of which will be a rational function.
  • Exam 1 Solutions
  • I recommend answering the following three items exactly as they appear in the notes.
  • State the limit definition of the derivative.
  • State the Intermediate Value Theorem.
  • State the Squeeze Theorem.
  • There will be a graph and you’ll be asked questions related to the graph (i.e. limits, derivatives, continuity, etc…)
  • Evaluate limits with indeterminate form 0/0.
  • Evaluate limits for a piecewise function.
  • Given a piecewise function with an unknown constant, find a choice of that constant so that the function is continuous at a particular \(x\) value or on \((-\infty, \infty)\).
  • Evaluate limits: from the left, right, both-sides.
  • Find an equation of the tangent line.
  • Find the derivative of a function using basic rules and general properties of differentiation. This includes any of the derivative rules that can be found on the Derivative Rules Reference Page.
  • Find the derivative of a function using the limit definition of the derivative.
  • Find higher order derivatives.
  • Find the derivative using implicit differentiation.
  • Find an equation of the tangent line to the graph of an equation that is relates y as a function of x implicitly.