The following are typical errors I see when students come to me for help with AP Calculus AB and BC:
- Notation errors: Using incorrect or inconsistent notation, such as writing dy/dx as d(y)/d(x) or mixing up integration and differentiation symbols.
- Chain rule mistakes: Forgetting to apply the chain rule when differentiating or integrating composite functions, leading to incorrect results. Remember, the outside function is usually a trig function: sin (3x+5) , the base of an exponential function: e5x-3, or a logarithm ln(6x).
- Improper use of limits: Misunderstanding or misapplying the concept of limits, such as when calculating derivatives or evaluating definite integrals, especially as the denominator approaches 0 or infinity.
- Integration errors: Failing to recognize the need for substitution, integration by parts, or other techniques when evaluating integrals.
- Mistakes with u-substitution: Forgetting to change the limits of integration when performing u-substitution, or not correctly substituting back the original variable after integrating.
- Confusing related rates and optimization problems: Misinterpreting the given information or not correctly setting up equations to solve related rates or optimization problems. There are a handful of types of each problem that you will likely be expected to know how to set up.
- Overlooking the Mean Value Theorem (MVT) or Rolle’s Theorem: Failing to recognize when these theorems can be applied to support solutions or provide insights.
- Calculating areas and volumes incorrectly: Misapplying methods for finding areas under curves, or volumes of solids, such as forgetting to square the radius in the disk method or not using the correct axis of rotation for the shell method.
- Errors in interpreting the graph: Misreading or misinterpreting the information given by a graph, such as mistaking relative extrema for absolute extrema or not recognizing points of inflection.
- Arithmetic and algebraic errors: Making simple arithmetic or algebraic mistakes, like incorrectly factoring or expanding expressions, forgetting negative signs, or miscalculating derivatives or integrals.
- Not practicing answering the FRQ (free response questions) with official solutions in order to understand how to show your work for full credit
To avoid these mistakes, students should practice problems, review concepts, and develop good test-taking strategies, like double-checking work and managing time effectively.