Proven strategies, common pitfalls, and exam day preparation for AP® Calculus.
A ranked list of the errors that cost students points most often, drawn directly from College Board Chief Reader Reports.
AP Calculus Chief Reader Reports. Errors are ranked by how often they appear in the published reports, not by point cost. Year range varies by track — see Source years above.
Each mistake is one card. The card shows the category, where it tends to appear on the exam, what students actually write, and what to write instead. Read top to bottom on first pass. On a second pass, jump to the categories you keep losing points in.
The mistake. Omitting units, reversing numerator and denominator, writing "degrees Celsius per ."
Chief Reader · 2024“Overall, responses were more successful providing a correct approximation than with providing correct units.”
What to write. Always include units. Rates are [quantity] per [time]. Integrals of rates are in the numerator unit. Derivatives are numerator over denominator.
The mistake. Drawing a sign chart and stopping there.
Chief Reader · annual, 2008 to 2010“Sign charts without verbal commentary are not sufficient justification.”
What to write. " has a relative maximum at because changes from positive to negative." Name the test, connect the change to the conclusion.
The mistake. Picking the wrong integral: when the question asks distance, or when it asks displacement.
Chief Reader · 2009“Students confuse total distance traveled with displacement (net change in position).”
What to write. Distance . Displacement . "How far" means distance; "change in position" means displacement.
The mistake. Writing instead of , or leaving the integral incomplete.
Chief Reader · 2010, 2015“Always include the differential in integral expressions.”
What to write. .
The mistake. Leaving the calculator in degree mode on a trig problem.
Chief Reader · 2009, 2015, 2019, 2022“Some students solved this problem using the calculator in degree mode rather than radian mode.”
What to write. Check radians before the exam. If a numerical answer looks wildly off, check the mode.
The mistake. Justifying a local max when the question asks for a global max. Skipping endpoints.
Chief Reader · 2019“Some responses … failed to be complete enough to bridge the gap between justifying a local maximum and justifying a maximum across the entire interval.”
What to write. Candidates Test on closed intervals. On open intervals, show the single critical point and the end behavior.
The mistake. Plugging in numbers before taking the derivative, which freezes variables as constants.
Chief Reader · 2008, 2010“Substituting numerical values before differentiating.”
What to write. Equation, then differentiate (keep variables), then substitute, then solve.
The mistake. Computing the wrong "average" when the prompt is about a rate or a value.
Chief Reader · 2008, 2022“Computing average value instead of average rate of change.”
What to write. Average rate of change . Average value .
The mistake. Not recognizing when . Reusing as both the limit and the dummy variable.
Chief Reader · 2008, 2009“Not recognizing that from Fundamental Theorem of Calculus.”
What to write. Use different variables: , not .
The mistake. Wrong step size. Using new instead of old for the slope.
Chief Reader · 2010“Step size .”
What to write. at . Show the work in a table.
The mistake. Forgetting the , forgetting to square , wrong bounds.
Chief Reader · 2009“Area .”
What to write. Area . Between curves: .
The mistake. Treating velocity as if it were speed (always non-negative).
Chief Reader · 2008, 2009“Speed is , always non-negative.”
What to write. Velocity can be negative. Speed , or for parametric.
The mistake. Skipping the structural setup that earns the setup point.
Chief Reader · 2024“A sufficient setup would show the sum of three appropriate products.”
What to write. Show width height for each rectangle. Label the type (left, right, midpoint, trapezoidal).
The mistake. Using a theorem implicitly without naming it or stating its hypotheses.
Chief Reader · 2019“Many responses failed to present an appropriate difference quotient and often omitted the requisite condition that is continuous on the interval.”
What to write. Name it ("By MVT…"), state hypotheses, then state the conclusion.
The mistake. Dropping the inner derivative on composite expressions.
Chief Reader · 2015“Many students made chain rule errors or could not evaluate the derivative at .”
What to write. . For logs: .
The mistake. Reporting only the radius, or skipping endpoint tests.
Chief Reader · 2009, 2010“Radius is distance from center; interval requires checking endpoints separately.”
What to write. Ratio test for radius , then check and individually, then write the interval with the right brackets.
The mistake. Reversing outer and inner radius, or measuring from the wrong axis.
Chief Reader · 2009“Outer radius is distance from axis to outer curve, inner radius to inner curve.”
What to write. . Outer is farther from the axis. Inner is closer.
The mistake. Returning a number instead of a sentence with units and an interval.
Chief Reader · 2024“In general, responses had difficulty providing a correct interpretation, although quite a few responses did provide a correct interpretation that included the necessary key words/phrases.”
What to write. Three components: what it measures, the units, and the interval. e.g. "average temperature, in degrees Celsius, from to minutes."
The mistake. Mis-stating the bound or omitting where the maximum is taken.
Chief Reader · 2009“Error for some between and .”
What to write. , where is the center of the series, is an upper bound on on the interval between and , and is the polynomial degree.
The mistake. Using vague references or chaining equalities that are not actually equal.
Chief Reader · 2008, 2015, 2022“Use specific function names (). A common error was to use an equals sign to present a string of equalities, linking expressions that are not equal.”
What to write. Use the names from the problem. Don't chain equalities that aren't actually equal.