Calculus AB — calculator-active problems

The AP Calculus AB exam in May 2027 requires a graphing calculator for part of the multiple-choice section (13 questions in 38 minutes) and for the first two free-response questions (30 minutes). The course framework expects the calculator to do four things: graph a function, solve an equation numerically, compute a derivative at a point, and compute a definite integral. It expects the student to do everything else: choose what to compute, write the set-up in standard notation, keep the calculator in radian mode, store intermediate results, and report three places after the decimal point. This material trains that division of labor.

Each of the twelve quiz questions needs a calculator and asks for a three-decimal answer. You compute a derivative at a point for a function with a sine inside an exponential, and a definite integral of √(1 + x³), which has no elementary antiderivative. You find where cos x meets the line y = x, the area enclosed by a parabola and an exponential curve whose intersection points must be found and stored first, and the volume of the solid formed by revolving that same region about the x-axis. A particle with velocity 2 sin(t²/3) gives two questions, the time it changes direction and the total distance it travels, and a second particle asks for its position from a starting point and its velocity. A tank filled at a sinusoidal rate and drained at a rate that grows over time gives the amount of water after ten hours and the time when the amount is greatest. The average value of ln(1 + x²) and the value promised by the Mean Value Theorem for eˣ on [0, 2] complete the set.

The wrong options are the numbers these mistakes actually produce on a calculator: the result in degree mode, the value of the function where its derivative was asked for, limits of integration rounded to whole numbers, displacement reported as distance, an initial amount or an outflow left out, the integral given without dividing by the length of the interval, a two-rectangle estimate taken for the integral. Each explanation writes the set-up the way a free-response answer should show it, then the value the calculator returns.

The flashcards cover the three-decimal rule and storing intermediate values, radian mode, the four required calculator capabilities and the set-up they must be shown with, total distance, average value, intersections, the Mean Value Theorem equation, volumes of revolution and the condition for a change of direction.

This is independent practice written by Zestly, based on the published AP Calculus AB course and exam description; it is not produced or endorsed by the College Board.

• Use the four required calculator capabilities: graph, solve numerically, differentiate numerically, integrate numerically
• Write the set-up before the calculator result and report three places after the decimal point
• Find and store intersection points to compute area and volume
• Compute total distance, position and change of direction for a particle
• Model a tank with rate in minus rate out and find its amount and its maximum
• Compute an average value and a Mean Value Theorem point numerically

Practice material written by Zestly, based on the College Board AP Calculus AB course and exam description (calculator expectations: graph a function, solve equations numerically, numerical derivative, numerical definite integral; three places after the decimal point) and the May 2027 exam format (Section I Part B: 13 questions, 38 minutes, graphing calculator required; Section II Part A: 2 questions, 30 minutes), 2026–27 edition with its clarifications.