AP Calculus AB and BC

AP Calculus Review Games That Are Not Just Kahoot

The strongest AP Calculus review game makes a student justify a step, not just produce a number, because free response points come from justification, not computation. Below are ten games with timing, prep, and what each trains, three built on the site's own interactives, plus a plan for a full review day.

Why the last few weeks need a different game

A review game earns its class period only if it does something a worksheet cannot. Multiple choice drilling is available at any hour on the practice lab, so a live game should force the part of the exam a worksheet never checks: committing to a method out loud before working it, writing the justification sentence a rubric actually pays for, or reasoning backward from a target instead of forward from a prompt.

The ten games below name the exact setup, the timing, and what each one trains, so a game can be picked to match a specific gap instead of run because a period needs filling. Three run directly on the site's own interactives, so the reveal is the graph moving in front of the room rather than an answer key on a slide.

1. The graph relay

Time: 10 minutes per round. Prep: one whiteboard and one marker per team of four, plus a short list of functions or sign charts.

Give each team a sign chart for $f'$ : where it is positive, negative, and zero. Student one draws the axes and marks the critical numbers. Student two shades where $f$ is increasing and decreasing. Student three marks each local maximum and minimum and states which test justified it. Student four sketches the full curve, adding concavity from a second sign chart on $f''$ if the round is BC or late AB. Only a complete, correctly labeled board counts, and the marker passes hands after every step.

Trains: the exact sequence a curve sketching free response question rewards, sign first, then behavior, then justification, then the picture, run under time pressure with every team member responsible for one link. Units: 4 and 5, including when the sign chart comes from a velocity function instead of $f'$ .

2. The error hunt

Time: 8 minutes. Prep: one worked solution per round, projected, containing exactly three planted mistakes.

Teams find and correct all three errors. One point for finding a mistake, a second point for stating why the step is wrong in a full sentence. Plant errors that mirror the ones students actually make: differentiating the outer function without multiplying by the inner function's derivative, dropping the constant of integration, treating a removable discontinuity as a place where a limit fails to exist, or reporting an average rate of change as if it answered a question about an instantaneous one.

Trains: reading a solution the way a reader grades one, since spotting a wrong step requires knowing the method rather than recalling a memorized final answer. This is measurably harder than producing a correct solution from scratch and it lands closer to what a grader spends hours a day doing. Units: any, and it is the fastest way to reuse a unit test that already exists in a folder.

3. Predict, commit, reveal

Time: 12 minutes for three rounds. Prep: a projector and three of the site's interactives queued up. No teams, whole class, everyone commits at once.

f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Round one: open the secant to tangent interactive, hold h fixed at a visible width, and have every student write the number they expect the secant slope to approach as h slides to zero, before you drag anything.
Round two: open the Riemann sum slider on an increasing function set to the left sum, and have every student write overestimate or underestimate before you increase n and watch the rectangles tighten around the curve.
Round three: open the related rates scene on the sliding ladder, and have every student write faster or slower before you drag the base near the wall, answering whether the top slides down faster when the base is close to the wall or far from it.

Trains: the habit review usually skips, being wrong in public in a setting with no grade attached. A student remembers the correction to a prediction they committed to and forgets an explanation of a question they never answered. Units: 1 and 2 for the limit round, 6 for the Riemann sum round, 4 for the related rates round.

4. Category speed round

Time: 5 minutes per round. Prep: a stack of about twenty short expressions on cards or slides, no calculators.

Call an expression. Teams have five seconds to hold up a card naming the technique it needs, not the answer. For differentiation: power rule, product rule, quotient rule, or chain rule. For integration (BC adds integration by parts): direct antiderivative, u substitution, or (BC) integration by parts. For BC series: geometric, p series, ratio test, or alternating series test. Wrong technique costs the round even if a team could have finished the computation correctly.

Trains: recognition speed, which is what the multiple choice section rewards and what a mixed free response question tests before any arithmetic starts. Keep each call under five seconds so instinct is being measured rather than working the problem out first. Units: 2 and 3 for derivatives, 6 for integration technique, 9 and 10 for BC convergence tests. This round draws on the same recognition question the which integration technique and which convergence test guides answer in full.

5. The free response jigsaw

Time: 20 minutes. Prep: one released free response question, cut into its parts, one part per group of three or four.

Each group solves only its assigned part in full, with every step justified the way a rubric wants it, then teaches that part to the rest of the class in order. Group two usually discovers midway through that its part depends on group one's answer being correct, and that discovery is the most useful five minutes in the whole activity.

Trains: the fact that later parts of a free response question build on earlier ones rather than testing isolated skills, and it gives every student full ownership of one complete, well justified answer instead of a rushed attempt at all of one. Units: any, using the released archive linked from the practice page.

6. Two truths and a lie, series edition

Time: 10 minutes. Prep: none beyond paper, best run once series convergence has been taught.

Each team writes three statements about a series or a convergence test, two true and one false but plausible. For example: the harmonic series diverges, a geometric series with ratio one half converges to twice its first term, and the alternating harmonic series diverges. Teams trade papers and identify the lie, then state which test proves it.

Writing a convincing false statement is harder than writing a true one, because a student has to understand a test well enough to bend it without breaking it into something obviously wrong. This produces more careful thinking per minute than almost any other format here and it costs nothing to prepare. Units: 9 and 10, though the same format works on any unit with enough named rules to bend.

7. The sixty second explanation

Time: 1 minute per student. Prep: a stack of terms and, for each one, three banned words chosen in advance.

Draw a term at random. The student has sixty seconds to explain it to the class without using three banned words tied to that term. For the derivative, ban slope, rate, and instantaneous. For continuity, ban unbroken, connected, and gap. For the Mean Value Theorem, ban average and tangent.

Trains: understanding that does not depend on the textbook's own sentence. A student who only has the memorized definition runs out of words within ten seconds once the three words that carry the definition are removed, and the room notices immediately. Units: any, best used as a warm up before a unit test rather than as the main event.

8. Beat the tracer

Time: 8 minutes. Prep: a projector and the tangent line tracer interactive, one student at the keyboard, everyone else calling the target.

The class states a target for $f'$ that does not name a location: make the tangent go flat, make the derivative curve cross the x axis going from positive to negative, make $f'$ reach its own maximum. The student at the keyboard has to work out where on $f$ that target lives and drag the point there, with the class checking the traced $f'$ curve against the claim before the point moves on.

Trains: reasoning from an outcome back to a cause, the direction almost no worksheet asks for and the direction the harder free response parts require, since those questions describe a behavior and ask where it happens rather than the reverse. Units: 2 for basic derivative shape, 4 and 5 for the connection between $f$ , $f'$ , and extrema.

9. Set up, do not solve

Time: 90 seconds per prompt, several rounds. Prep: a short list of area or volume prompts, plus the solid of revolution builder to check the picture after each round.

V = \pi \int_{a}^{b} \left[R(x)^2 - r(x)^2\right] dx

Call a region and an axis of rotation. Teams have ninety seconds to write the correct integral, with correct bounds and the correct method named, disk or washer, and may not evaluate it. After time is called, open the interactive, build the same solid, and let the class confirm the method against the picture before anyone computes a number.

Trains: the setup step, which is where most volume and area points are actually lost, separated entirely from the arithmetic that follows it. A team that can set up the right integral in ninety seconds rarely misses the evaluation once it is allowed to compute. Units: 6 and 8, with the disk washer shell guide as the reference for the method itself.

10. The slope field trace off

Time: 6 minutes per round. Prep: one slope field drawn on the board or projected, a starting point marked on it, one marker per team.

Teams take turns tracing the solution curve through the marked point, one small segment at a time, following the direction of the nearest tick marks rather than sketching a smooth curve that only looks plausible. A team that jumps ahead of what the field actually shows at that spot loses the round even if the final curve looks reasonable.

Trains: reading the field instead of guessing the shape of a solution, which is the skill a slope field question exists to test and the one a smooth freehand curve fakes past without anyone noticing. Units: 7, and it doubles as a check for Euler's method once step by step estimates are introduced on the same field.

What to avoid in the final two weeks

Games that reward recall speed alone. The category speed round belongs earlier in the course, while recognition still needs building; running only speed formats in the final stretch trains the wrong skill at the point where the remaining points sit in justification, not recall.
Any format where one strong student can carry the whole team. The graph relay and the free response jigsaw fix this structurally by making every member responsible for one link nobody else can skip.
A review stretch with no writing. A large share of the exam is graded on a written justification sentence, and a team that never writes one during review has practiced half the test.

One rule that fixes most weak review games

If a team can win without writing a full sentence, the game is testing recall, not the exam. Add a required sentence to the scoring for every game above and the quality of the review goes up without changing the setup at all.

Sequencing the final weeks

A workable order for a review unit: category speed rounds and two truths and a lie early, while recall of names and rules still needs shoring up. Graph relays, error hunts, and set up do not solve rounds in the middle, once every method is back and the setup step is the remaining gap. Free response jigsaws and a full review day last, when the remaining gains sit in writing and in questions that combine several units rather than in knowing any single rule.

Predict, commit, reveal and beat the tracer work at any point in that order because they cost almost nothing to set up and reset a room's attention between longer formats.

Running a full review day

A single class period can carry five of these games back to back without feeling repetitive, because each one asks for a different kind of output: a drawing, a correction, a prediction, a called out technique, and a taught explanation.

Minutes	Game	Focus
0 to 12	Predict, commit, reveal	Warm the room up with a low stakes public prediction on one interactive
12 to 22	Category speed round	Rebuild recognition speed across the units the test mixes together
22 to 34	Graph relay or set up, do not solve	Rebuild the setup and sequencing steps a free response question rewards
34 to 49	The error hunt	Sharpen reading of a solution the way a grader reads one
49 to 69	Free response jigsaw close out	End on one full, correctly justified answer built and taught by the room

Keep score across the day if a class responds to competition, but grade nothing from the games themselves. The only grade that should follow a review day is a short quiz a day or two later, once the corrections have had time to settle rather than being tested while they are still fresh from the room's own memory of who said what.

For a day you cannot run yourself, build a substitute plan around worksheets and the walkthroughs instead, since the interactive rounds need someone in the room deciding what the class calls next.

Worked examples

Worked example

The cone tank rate, worked in full

A conical tank has its point down, a top radius of 4 feet, and a height of 12 feet. Water is pumped in at 9 cubic feet per minute. Find the rate at which the water depth is rising when the depth is 6 feet.

Relate the radius and height of the water's surface with similar triangles: the full cone has radius $4$ at height $12$ , so at any depth $h$ the water's radius is $r = \frac{h}{3}$ .
Write volume in terms of $h$ alone: $V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \left(\frac{h}{3}\right)^2 h = \frac{\pi h^3}{27}$ .
Differentiate with respect to time: $\frac{dV}{dt} = \frac{\pi}{27}(3h^2)\frac{dh}{dt} = \frac{\pi h^2}{9}\frac{dh}{dt}$ .
Substitute the known values, $\frac{dV}{dt} = 9$ and $h = 6$ : $9 = \frac{36\pi}{9}\frac{dh}{dt} = 4\pi \frac{dh}{dt}$ , so $\frac{dh}{dt} = \frac{9}{4\pi}$ .

The depth is rising at $\frac{9}{4\pi}$ feet per minute, about 0.72 feet per minute.

Worked example

Washer, not disk: setting up before evaluating

The region between $y = x$ and $y = x^2$ on $[0, 1]$ is revolved about the x axis. Set up, without evaluating, the integral for its volume.

Find where the curves meet: $x = x^2$ gives $x = 0$ and $x = 1$ , so the region sits between those two bounds.
Check which curve is farther from the axis of rotation on that interval: at $x = 0.5$ , $y = x$ gives $0.5$ and $y = x^2$ gives $0.25$ , so the line is the outer radius and the parabola is the inner radius.
Because the inner radius $r(x) = x^2$ is strictly positive for every $x$ in $(0, 1]$ and equals zero only at the single left endpoint $x = 0$ , the solid has a nonzero hole for virtually the whole interval, so this is a washer, not a disk. It is not the pinch at $x = 1$ , where the two curves meet each other rather than touch the axis of rotation, that matters here: $V = \pi \int_{0}^{1} \left[x^2 - (x^2)^2\right] dx = \pi \int_{0}^{1} \left(x^2 - x^4\right) dx$ .

$V = \pi \int_{0}^{1} (x^2 - x^4)\,dx = \frac{2\pi}{15}$ .

Frequently asked questions

What is the best AP Calculus review game to start with?

The graph relay. Teams of four share one marker and one whiteboard: one student marks the critical numbers from a sign chart, one shades where the function rises and falls, one marks and justifies each extremum, and one sketches the full curve. It trains the exact sequence a curve sketching free response question rewards and it shows a team which link in that chain is weakest.

How do you review AP Calculus without just running more practice tests?

Use formats that require a justification sentence rather than a final number. The error hunt, where teams find and correct planted mistakes in a worked solution, and set up do not solve rounds, where a team writes the integral without evaluating it, both isolate the step where free response points are actually lost.

Are Kahoot style games still useful for AP Calculus review?

They are useful earlier in a unit, when the goal is building recognition speed for names and rules. In the final two weeks the remaining points sit in written justification, so a review stretch built only on speed and recall formats trains the wrong skill at the point it matters least.

How many of these games need the site's interactives?

Three do. Predict, commit, reveal cycles through the secant to tangent, Riemann sum slider, and related rates scene interactives for a public prediction before each one is dragged. Beat the tracer runs entirely on the tangent line tracer. Set up do not solve checks its answer against the solid of revolution builder after teams write their integral.