Calculus & Probability Lab

Precalculus, derivatives & integrals on 3D graphs, stats dice simulator, AP plan

Calculus & Probability Lab turns derivatives, integrals and probability distributions into interactive 3D graphs you can drag, orbit and zoom. Move a point along a curve and watch the slope change, or roll dice until a histogram settles into the bell curve.

Built for students in AP Calculus AB or a first college course (Calculus 1, intro stats), and for anyone who wants to learn calculus again. The first world doubles as a precalculus refresher: functions, slope, exponentials and logs.

FUNCTION LAB: 3D GRAPHS
• 22 function families: lines, parabolas, cubics, sine and cosine waves, exponentials, logs, square roots, logistic S-curves and more
• True z = f(x, y) surfaces such as the paraboloid, saddle, ripple, cone and egg carton. Drag to orbit, pinch to zoom
• Tangent line overlay: move a point and see the exact derivative f'(x) update live
• Riemann sum overlay: slide from 1 to 60 rectangles and watch the sum approach the exact definite integral
• Riemann ladder challenge: find the fewest rectangles that stay within 1%, then 0.1%, of the true value
• Save lab setups and reload them later

PROBABILITY LAB: DICE SIMULATOR
• 18 scenarios: dice sums (d4, d6, d20), coin flips, binomial trials and Poisson arrivals
• Build a histogram roll by roll and compare it with the exact probability distribution on the same chart
• Watch the Central Limit Theorem: add dice and the sum moves toward the normal distribution
• Track your running mean against the theoretical mean, plus how far your results still are from theory

LEARNING PATH: 4 WORLDS, 50 LESSONS
• Functions & Limits: families of curves, one- and two-sided limits, continuity, rate of change
• Derivatives: power, product, quotient and chain rules, partial derivatives, related rates, optimization, the Mean Value Theorem
• Integral calculus: Riemann sums, antiderivatives, the Fundamental Theorem of Calculus, area between curves, volumes of revolution
• Probability and statistics: sample spaces, random variables, expected value, binomial and Poisson models, the normal curve
• Each lesson has quiz questions and opens the matching lab
• A wrong answer names the mistake behind it and shows a lab setup that makes it visible

AP EXAM PRACTICE
• Study plan: enter your AP Calculus AB exam date and where your class is, and get a day-by-day plan counted back from that date
• Free-response practice: one AP-style justification question per world, graded point by point against a rubric by AI
• 60-second warm-up: fresh derivative, integral and expected-value problems, weighted toward topics you missed

AI TUTOR
• Tap Explain on any curve, surface or dice distribution for a plain-language breakdown of your coefficients, your slope, your mean and spread

FREE AND PRO
Free: the first 3 lessons of every world (12 of 50), 6 function families, 4 dice scenarios, 50 dice rolls a day (a short ad adds 25 more, twice a day), 2 AI explanations and 2 free-response gradings a day, 3 saved setups, the study plan and warm-ups. The free version shows ads.
Pro: all 50 lessons, all 22 function families, all 18 dice scenarios, unlimited rolls and AI explanations, up to 20 free-response gradings a day, unlimited saves, no ads. Prices are shown in the app; cancel anytime in Google Play.

Progress is tracked across every world and lesson. The app is available in 10 languages: English, German, Spanish, French, Japanese, Korean, Portuguese, Russian, Turkish and Chinese.

AP is a trademark of the College Board, which is not affiliated with this app.

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