Calculus & Probability Lab

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. Privacy Policy: https://coddykit.com/terms/privacy-policy