🕹️ Practice arcade
Extra games, not extra homework — timed sprints, survival runs that end when your lives run out, and mastery drills built from the same skills Calculus I — Differential & Integral Calculus teaches.
⚡ Sprints
Beat the clock.
🧩 Factoring Frenzy
Factor trinomials — easy ones first, then the ones where the leading coefficient isn't 1.
🎯 Limit Factoring Frenzy
0/0 from direct substitution? Factor, cancel, substitute again — as many as you can in 90 seconds.
⚡ Simplify Radicals Sprint
Pull out perfect-square factors and rationalize denominators — 90 seconds.
⚡ Function Fundamentals Sprint
Evaluate functions, find a domain's left endpoint, average rate of change, horizontal shifts, and inverse functions — 120 seconds.
⚡ Exponential and Logarithmic Fundamentals Sprint
Exponential models, evaluating and bracketing logarithms, and expanding log properties — 120 seconds.
⚡ Unit Circle Definitions Sprint
Find the missing coordinate of a point on the unit circle — 60 seconds.
📉 Limits Sprint
Estimate, compute, and combine limits — including trig limits and the squeeze theorem — 2.5 minutes.
📐 Derivative Rules Sprint
Apply the sum/difference, product, and trig derivative rules, plus higher-order derivatives and physical rates — 2.5 minutes.
🔗 Chain Rule Techniques Sprint
Apply the chain rule with trig, exponential/log, product/quotient combinations, and implicit/inverse-function differentiation — 2.5 minutes.
📏 Rates & Approximations Sprint
Solve related-rates scenes (product, circle, sphere) and estimate change with differentials — 2.5 minutes.
📈 Shape of a Graph Sprint
Find critical numbers, absolute extrema, inflection points, and evaluate limits with L'Hopital's rule — 3 minutes.
🎯 Optimization Sprint
Solve geometric and applied optimization problems — maximize area, minimize fencing, minimize cost — 2.5 minutes.
∫ Antiderivatives & Definite Integral Sprint
Find antiderivatives with initial conditions, evaluate Riemann sums, signed area, and the trapezoidal rule — 3 minutes.
🔑 Fundamental Theorem Sprint
Apply the FTC with a chain-rule twist, the Net Change Theorem, and worked applications — 2.5 minutes.
🔄 Substitution & Applications Sprint
Apply u-substitution to indefinite and definite integrals, trig/exponential integrands, volumes, and average value — 3 minutes.
🧮 Composition & Difference Quotient Sprint
Evaluate composite functions and simplify difference quotients — ninety seconds of pre-derivative footwork.
📐 Power & Quotient Rule Sprint
The power rule, the quotient rule, and the generalized power rule — as many derivatives as ninety seconds allows.
📏 Tangent Line Applications Sprint
Implicit tangent slopes, linear approximation, and one step of Newton's method — the tangent line, three ways, 2.5 minutes.
∫ Integration Warm-Up Sprint
Antiderivatives by the power rule, left-endpoint Riemann sums, FTC evaluation, and area between curves — 2.5 minutes.
💀 Survival
Each miss costs a life — lose them all and the run ends.
🎯 Mastery
No clock — just get N in a row.
🎯 Transformation Mastery
Five in a row, no time pressure — prove you've really got horizontal/vertical shifts down.
🎯 What Makes an Antiderivative
Verify an antiderivative by differentiating, not integrating again — four in a row.
🎯 Definite Integral Properties
Reversing the bounds negates the whole answer — four in a row.
🎯 Function Fundamentals Concepts
Is it a function, reading increasing/decreasing from turning points, and classifying even/odd/neither — five in a row.
📉 Continuity Concepts Mastery
Reason through limit intuition, infinite limits, continuity conditions, discontinuity types, and the IVT.
📐 Derivative Concepts Mastery
Read a derivative's sign from graph behavior and reason about differentiability vs. continuity.
🔗 Composite Structure Mastery
Identify the outer and inner functions of a composite before applying the chain rule.
🔗 Inverse Trig Derivatives Mastery
Differentiate arcsin and arctan of a linear inner function.
📈 MVT Theorems Mastery
Reason through the EVT, Rolle's theorem, and consequences of the Mean Value Theorem.
📈 Curve Sketching Concepts Mastery
Classify extrema and graph features, read end behavior, identify indeterminate forms, and reconstruct f from f'.
🔄 Substitution Concepts Mastery
Choose the right u for a substitution and decompose a composite function into (f, g).
🧮 Conjugate Reciprocal Mastery
Use the conjugate to find the real part of $1/z$ — four in a row.
📉 Limits at Infinity Mastery
Same degree top and bottom — read the horizontal asymptote from the leading coefficients.
📈 Mean Value Mastery
Find the $c$ the Mean Value Theorem guarantees for a cubic.
📈 Second Derivative Test Mastery
Classify a critical point by the sign of $f''$ — four in a row.
🎯 Optimization Strategy Mastery
Set up fixed-sum problems and remember the endpoint check when the domain is restricted.
∫ Accumulation Derivative Mastery
Differentiate an accumulation function straight from FTC Part 1 — no integrating required.
∫ Integral Additivity Mastery
Split and rejoin integrals over adjacent intervals — four in a row.
🔑 Initial Value Mastery
Integrate, then use the initial condition to pin down $C$.
🧠 Recall
Memorize it — no clock, no timer.