🕹️ Practice arcade

⚡ Geometric Vectors Sprint

Vector components from magnitude/direction, and unit vector components — 90 seconds.

⚡ Vector Arithmetic Sprint

Distance, magnitude, dot products, cross products, projections -- the whole vector toolkit, ninety seconds to rack up as many as you can.

⚡ Vector Function Basics Sprint

Evaluate, take a limit, differentiate -- component by component, as fast as you can.

⚡ Multivariable Evaluation Sprint

Plug in, freeze a variable, read off a rate -- how many two- and three-variable functions can you evaluate in a minute?

⚡ Partial Derivatives Sprint

Freeze a variable, differentiate the rest -- as many partials as you can find in sixty seconds.

⚡ Chain Rule and Approximation Sprint

Differentials, the multivariable chain rule, implicit differentiation, a Taylor coefficient -- ninety seconds, go.

⚡ Gradient Vector Sprint

Build the gradient vector, then its magnitude -- as many as you can in a minute.

⚡ Critical Points and Boundary Sprint

Find the critical point, then check the boundary -- as many extrema hunts as you can finish in ninety seconds.

⚡ Double Integral Setup Sprint

A Riemann sum, an iterated integral, a general region -- set them up and evaluate, ninety seconds on the clock.

⚡ Triple Integral Setup Sprint

A box, a sloped ceiling, a tetrahedron -- set up and evaluate as many triple integrals as you can.

⚡ Vector Fields and Potentials Sprint

Evaluate a field, build one from a gradient, find its potential function -- as many as you can in a minute.

⚡ Parametric Surfaces Sprint

Plug into a parametrization, place a point on a surface of revolution, find a tangent plane -- as many as you can in a minute.

⚡ Divergence and Curl Sprint

Divergence at a point, solve for an incompressible field's missing coefficient, curl's component and magnitude -- as many as you can in a minute.

💀 Multivariable Limits Survival

Does the limit exist? One wrong path and the run ends -- how far can you push it?

🎯 Angles and Quadrics

Classify the angle a dot product implies, then the family a quadric surface belongs to — five in a row.

📐 Angle Classification

Classify the angle a dot product's sign implies -- five in a row.

🎯 Domains and Discontinuities

Spot the domain restriction, then the point where a quotient breaks continuity — five in a row.

🎯 Differentiability Check

Existing partials aren't enough — decide whether a function is actually differentiable, five in a row.

🎯 Peaks, Valleys, and Saddles

Second Derivative Test values in, classification out — five correct in a row.

🎯 Pick a Coordinate System

Rectangular, cylindrical, or spherical — read the boundary, pick the system that fits, five in a row.

🎯 Conservative or Not

Cross-partials in, verdict out — is this vector field conservative? Five correct in a row.

🎯 Reversing the Order

Given a re-sketched region, pick the correctly reversed bounds — five in a row.

🎯 Which Way Is Out?

Outward or inward — read a surface's normal convention correctly, five in a row.

🎯 Parametric Curve Basics

Plot a point from a parametrization, and know what trace vs. parametrization means — four in a row.

🎯 Polar Coordinate Basics

What r and theta mean, negative r, and converting between polar and rectangular — five in a row.

∫ Accumulation Derivative Mastery

Differentiate an accumulation function straight from FTC Part 1 — no integrating required.

∫ Accumulation Function Mastery

Evaluate an accumulation function built from a constant rate.

📏 Arc Length Mastery

Find the arc length of a line segment over an interval.

🎯 Lines, Planes, and Volume

Parametrize a line, pin down a plane, measure the distance between them, then find a parallelepiped's volume -- five in a row.

🎯 Curvature, Motion, and Arc Length

Curvature, torsion, the unit tangent, a projectile's landing time, arc length along a helix -- five correct in a row.

🎯 Traces and Level Sets

Slice a surface, read a level curve, read a level surface -- five in a row, no clock.

🎯 Higher-Order Partials and Tangent Planes

Mixed partials, second pure partials, and the tangent plane they build -- five correct in a row.

🎯 Directional Derivatives and Steepest Ascent

Point the gradient in any direction, then find the one direction that climbs fastest -- six in a row.

📐 Gradient Geometry

The gradient is perpendicular to the level set it came from -- use that fact to find a normal, a tangent plane, a normal line, five in a row.

🎯 Lagrange Multipliers Mastery

One constraint, then two at once, then a least-squares fit -- five correct in a row, no clock.

🎯 Mass, Moments, and Inertia

A double integral computes surface area, mass, a moment, a moment of inertia -- same tool, four different physical questions. Five in a row.

🎯 Cylindrical, Spherical, and the Jacobian

Switch coordinate systems, then account for how the volume element stretches -- five correct in a row.

🎯 Line Integrals and Work

Integrate along a curve, compute the work a field does, then use the Fundamental Theorem to skip the parametrization -- five in a row.

🎯 Surface Integrals and Flux

Surface area, mass over a surface, flux through it -- five correct in a row.

🎯 Green's, Stokes', and the Divergence Theorem

Three fundamental theorems, one family -- turn a boundary integral into a region integral, or back, six times in a row.