Subject entry4 topics16 concepts2 starter tracks1 bridge376 min

Math

Enter the current math slice through graph transformations, rational-function asymptotes, exponential change, vectors, complex-plane geometry, trig identities, inverse-angle reasoning, polar coordinates, and parametric motion without leaving the same live-bench product language used elsewhere on the site.

Math is still intentionally compact, but it now has more than one durable branch. Start here when you want the graph-first launch path through transformations, rational asymptote behavior, and exponential change, then widen into plane-based complex numbers, unit-circle and polar geometry, trig identities, inverse-angle recovery from ratios, parametric motion from equations, or the vectors bridge back into mechanics.

Start Functions and Change Open Functions New here? Start here Search Math Browse Math concepts

Starter tracks

Start with a bounded path before branching wider.

Open concept library

Starter track6 concepts139 min5 checkpoints

Functions and Change

Track not started

Keep the first math path compact: read parent-curve moves first, then rational asymptotes and domain breaks, then exponential growth and decay, local slope, visible limit behavior, and finally accumulation so change stays graph-first all the way through.

Parent-curve movesShifts and reflectionsRational asymptotes and holesExponential growth and decayTarget time from logsTangent slopeOne-sided limits and continuityLocal rate of changeSigned area and accumulation

Track progress

0 of 11 moments complete

0 of 6 concepts complete and 0 of 5 checkpoints cleared.

1Graph Transformations

Start here

2Rational Functions / Asymptotes and Behavior

Ahead

3Exponential Change / Growth, Decay, and Logarithms

Ahead

4Derivative as Slope / Local Rate of Change

Ahead

5Limits and Continuity / Approaching a Value

Ahead

6Integral as Accumulation / Area

Ahead

Graph Transformations opens this track and sets up the rest of the path.

Start track Jump to Graph transforms

Starter track6 concepts140 min4 checkpoints

Complex and Parametric Motion

Track not started

Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).

Complex points on a planeUnit-circle and polar geometryTrig identities from one pointQuadrant-aware inverse trigPath vs traversal

Track progress

0 of 10 moments complete

0 of 6 concepts complete and 0 of 4 checkpoints cleared.

1Complex Numbers on the Plane

Start here

2Unit Circle / Sine and Cosine from Rotation

Ahead

3Polar Coordinates / Radius and Angle

Ahead

4Trig Identities from Unit-Circle Geometry

Ahead

5Inverse Trig / Angle from Ratio

Ahead

6Parametric Curves / Motion from Equations

Ahead

Complex Numbers on the Plane opens this track and sets up the rest of the path.

Start track Jump to Complex numbers

Cross-subject bridge

Keep the bridge visible when it genuinely connects subjects.

Starter track2 concepts50 min

Vectors and Motion Bridge

Start with vectors as geometric objects on a 2D plane, then carry the same component language into the existing motion-facing vectors bench.

Starts with Vectors in 2D across 2 concepts.

Start track

Topics

Use topics when you want the subject shaped into a clearer map.

TopicMath3 concepts65 min1 starter track

Functions

Use parent-curve moves, a shifted reciprocal family, and one exponential bench so graph moves, asymptotes, domain breaks, growth versus decay, and target-time questions stay tied to the same visual branch before the math path widens into local and accumulated change.

Parent-function movesRational functions and asymptotesExponential growth and decay

Best first concepts

Graph transforms Rational functions Exponential change

Open topic Start Graph transforms

TopicMath4 concepts98 min1 starter track

Calculus

Start from slope on the graph itself, use one constrained rectangle bench to make a real maximum visible, keep limit and continuity behavior available on one target point, and then widen into signed area and accumulation so rate and total change stay connected on one visual branch.

Tangent and local changeLimits and visible continuityConstrained maxima and minima

Best first concepts

Derivative as slope Limits and continuity Optimization and constraints

Open topic Start Derivative as slope

TopicMath6 concepts140 min1 starter track

Complex Numbers and Parametric Motion

Use one bounded math branch where the complex plane, unit-circle rotation, polar coordinates, trig identities, inverse-angle reasoning, and motion traced from equations all stay tied to the same coordinate language.

Complex plane geometryRotation and projectionsRadius-angle coordinates

Best first concepts

Complex numbers Unit circle rotation Polar coordinates

Open topic Start Complex numbers

TopicMath3 concepts73 min1 starter track

Vectors

Use one 2D plane to read vectors as arrows, ordered pairs, matrix actions, alignment measures, and projections before the same language bridges into motion.

Combination and scalingLinear actions on the planeAlignment and projection

Best first concepts

2D vectors Matrix transforms Dot product

Open topic Start 2D vectors

Best first concepts

Start with one strong concept when you do not need the full path yet.

MathFunctions

Graph Transformations

Move one parent curve with honest controls so shifts, vertical scale, and reflections stay tied to the same overlaid graph and landmark points.

Open Graph transforms

MathFunctions

Rational Functions / Asymptotes and Behavior

Vary one shifted reciprocal family so domain breaks, vertical and horizontal asymptotes, intercepts, and removable-hole behavior stay tied to the same graph.

Open Rational functions

MathFunctions

Exponential Change / Growth, Decay, and Logarithms

Change one starting value, one rate, and one target so growth, decay, doubling or half-life, and logarithmic target time all stay tied to the same live curve.

Open Exponential change