Subject entry4 topics6 concepts2 starter tracks1 bridge145 min

Math

Enter the current math slice through functions, change, vectors, complex-plane geometry, 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, then widen into plane-based complex numbers, 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 track3 concepts70 min2 checkpoints

Functions and Change

Not started

Keep the first math path compact: read parent-curve moves first, then local slope, and then accumulation so change stays graph-first all the way through.

Parent-curve movesShifts and reflectionsTangent slopeLocal rate of changeSigned area and accumulation

Track progress

0 / 5 moments complete

0 / 3 concepts and 0 / 2 checkpoints cleared.

1Graph Transformations

Start here

2Derivative as Slope / Local Rate of Change

Ahead

3Integral as Accumulation / Area

Ahead

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

Start track Jump to Graph transforms

Starter track2 concepts50 min2 checkpoints

Complex and Parametric Motion

Not started

Start with complex numbers as points on one plane, then carry that same coordinate language into motion traced from x(t) and y(t).

Complex points on a planeMagnitude and argumentScale and rotationPath vs traversal

Track progress

0 / 4 moments complete

0 / 2 concepts and 0 / 2 checkpoints cleared.

1Complex Numbers on the Plane

Start here

2Parametric 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 min2 checkpoints

Vectors and Motion Bridge

Not started

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

Magnitude and directionAddition and subtraction

Track progress

0 / 4 moments complete

0 / 2 concepts and 0 / 2 checkpoints cleared.

1Vectors in 2D

Start here

2Vectors and Components

Ahead

Vectors in 2D opens this track and sets up the rest of the path.

Start track Jump to 2D vectors

Topics

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

TopicMath1 concepts20 min1 starter track

Functions

Use one parent-curve bench to read shifts, reflections, and vertical scale as visible moves on the graph before the math path widens into local and accumulated change.

Parent-function moves

Best first concepts

Graph transforms

Open topic Start Graph transforms

TopicMath2 concepts50 min1 starter track

Calculus

Start from slope on the graph itself, then widen into signed area and accumulation so rate and total change stay connected on one visual branch.

Tangent and local changeAccumulation and area

Best first concepts

Derivative as slope Integral as area

Open topic Start Derivative as slope

TopicMath2 concepts50 min1 starter track

Complex Numbers and Parametric Motion

Use one bounded math branch where the complex plane, geometric multiplication, and motion traced from equations all stay tied to the same coordinate language.

Complex plane geometryPlane motion from equations

Best first concepts

Complex numbers Parametric curves

Open topic Start Complex numbers

TopicMath1 concepts25 min1 starter track

Vectors

Use one 2D plane to read vectors as both arrows and ordered pairs, then bridge that same language into motion without building a separate math system.

Combination and scaling

Best first concepts

2D vectors

Open topic Start 2D vectors

Best first concepts

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

MathFunctionsIntro20 minNot startedMastery: New

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.

Left and right shiftsUp and down shifts

Open concept

MathComplex Numbers and Parametric MotionIntro25 minNot startedMastery: New

Complex Numbers on the Plane

Read complex numbers as points and vectors on one plane, then keep addition and multiplication geometric instead of symbolic-only.

Real and imaginary partsMagnitude and argument

Open concept

MathComplex Numbers and Parametric MotionIntro25 minNot startedMastery: New

Parametric Curves / Motion from Equations

Keep x(t), y(t), the traced path, and the moving point visible together so shape and traversal stay distinct.

x(t) and y(t) togetherPath vs traversal

Open concept

MathCalculusIntro25 minNot startedMastery: New

Derivative as Slope / Local Rate of Change

Slide a point along one curve, tighten a secant into a tangent, and connect local steepness to the derivative graph without leaving the same live bench.

Secant to tangentLocal rate of change

Open concept

MathVectorsIntro25 minNot startedMastery: New

Vectors in 2D

Combine, subtract, and scale vectors on one plane so magnitude, direction, and components stay tied to the same live object.

Tip-to-tail combinationComponents on the plane

Open concept