Visual Labs — Interactive Math Visualizers
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2026-03-15
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Live interactive tools for the major Maths I patterns. Drag points, move sliders, and rehearse calculus structure.
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Relevant recall pieces for this note
Maths I — Interactive Visual Aids
These are the quickest revision tools for the high-risk Maths I patterns.
Use them when the question is about geometry, slope, roots, sets, or calculus structure.
Week 5 / 6 - Derivative and Tangent Intuition
Derivative VisualizerThe CurveThis is f(x) = x². As x grows, the curve gets steeper.
→The steepness at any point is what we want to measure.
The derivative visual is the fastest way to refresh secant-to-tangent thinking before a calculus-heavy assignment.
Week 2 — Coordinate Geometry
1. Distance & Midpoint Formulæ
The two foundational tools for working with points in a plane. Use the interactive tool below, drag points A and B and switch between Distance and Midpoint tabs.
Interactive • Drag the points
Coordinate Geometry
Formula
d = √[(x₂-x₁)² + (y₂-y₁)²]Substituted
= √[(6 - -4)² + (5 - -3)²]
= √[10² + 8²]
= √[100 + 64]
= 12.8062
💡 Drag points A and B on the graph — all values update live.
Distance uses subtraction, midpoint uses addition. The exam trap is mixing up spread versus average.
Week 3 — Straight Lines
2. The Slope-Intercept Form
A straight line can always be written as where:
- = slope
- = y-intercept
Interactive Simulation
Straight Lines — y = mx + b
y = 1x + 2m (slope)1b (y-intercept)2📐 Slope = rise / run = 1
↔ X-intercept: (-2, 0)
↕ Y-intercept: (0, 2)
Parallel lines have the same slope. Perpendicular slopes multiply to -1.
Week 4 — Quadratic Functions & Polynomials
3. The Parabola Sandbox
The general quadratic form is . Use the sliders to manipulate all three coefficients and watch the vertex, roots, and discriminant.
Interactive Simulation
Quadratic Function — f(x) = ax² + bx + c
f(x) = 1x² + 0x + -4aopens up if +1bhorizontal shift0cy-intercept-4📍 Vertex: (0, -4)
📐 Axis of Symmetry: x = 0
△ Discriminant (b²-4ac): +16 (2 real roots)
🎯 Roots: 2, -2
Note
gives two roots, gives one repeated root, and gives no real roots.
Week 1 — Set Theory
4. Venn Diagram Explorer
Conceptual Lab
Venn Logic Sandbox
Set ASet BComputation
A ∩ BElements common to both A and B.
Cardinality245
De Morgan's Laws are the fastest mark pickup in this unit.
5. Relation & Mapping Arrows
Theory Visualizer
Relations & Mapping
Set A (Domain)Set B (Codomain)Live Telemetry
StatusNot a FunctionConnect elements to begin mapping analysis.
One-to-OneOntoDomain:{}Range:{}Codomain (B):{1, 2, 3, 4}
A function needs every domain element to have one and only one arrow.
Signed Area and FTC
Step 0 / 0Scene InitializationManim Core v0.1
If the graph sits below the axis, the answer becomes negative. Do not silently turn it into absolute area.
Best Practices
Study Strategy for Visualizers
Predict the answer first, then use the visualizer to confirm or correct your intuition. That builds genuine understanding instead of passive watching.