Visual Labs — Interactive Math Visualizers

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2026-03-15

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Maths I — Interactive Visual Aids

These are live, interactive tools for every major concept in the Maths I syllabus.
Drag points, move sliders, change operations — the math updates instantly.

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.

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

M = \left(\frac{x_1+x_2}{2},\; \frac{y_1+y_2}{2}\right)

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.

Tip

Pattern Recognition: Distance uses subtraction (spread apart), Midpoint uses addition (average together). Classic exam trap: confusing which uses +/-.

Week 3 — Straight Lines

2. The Slope-Intercept Form

A straight line can always be written as

y = mx + b

where:

$m$ = slope (steepness, sign of direction)
$b$ = y-intercept (where it crosses the y-axis)

Adjust the sliders to see how slope and intercept change the line. Notice the dashed rise/run triangle that appears to visualize what slope physically means.

Interactive Simulation
Straight Lines — y = mx + b
y = 1x + 2
m (slope)1
b (y-intercept)2
📐 Slope = rise / run = 1
↔ X-intercept: (-2, 0)
↕ Y-intercept: (0, 2)

Important

Parallel Lines have the same slope (

m_1 = m_2

).
Perpendicular Lines have slopes that multiply to −1 (

m_1 \times m_2 = -1

Week 4 — Quadratic Functions & Polynomials

3. The Parabola Sandbox

The general quadratic form is

f(x) = ax^2 + bx + c

. Use the sliders to manipulate all three coefficients and watch:

The vertex (min/max point) move
The roots (x-intercepts) appear, merge, or vanish
The discriminant ( $b^2 - 4ac$ ) tell you how many real roots exist

Interactive Simulation
Quadratic Function — f(x) = ax² + bx + c
f(x) = 1x² + 0x + -4
aopens up if +1
bhorizontal shift0
cy-intercept-4
📍 Vertex: (0, -4)
📐 Axis of Symmetry: x = 0
△ Discriminant (b²-4ac): +16 (2 real roots)
🎯 Roots: 2, -2

Note

Discriminant Decision Tree:

$\Delta > 0$ → 2 distinct real roots (line cuts parabola in two places)
$\Delta = 0$ → 1 repeated root (line is tangent)
$\Delta < 0$ → no real roots (line doesn't touch)

Week 1 — Set Theory

4. Venn Diagram Explorer

Select an operation from the buttons to see which elements get highlighted in the Venn diagram.

\text{Operations: } A \cup B,\; A \cap B,\; A - B,\; B - A,\; A',\; B'

Conceptual Lab
Venn Logic Sandbox
Set A
Set B
Computation
A ∩ B
Elements common to both A and B.
Cardinality
2
4
5

Tip

De Morgan's Laws (crucial for exams):

$(A \cup B)' = A' \cap B'$
$(A \cap B)' = A' \cup B'$ Mnemonic: Break the bar, flip the operator.

5. Relation & Mapping Arrows

Visualize relations between Set A (Domain) and Set B (Codomain). Create arrows to see if a relation is a Function, One-to-One, or Onto.

Theory Visualizer
Relations & Mapping
Set A (Domain)
Set B (Codomain)
Live Telemetry
StatusNot a Function
Connect elements to begin mapping analysis.
One-to-One
Onto
Domain:{}
Range:{}
Codomain (B):{1, 2, 3, 4}

Note

Function Rules:

Every element in A must have an arrow.
No element in A can have MORE than one arrow.

Best Practices

Study Strategy for Visualizers Try to predict the answer first (e.g., "if I make a=0, the parabola becomes a straight line"), then use the visualizer to confirm or correct your intuition. This builds genuine understanding vs passive watching.

Maths I — Interactive Visual Aids

Week 2 — Coordinate Geometry

1. Distance & Midpoint Formulæ

Coordinate Geometry

Week 3 — Straight Lines

2. The Slope-Intercept Form

Straight Lines — y = mx + b

Week 4 — Quadratic Functions & Polynomials

3. The Parabola Sandbox

Quadratic Function — f(x) = ax² + bx + c

Week 1 — Set Theory

4. Venn Diagram Explorer

Venn Logic Sandbox

5. Relation & Mapping Arrows

Relations & Mapping

Live Telemetry

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