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Drill Modes & Controls
Train rapid conceptual recognition and piecewise graph construction.
- Untimed Practice: Untimed and pressure-free. Focus on conceptual graph reasoning without a ticking clock. If you make an error, the drill pauses so you can compare the graphs. Click ↺ Reset to retry the current graph or ↻ New Graph to advance.
- Pick Mode: Study the source curve. Click or press keys 1–4 to identify the correct partner graph.
- Build Mode: Construct the target curve segment-by-segment! Click or press keys 1–9 to assign shapes to each time interval.
- Sprint (90s): Race against the clock. Stop anytime with Stop Sprint.
- Reset Controls: Use ↺ Reset to clear current selections, or Reset Score in the HUD to start a fresh practice session.
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Slope Rules (x → v → a)
Remember: Slope takes you down from Position to Velocity to Acceleration.
- x–t → v–t (Slope of Position is Velocity):
• Tangent slope is positive ⇒ v > 0 (above zero time axis).
• Tangent slope is negative ⇒ v < 0 (below zero time axis).
• Horizontal tangent / peak / valley ⇒ v = 0 (instantaneous rest / turnaround).
- v–t → a–t (Slope of Velocity is Acceleration):
• Rising straight line (/) ⇒ constant positive acceleration (+a).
• Falling straight line (\) ⇒ constant negative acceleration (−a).
• Horizontal line (—) ⇒ zero acceleration (a = 0).
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Area & Concavity Shortcuts
Remember: Area takes you up from Acceleration to Velocity to Position.
- Area Under Curves:
• Area under a–t curve between t1 and t2 = Δv (change in velocity).
• Area under v–t curve between t1 and t2 = Δx (displacement).
- Concavity on x–t:
• Concave up (∪, smiling curve): Positive acceleration (a > 0).
• Concave down (∩, frowning curve): Negative acceleration (a < 0).
• Straight line (no curve): Zero acceleration (a = 0).
- Speeding Up vs Slowing Down:
• Same signs (v > 0, a > 0 OR v < 0, a < 0) ⇒ speeding up (moving away from v = 0).
• Opposite signs (v > 0, a < 0 OR v < 0, a > 0) ⇒ slowing down (approaching v = 0).
- Curvature & Tangent Tools:
• Interactive Tangent Wand: Hover or touch/drag across any curve to probe its slope. If the wand stays at a fixed angle, the slope is constant (⇒ straight line, a = 0). If the wand continuously tilts/rotates, the slope is changing (⇒ accelerated parabola).
• Straight Reference (📏): Click Straight Reference above the graph to overlay dashed straight chords across segment boundaries, instantly highlighting any parabolic sagitta/bulge.