Periodic Phenomena
Periodic behavior repeats a full pattern on a fixed interval, and three numbers summarize it: the period (length of one cycle), the midline (the center level, the average of max and min), and the amplitude (half the total swing, measured from the midline). One measured cycle predicts the function arbitrarily far away by adding whole periods.
The mistakes are measurement mistakes: calling peak-to-trough a full period when it is half, quoting the full swing as the amplitude when amplitude is half of it, confusing period with frequency (they are reciprocals), and losing count of whole cycles when predicting ahead. Each is drilled in the lesson.
The work
3 ways in · any order
Lesson
Periodic Phenomena
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One cycle tells all. The lesson measures period, midline, and amplitude off graphs and contexts, splits period from frequency, and predicts far-away values by whole-cycle counting. Ten scenarios close it out: tides, wheels, heartbeats, and graphs described in words.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 3.1 misconceptions: half-cycle and reciprocal errors around the period, and mapping context features onto the wrong sinusoid measurement. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.