Circles
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalCircle questions run on three moves. The points leak in the conversion, a diameter squared in the area formula or handed back when the radius was asked, in the whole, an angle fraction multiplied into the area when an arc was asked, or taken out of 180, and in the equation: a center read with both signs flipped, or r-squared reported as the radius.
These patterns aren't really about whether you know the circle formulas. They're about whether the diameter got halved before touching one, whether the fraction met the circumference for arcs and the area for sectors, and whether the equation's parentheses got zeroed instead of copied.
The work
4 ways in · any order
Lesson
Circles
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Halve diameters before the formulas see them, portion arcs from the circumference and sectors from the area out of 360, and read the circle equation by zeroing each parenthesis and rooting the right side. The lesson works the method and the three patterns that derail it, and it saves the trap for last: the signs copied straight off the equation.
Diagnostic
10-item topic check
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Ten items across the three patterns: radius-diameter conversions missed, arc and sector proportionality crossed, and circle-equation centers or radii misread. A mix of forward and backward formula work, central angles, and equations read, built, and pinned through a point. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.