Conic Sections
Unit 4 is not assessed on the AP exam; schools include it based on local requirements, and everything here still builds directly toward calculus. The four conic families are told apart by structure: one squared variable makes a parabola; two squared terms added make a circle (equal coefficients) or ellipse (unequal), and subtracted make a hyperbola. Standard forms carry the center in flipped signs and the radius as a square root.
The mistakes are pattern-matching mistakes: classifying by "both are squared" without checking the sign between them, reading the 16 in x squared plus y squared equals 16 as the radius, flipping center signs, dropping the compensating constants while completing the square, and demoting a circle to "not a valid graph" because it fails the vertical line test. Each is drilled in the lesson.
The work
3 ways in · any order
Lesson
Conic Sections
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Count the squared variables, check the sign between them, balance the books when completing the square. The lesson classifies all four conic families by structure, extracts centers and radii without sign or square-root slips, and closes with ten scenarios of classification and conversion.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 4.6 misconceptions: conic classification by surface pattern instead of sign structure, and vertical-line-test verdicts misread as validity verdicts. 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.