Vectors
Unit 4 is not assessed on the AP exam; schools include it based on local requirements, and everything here still builds directly toward calculus and physics. A vector is a magnitude with a direction, written in component form and drawable from any starting point: it is an instruction, not an address. Its arithmetic is componentwise, its magnitude is Pythagorean, and its dot product collapses two vectors into one meaningful number.
The mistakes are identity mistakes: treating a vector as the point at its tip, adding components (or whole magnitudes) to get a length, letting a negative scalar "rotate" a vector somewhere other than exactly backward, and giving the dot product a direction it does not have. Each is named and drilled in the lesson.
The work
3 ways in · any order
Lesson
Vectors
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How far and which way, as one object. The lesson builds component form, the Pythagorean magnitude, tip-to-tail arithmetic, scalar multiples, unit vectors, and the scalar-valued dot product. Ten scenarios close it out, including the classic magnitudes-do-not-add trap.
Diagnostic
10-item topic check
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Ten items spanning the two Topic 4.8 misconceptions: vectors read as points with magnitudes read as sums, and componentwise arithmetic done wrong. 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.