Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 50 minutes, as an unvalidated planning estimate. This collection contains 3 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Use radians, equal Cartesian scales and complete angle restrictions. Preserve signed radii when constructing points.
Retain interpolation inputs and assumptions; a numerical estimate does not certify the unobserved curve.
Graph constructions and explanations require rubric review, not a text-length or numeric-only mastery claim.
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0 of 3 tasks have recorded responses. No overall mastery score is assigned.
Construct r=2+4 sin θ over 0≤θ≤2π. List both origin angles, the inner-loop interval and one farthest point. Then identify all angles whose Cartesian x coordinate is nonnegative; show the required product sign chart rather than relying on angle alone.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
For r=4 cos(2θ), construct the complete four-petal curve and select the bottom petal using one contiguous angular interval in [0,2π]. On that interval, state signed-radius and distance trends, every origin endpoint and the farthest point.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
A synthetic table gives r=−3 at θ=π/4 and r=5 at θ=3π/4. Use the interpolation tool to estimate at θ=π/2; report signed radius,distance,Cartesian point and average signed change per radian. Then exhibit another continuous radial function matching the endpoints but giving signed radius −2 at the query. Explain the evidence boundary.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
Construct r=2+4 sin θ over 0≤θ≤2π. List both origin angles, the inner-loop interval and one farthest point. Then identify all angles whose Cartesian x coordinate is nonnegative; show the required product sign chart rather than relying on angle alone.
For r=4 cos(2θ), construct the complete four-petal curve and select the bottom petal using one contiguous angular interval in [0,2π]. On that interval, state signed-radius and distance trends, every origin endpoint and the farthest point.
A synthetic table gives r=−3 at θ=π/4 and r=5 at θ=3π/4. Use the interpolation tool to estimate at θ=π/2; report signed radius,distance,Cartesian point and average signed change per radian. Then exhibit another continuous radial function matching the endpoints but giving signed radius −2 at the query. Explain the evidence boundary.
