Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 65 minutes, as an unvalidated planning estimate. This collection contains 4 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 and give complete domains, all branches and relevant units.
Retain actual fitting inputs, equations, residuals and unused predictions; a selected candidate period is not a global identification.
Graph constructions and explanations require rubric review rather than a text-length or numeric-only mastery claim.
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0 of 4 tasks have recorded responses. No overall mastery score is assigned.
A stipulated sinusoid has maximum 6 at t=−1 and t=7, minimum −2 at t=3, and is falling between −1 and 3. Construct one full graph cycle, recover a cosine rule, and list increasing/decreasing and concavity intervals on [−1,7]. Compare average rates on [3,4] and[4,5].
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.
Run the workbench on x=0,1,2,3,4,5,6,7 and responses 4,2,0,2,4,2,0,2. Compare candidate periods 4 and 4/3; enter the latter to sufficient decimal precision. Retain both equations,SSEs and predictions at x=0.5 before comparing fresh reading 3.5±0.2. Explain why the fitting rows alone cannot choose a period. Tolerance 0.002.
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.
Construct y=2−cot(2x) on 0<x<π, including both branches, and solve y≥3 throughout that window. Give all excluded points and equality endpoints.
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(x)=3−2 sec(x/2), construct a full cycle on −π<x<3π. State all poles,branch vertices,range and directions. SolveR(x)≤1 within that window.
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
A stipulated sinusoid has maximum 6 at t=−1 and t=7, minimum −2 at t=3, and is falling between −1 and 3. Construct one full graph cycle, recover a cosine rule, and list increasing/decreasing and concavity intervals on [−1,7]. Compare average rates on [3,4] and[4,5].
Run the workbench on x=0,1,2,3,4,5,6,7 and responses 4,2,0,2,4,2,0,2. Compare candidate periods 4 and 4/3; enter the latter to sufficient decimal precision. Retain both equations,SSEs and predictions at x=0.5 before comparing fresh reading 3.5±0.2. Explain why the fitting rows alone cannot choose a period. Tolerance 0.002.
