Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 55 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.
Show interval widths, intermediate values and units where applicable.
Draw labeled graphs when requested; coordinate descriptions with sufficient shape and landmark information are acceptable.
These are public written practice tasks requiring rubric review, not independently certified mastery.
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A stipulated position model is s(t)=t²−4t+7 meters on [0,5] seconds. Compare right secants at t=1 and t=4 with widths 0.5 and 0.05. Identify the restricted minimum from a completed square and explain why comparing position levels alone would miss the opposite motion directions. Sketch the graph using its vertex and endpoints; compare it with the chord from t=1 to t=4 to explain the direction of bending.
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 quadratic model sampled every 2 hours has q(0)=5 and successive output changes 6,−2,−10. Recover its equation, show the second-difference and interval-rate patterns, and find its extrema on [0,6]. State what its end limits mean only when the polynomial is extended to all real inputs.
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.
Observed pairs are (−1,4),(0,1),(1,0),(2,1). Fit a quadratic using equal-step differences. Construct a degree-4 alternative matching every pair but 2 units larger at x=1/2. Compare the two models’ end behavior and explain why taking more nearby secants at only the same recorded endpoints would not determine the unsampled value.
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 position model is s(t)=t²−4t+7 meters on [0,5] seconds. Compare right secants at t=1 and t=4 with widths 0.5 and 0.05. Identify the restricted minimum from a completed square and explain why comparing position levels alone would miss the opposite motion directions. Sketch the graph using its vertex and endpoints; compare it with the chord from t=1 to t=4 to explain the direction of bending.
A quadratic model sampled every 2 hours has q(0)=5 and successive output changes 6,−2,−10. Recover its equation, show the second-difference and interval-rate patterns, and find its extrema on [0,6]. State what its end limits mean only when the polynomial is extended to all real inputs.
Observed pairs are (−1,4),(0,1),(1,0),(2,1). Fit a quadratic using equal-step differences. Construct a degree-4 alternative matching every pair but 2 units larger at x=1/2. Compare the two models’ end behavior and explain why taking more nearby secants at only the same recorded endpoints would not determine the unsampled value.
