Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 80 minutes, as an unvalidated planning estimate. This collection contains 8 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.
Work independently before revealing solutions. Supply labeled sketches or precise coordinate-and-segment descriptions when requested.
All contexts are synthetic. Written responses require mathematical review; saving or completing this assessment is not an automatic claim of mastery.
Loading saved assessment responses…
0 of 8 tasks have recorded responses. No overall mastery score is assigned.
A rectangular display measures 24.0±0.2 cm by 15.0±0.1 cm as guaranteed bounds. Compute area bounds in cm² and m². Choose a report precision. Explain how an area graph with vertical origin 350 cm² should be labeled.
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 complete piecewise-linear tank graph has vertices (0,6),(2,18),(7,28), with minutes and liters. Sketch it and calculate both segment rates and the whole-period rate. Compare with B(t)=5+4t at t=2 and t=7; explain why comparing increments alone misleads.
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.
Describe graphs y=−cuberoot(x+2)+1 and C(t)=7ceil(t/3) on 0≤t≤9 with C(0)=0. Give five root landmarks, all step endpoints, domains and ranges.
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 function is f(x)=(1/2)^(x−2)+3. Give its asymptote and three landmarks; describe transformations from the decay parent. Find inverse values at outputs4 and 5 and state inverse domain/range.
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 sequence a₀=3, aₙ₊₁=−2aₙ is defined for integer n≥0. Give four terms and explicit form. Does alternation make it an odd function? Separately classify h(x)=x³+x on the symmetric domain [−2,2].
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 quantity rises from 12 to 27 in two months under a positive exponential model. Find a monthly formula, express it in years, and find the first whole month at or above 100.
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 integer n≥1 compare 4^n and 50n². Locate the first strict exponential lead and prove it persists. Explain why a plot through n=3 is insufficient.
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.
Sketch p(x)=(x+1)²(x−2) and r(x)=(x²−9)/(x−3), stating crossings, touches, end behavior and holes. A separate seller has demand q=12−p for price 0≤p≤12 and cost C(q)=2q+6. Build revenue and profit, find the maximum profit and explain the contextual domain.
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 rectangular display measures 24.0±0.2 cm by 15.0±0.1 cm as guaranteed bounds. Compute area bounds in cm² and m². Choose a report precision. Explain how an area graph with vertical origin 350 cm² should be labeled.
A complete piecewise-linear tank graph has vertices (0,6),(2,18),(7,28), with minutes and liters. Sketch it and calculate both segment rates and the whole-period rate. Compare with B(t)=5+4t at t=2 and t=7; explain why comparing increments alone misleads.
A function is f(x)=(1/2)^(x−2)+3. Give its asymptote and three landmarks; describe transformations from the decay parent. Find inverse values at outputs4 and 5 and state inverse domain/range.
A sequence a₀=3, aₙ₊₁=−2aₙ is defined for integer n≥0. Give four terms and explicit form. Does alternation make it an odd function? Separately classify h(x)=x³+x on the symmetric domain [−2,2].
A quantity rises from 12 to 27 in two months under a positive exponential model. Find a monthly formula, express it in years, and find the first whole month at or above 100.
Sketch p(x)=(x+1)²(x−2) and r(x)=(x²−9)/(x−3), stating crossings, touches, end behavior and holes. A separate seller has demand q=12−p for price 0≤p≤12 and cost C(q)=2q+6. Build revenue and profit, find the maximum profit and explain the contextual domain.
