Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 90 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.
Attempt the set before revealing criteria or worked solutions. Choose your own methods and show the intermediate reasoning on paper or in the written responses.
Check domains, hypotheses and units. An exact answer match only checks the requested value; written work needs review.
Suggested time is guidance, not an access limit. First responses and known answer guidance remain in saved history. These public tasks do not certify independent mastery or readiness for a whole course examination.
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0 of 8 tasks have recorded responses. No overall mastery score is assigned.
Let f(t)=√(t+2), with its full real domain, and g(x)=3−2f(4−x). Find the domain and range of g. Map the endpoint of the graph of f to the corresponding point of g, explaining both input and output transformations.
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 delivery tariff is T(w)=6 for 0<w≤2 and T(w)=6+3(w−2) for w>2, in dollars for weight w in kilograms. Packaging adds 1/2 kg to a positive item mass m. Write the cost as a piecewise function of m, evaluate it at m=3/2 and m=5/2, and explain which branch contains the 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.
For f(x)=(x−3)²+2 restricted to x≥3, derive its inverse, stating the inverse domain and range. Verify both compositions on their respective domains. Explain why the negative square-root branch is inappropriate.
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.
Find all intersections of y=x²−2x and y=2x+5. Give coordinates and check both equations. Explain why solving only for the positive x-value would lose a valid intersection.
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.
Let p(x)=x³−4x²+5x−2. Divide by x−2, factor the quotient, and describe each real zero, its multiplicity and whether the graph crosses or touches the axis there. Give the end behavior.
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.
Analyze r(x)=(x²−x−6)/(x²−4) on its original real domain: identify exclusions, a removable hole with its missing output, any vertical asymptote and its one-sided signs, and the horizontal asymptote.
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.
Solve log₂(x−1)+log₂(x−3)=3 over the real numbers. Give the only valid x-value.
Integers, fractions and finite decimals are accepted. Expressions such as sqrt(2) are not parsed by this checker.
Two modeled weekly production sequences start at 80 units in week 1. A adds 20 units each week; B multiplies the previous week by 3/2. Find each week-4 output and the total over weeks 1–4. State formulas for aₙ and bₙ with correct indexing and explain why the models eventually behave differently.
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
Let f(t)=√(t+2), with its full real domain, and g(x)=3−2f(4−x). Find the domain and range of g. Map the endpoint of the graph of f to the corresponding point of g, explaining both input and output transformations.
A delivery tariff is T(w)=6 for 0<w≤2 and T(w)=6+3(w−2) for w>2, in dollars for weight w in kilograms. Packaging adds 1/2 kg to a positive item mass m. Write the cost as a piecewise function of m, evaluate it at m=3/2 and m=5/2, and explain which branch contains the boundary.
For f(x)=(x−3)²+2 restricted to x≥3, derive its inverse, stating the inverse domain and range. Verify both compositions on their respective domains. Explain why the negative square-root branch is inappropriate.
Find all intersections of y=x²−2x and y=2x+5. Give coordinates and check both equations. Explain why solving only for the positive x-value would lose a valid intersection.
Let p(x)=x³−4x²+5x−2. Divide by x−2, factor the quotient, and describe each real zero, its multiplicity and whether the graph crosses or touches the axis there. Give the end behavior.
Analyze r(x)=(x²−x−6)/(x²−4) on its original real domain: identify exclusions, a removable hole with its missing output, any vertical asymptote and its one-sided signs, and the horizontal asymptote.
Two modeled weekly production sequences start at 80 units in week 1. A adds 20 units each week; B multiplies the previous week by 3/2. Find each week-4 output and the total over weeks 1–4. State formulas for aₙ and bₙ with correct indexing and explain why the models eventually behave differently.
