Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 60 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.
Try the entire set before revealing worked solutions. You may use paper for calculations and diagrams. The suggested time is guidance; no timer limits access.
Show your reasoning for every task, including domain restrictions and checks in the original statement. Exact-value matches assess only the requested result.
Written arguments require review against the supplied rubric. Recording a response or marking a lesson complete does not certify mastery.
These are public practice assessments. First responses and solution exposure are retained; another attempt is practice, not a new independent examination.
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0 of 8 tasks have recorded responses. No overall mastery score is assigned.
A workshop charges 18 dollars per group and 7 dollars per participant n. A learner writes 25n. Give the correct cost expression, calculate both expressions for n=4, and determine every real n for which the expressions agree. Explain the relevant 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.
Solve (3x−2)/4 − (x+1)/6 = 5/3. Give the exact solution.
Integers, fractions and finite decimals are accepted. Expressions such as sqrt(2) are not parsed by this checker.
A transport model is C=f+pn, where f is a fixed charge, p a per-person charge, and n a nonnegative integer. Derive the budget condition C≤B for p>0, then solve it for f=31, p=8 and B=100. Explain p=0 separately.
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 real solutions of |3x+1|=8. Enter the finite solution set.
Integers, fractions and finite decimals are accepted. Separate values with commas; type none for no solutions. Expressions such as sqrt(2) are not parsed by this checker.
Solve (x²−9)/(x−3)=6 over its original real domain. Explain why simplifying the expression does not restore an excluded input.
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 √(3x+4)=x over the real numbers. Enter every valid solution.
Integers, fractions and finite decimals are accepted. Separate values with commas; type none for no solutions. Expressions such as sqrt(2) are not parsed by this checker.
Solve 2x²+4x+5=0 over the complex numbers, show a completing-the-square derivation, and explain why there are no real solutions.
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.
Classify the real solutions of (a−2)x=6 as a varies. Then, for a<2, solve (a−2)x≤6 and explain the direction of the inequality.
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 workshop charges 18 dollars per group and 7 dollars per participant n. A learner writes 25n. Give the correct cost expression, calculate both expressions for n=4, and determine every real n for which the expressions agree. Explain the relevant contextual domain.
A transport model is C=f+pn, where f is a fixed charge, p a per-person charge, and n a nonnegative integer. Derive the budget condition C≤B for p>0, then solve it for f=31, p=8 and B=100. Explain p=0 separately.
