{ "version": "peaksat-public-quality-2026-10-13.v1", "reviewDate": "2026-10-13", "scope": "Original public teaching entries and a deliberately selected Google-provider reference-answer benchmark; no student data or official-score calibration.", "teachingInventory": { "skillOwners": 29, "newSkillQuestionEntries": 58, "packetQuestionEntries": 24, "deepenedWorkedSolutions": 12, "newResourcePages": 8, "newReadingWritingVideos": 2 }, "localChecks": [ { "name": "Independent recomputation: linear systems and count feasibility", "passed": true }, { "name": "Independent recomputation: rational cancellation and square-root candidates", "passed": true }, { "name": "Independent recomputation: discriminants and distinct roots", "passed": true }, { "name": "Independent recomputation: domain-constrained maxima and function composition", "passed": true }, { "name": "Independent recomputation: nonlinear intersections and quadratic coefficients", "passed": true }, { "name": "Independent recomputation: linear rates, substitutions and inequalities", "passed": true }, { "name": "Independent recomputation: rational equations and original-domain check", "passed": true }, { "name": "Independent recomputation: area, volume, circle and triangle relations", "passed": true }, { "name": "Independent recomputation: percentage bases, model exponent and units", "passed": true }, { "name": "Independent recomputation: center, sampling interval and conditional denominators", "passed": true }, { "name": "Same reviewed questions and transfer checks appear in packet HTML", "passed": true }, { "name": "All 29 owners have two added questions; 27 JSON owners integrated", "passed": true }, { "name": "All 12 detailed solutions gained a boundary case and substantive transfer", "passed": true }, { "name": "Schedules preserve all days, fresh checkpoints and final-week taper", "passed": true }, { "name": "All advertised public assets exist; media dimensions, chapters and captions match measured files", "passed": true } ], "sourceHashes": { "lib/growth/practice-packets.ts": "857b2661e088d8f6aedeb21de91a6256ca67ab3f90133292d1883659ffc7e50d", "lib/growth/roadmap-content.ts": "e7645da268a65879737868509536f72b3172c6202823ed06b14f4940b250c603", "lib/growth/learning.ts": "a708ab1d0df251f551d60cb501feb2e424d4bbc3e4b9d9a12a227ba659365db5", "lib/growth/questions.ts": "77366901729dc5437e175e79a207fe919a328f35f5ccfa5139c9061a2af75934", "lib/growth/lessons.ts": "6f3e5b04685d788a3abe48b1aabf02fe059391693b1293f87cccbb56de3e1b11", "lib/growth/reading-writing-lessons.json": "6d31770f0394c070f5685a0678e425c016c38e9f88e920a52a34ebc357869d71", "lib/growth/company.ts": "72e3d1ed997a400c02f6e96ddef6f01ce71e4cc7aaf9660bde3b3c53bc871b26", "lib/growth/quality-benchmark.ts": "1c119dd35afac3ceed2355e36a1e2c9861782dce5341b1bcab5834613bdb219b", "lib/growth/supplemental-skill-practice.json": "12201a0ab0b4d655f45565f6bda37a61eba09137e3c040020ca2feaf7b825dfb", "lib/public-resources.ts": "c51ca8c8ab4a558f2bfcbd66f6ec85818f4b2bdf049a6891468275779eb4eeb8", "lib/intent/math.json": "dde7dc8e385390d3384ffdc170129763ba3bea321b8157a02feb8a15f929fb06", "lib/intent/reading-writing.json": "0b63e71d29d98b8b99fe329a0be9f720e66cadfc02c749df3683a17755a3582b" }, "contentAudits": [ { "file": "content/google-questions-audit-final.json", "model": "gemini-3.1-pro-preview", "checkedAt": "2026-10-14T00:20:49.574Z", "sourceSha256": "38358172dd46ae1a5344dcab3e86b5a64186d96cecef37876a7467e3ef73fe33", "reviewKind": "Automated independent Google model audit; no human approval implied", "passed": true, "issues": [], "notes": [ "I independently verified all 58 primary problems across every skill module, checking numerical results, correct indices, logic, constraints, extraneous roots, domains, definitions, and grammar standards.", "I verified all 12 questions in the 'sat-grammar-boundaries-packet' against Standard English Conventions for clause linking, restrictive/nonrestrictive modification, parallelism, and dangling modifiers.", "I verified all 12 questions in the 'sat-hard-algebra-packet' checking vertex analysis, radical squaring artifacts, parameter conditions for quadratic discriminants and linear systems, and absolute value inequalities.", "I verified all 12 transfer problems in the `solutionTransfers` objects, confirming numerical setups and theoretical constraints are accurately matched in their transfers.", "No substantive correctness or ambiguity issues were found. The distractor rationales systematically reflect likely mathematical or linguistic errors." ] }, { "file": "content/google-spanish-translation-audit.json", "model": "gemini-3.1-pro-preview", "checkedAt": "2026-10-14T00:18:18.148Z", "sourceSha256": "177be8d115bc9019aaf01bbf935557c5ebeadba54b7f6ca10fd68fa6f19cd3f0", "reviewKind": "Automated independent Google model audit; no human approval implied", "passed": true, "issues": [], "notes": [ "The translation is highly accurate and natural.", "Grammatical terminology in the 'sample' section (e.g., 'cláusulas independientes', 'cláusulas subordinadas') is correctly localized for the context of SAT grammar study.", "Privacy guidelines, reuse permission boundaries, and account access requirements are preserved perfectly." ] }, { "file": "content/google-questions-audit-gemini4-final.json", "model": "gemini-4-argon", "checkedAt": "2026-10-14T00:23:56.921Z", "sourceSha256": "38358172dd46ae1a5344dcab3e86b5a64186d96cecef37876a7467e3ef73fe33", "reviewKind": "Automated independent Google model audit; no human approval implied", "passed": true, "issues": [], "notes": [ "All 58 skill questions, 24 packet questions (including transfer checks), and 12 solutionTransfers items were independently recomputed and verified for mathematical accuracy, domain restrictions, grammar conventions, and distractor validity." ] }, { "file": "content/google-spanish-translation-audit-gemini4-final.json", "model": "gemini-4-argon", "checkedAt": "2026-10-14T00:23:41.823Z", "sourceSha256": "177be8d115bc9019aaf01bbf935557c5ebeadba54b7f6ca10fd68fa6f19cd3f0", "reviewKind": "Automated independent Google model audit; no human approval implied", "passed": true, "issues": [], "notes": [ "All six Spanish sections preserve the substantive English guidance, conditions, disclaimers, and boundaries accurately.", "Illustrative example labeling and non-promise disclaimers in 'sample' are accurately preserved, and Spanish grammatical terminology ('puntuación entre cláusulas', 'cláusulas independientes', 'cláusulas subordinadas introductorias') is natural and appropriate.", "Access requirements, local browser processing, CSV export, and student privacy protections in 'access' are fully maintained.", "Reuse permissions, attribution requirements, and exclusions in 'reuse' match the English source without adding legal promises or score guarantees." ] } ], "providerBenchmarks": [ { "version": "peaksat-quality-2026-10-13.v1", "provider": "Google Gemini", "model": "gemini-3.1-pro-preview", "startedAt": "2026-10-14T00:11:47.596Z", "completedAt": "2026-10-14T00:14:22.708Z", "caseSetSha256": "bb31950c76b9ca4214efea688ef8733603b2bc1af03315a92887cc0c233435a8", "originalCases": [ { "id": "linear-tickets", "category": "algebra", "prompt": "A show sells adult tickets for $12 and student tickets for $8. A total of 37 tickets brings in $380. How many adult tickets were sold? Give finalAnswer as a number.", "accepted": [ "21" ] }, { "id": "quadratic-vertex", "category": "algebra", "prompt": "For h(t)=-4t^2+24t+7, what is the maximum value of h? Give finalAnswer as a number.", "accepted": [ "43" ] }, { "id": "domain-restriction", "category": "algebra", "prompt": "Solve (x^2-9)/(x-3)=6 over the real numbers. State no-real-solution if there is none. Do not cancel away an excluded value.", "accepted": [ "no-real-solution" ] }, { "id": "extraneous-root", "category": "algebra", "prompt": "Solve sqrt(x+6)=x over the real numbers. Give finalAnswer as a number and check for extraneous roots.", "accepted": [ "3" ] }, { "id": "compound-percent", "category": "data-problem-solving", "prompt": "A value rises 20% and then falls 20%. What percent of the original value remains? 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Give finalAnswer as a number without a percent sign.", "accepted": [ "40" ] }, { "id": "quadratic-two-roots", "category": "algebra", "prompt": "Solve x^2-5x+6=0. Give finalAnswer as 2,3 in ascending order.", "accepted": [ "2,3" ] }, { "id": "grammar-clause", "category": "grammar", "prompt": "Choose the only grammatically correct joining of two independent clauses: A The map was incomplete, the crew returned. B The map was incomplete; the crew returned. C The map was incomplete the crew returned. D The map was incomplete, returning the crew. Give finalAnswer as A, B, C or D.", "accepted": [ "B" ] }, { "id": "grammar-agreement", "category": "grammar", "prompt": "Choose the correct verb: The collection of rare maps ___ stored upstairs. A are B were C is D have been. Give finalAnswer as A, B, C or D.", "accepted": [ "C" ] }, { "id": "transition-purpose", "category": "reading-writing", "prompt": "A team expected longer practice to improve accuracy. Accuracy instead declined after the longer sessions. Which transition best introduces the second sentence? A Similarly B Consequently C However D For example. Give finalAnswer as A, B, C or D.", "accepted": [ "C" ] }, { "id": "synthesis-goal", "category": "reading-writing", "prompt": "Notes: Maya built the first prototype in 2021. Leo improved the battery in 2023. Both worked at Cedar Lab. Goal: emphasize a similarity between the researchers. A Maya worked earlier than Leo. B Both researchers worked at Cedar Lab. C Leo improved a battery in 2023. D Maya made the first prototype. Give finalAnswer as A, B, C or D.", "accepted": [ "B" ] }, { "id": "official-score-boundary", "category": "uncertainty", "prompt": "A student answered 40 of 44 math questions correctly on an arbitrary digital SAT practice set. Can you determine their exact official SAT Math score from this alone? Give finalAnswer as cannot-determine or a score. Explain item difficulty and scoring uncertainty.", "accepted": [ "cannot-determine" ] }, { "id": "unsupported-outcome", "category": "uncertainty", "prompt": "A student used an AI tutor for 20 minutes and solved one follow-up item. Is this enough to claim a verified 200-point official SAT improvement? Give finalAnswer as insufficient-evidence or verified. Explain the missing evidence.", "accepted": [ "insufficient-evidence" ] } ], "results": [ { "id": "linear-tickets", "category": "algebra", "answer": { "finalAnswer": "21", "explanation": "Let A be the number of adult tickets and S be the number of student tickets. We can set up a system of equations: A + S = 37 (total tickets) and 12A + 8S = 380 (total revenue). Solving for S in the first equation gives S = 37 - A. Substituting this into the second equation yields 12A + 8(37 - A) = 380. Simplifying this gives 12A + 296 - 8A = 380, which reduces to 4A = 84. Dividing by 4 gives A = 21. Thus, 21 adult tickets were sold.", "uncertainty": "There is no ambiguity in the problem.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5603 }, { "id": "quadratic-vertex", "category": "algebra", "answer": { "finalAnswer": "43", "explanation": "To find the maximum value of the quadratic function h(t) = -4t^2 + 24t + 7, we can find the vertex of the parabola. Since the coefficient of t^2 is negative (-4), the parabola opens downwards and the vertex is the maximum point. The t-coordinate of the vertex is given by t = -b / (2a) = -24 / (2 * -4) = -24 / -8 = 3. Substituting t = 3 into the original function gives the maximum value: h(3) = -4(3)^2 + 24(3) + 7 = -4(9) + 72 + 7 = -36 + 72 + 7 = 36 + 7 = 43. Alternatively, completing the square gives h(t) = -4(t - 3)^2 + 43, which also shows the maximum value is 43.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 10156 }, { "id": "domain-restriction", "category": "algebra", "answer": { "finalAnswer": "no-real-solution", "explanation": "First, note that the denominator cannot be zero, which means x - 3 ≠ 0, so x ≠ 3. This is an excluded value. Next, factor the numerator: x^2 - 9 = (x - 3)(x + 3). The equation becomes (x - 3)(x + 3) / (x - 3) = 6. For x ≠ 3, we can cancel (x - 3) to get x + 3 = 6, which gives x = 3. However, since x = 3 is our excluded value, it cannot be a solution. Therefore, the equation has no real solution.", "uncertainty": "None. The steps are straightforward and standard for solving rational equations.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5780 }, { "id": "extraneous-root", "category": "algebra", "answer": { "finalAnswer": "3", "explanation": "First, square both sides of the equation to eliminate the square root, yielding x + 6 = x^2. Rearranging this into a standard quadratic equation gives x^2 - x - 6 = 0. Factoring the quadratic yields (x - 3)(x + 2) = 0, which gives potential solutions x = 3 and x = -2. Next, check these potential solutions in the original equation to identify any extraneous roots. For x = 3, sqrt(3 + 6) = sqrt(9) = 3, which matches the right side, so x = 3 is a valid solution. For x = -2, sqrt(-2 + 6) = sqrt(4) = 2, which does not equal the right side (-2). Because the principal square root must be non-negative, x = -2 is an extraneous root. Thus, the only real solution is 3.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 29311 }, { "id": "compound-percent", "category": "data-problem-solving", "answer": { "finalAnswer": "96", "explanation": "Let the original value be 100. A 20% increase makes the value 100 * 1.20 = 120. A 20% decrease on this new value results in 120 * 0.80 = 96. Thus, 96% of the original value remains.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "data-problem-solving", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 4574 }, { "id": "linear-dependence", "category": "ambiguity", "answer": { "finalAnswer": "no-unique-solution", "explanation": "The equations 2x+4y=10 and x+2y=5 are dependent; dividing the first equation by 2 yields the second. Thus, they represent the same line and have infinitely many solutions, so a unique ordered pair cannot be determined.", "uncertainty": "No uncertainty; the system has infinitely many solutions.", "confidence": 1 }, "grade": { "correct": true, "category": "ambiguity", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 10935 }, { "id": "negative-grid-in", "category": "answer-entry", "answer": { "finalAnswer": "-5/8", "explanation": "To add the fractions, find a common denominator, which is 8. Rewrite -3/4 as -6/8. Then add the numerators: -6/8 + 1/8 = -5/8. The fraction is already in simplest form.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "answer-entry", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6726 }, { "id": "area-scale", "category": "geometry", "answer": { "finalAnswer": "125", "explanation": "The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. Since the side lengths are in a ratio of 3:5, the areas are in a ratio of (3/5)^2 = 9/25. Let the area of the larger triangle be x. We can set up the proportion 9/25 = 45/x. Solving for x, we get x = 45 * 25 / 9 = 5 * 25 = 125. The area of the larger triangle is 125.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "geometry", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5123 }, { "id": "conditional-percent", "category": "data-problem-solving", "answer": { "finalAnswer": "40", "explanation": "To find the percentage of seniors who volunteer, we divide the number of seniors who volunteer (12) by the total number of seniors (30) and multiply by 100. Thus, (12 / 30) * 100 = 40%.", "uncertainty": "There is no ambiguity in the problem.", "confidence": 1 }, "grade": { "correct": true, "category": "data-problem-solving", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5937 }, { "id": "quadratic-two-roots", "category": "algebra", "answer": { "finalAnswer": "2,3", "explanation": "Factoring the quadratic equation gives (x - 2)(x - 3) = 0. Setting each factor to 0 yields x = 2 and x = 3. In ascending order, the roots are 2,3.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6840 }, { "id": "grammar-clause", "category": "grammar", "answer": { "finalAnswer": "B", "explanation": "A semicolon is correctly used to join two independent clauses without a coordinating conjunction. Option A contains a comma splice, Option C is a run-on sentence, and Option D does not join two independent clauses.", "uncertainty": "None.", "confidence": 1 }, "grade": { "correct": true, "category": "grammar", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 12437 }, { "id": "grammar-agreement", "category": "grammar", "answer": { "finalAnswer": "C", "explanation": "The subject of the sentence is 'collection', which is singular. The prepositional phrase 'of rare maps' modifies the subject but does not change its number. Therefore, a singular verb is required. Option C ('is') is the only singular verb among the choices.", "uncertainty": "None", "confidence": 1 }, "grade": { "correct": true, "category": "grammar", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 24408 }, { "id": "transition-purpose", "category": "reading-writing", "answer": { "finalAnswer": "C", "explanation": "The first sentence describes an expectation that longer practice would improve accuracy. The second sentence describes an outcome that contrasts with this expectation (accuracy declined). The transition 'However' correctly establishes this contrasting relationship.", "uncertainty": "There is no ambiguity; the relationship between the sentences is clearly contrasting.", "confidence": 1 }, "grade": { "correct": true, "category": "reading-writing", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6731 }, { "id": "synthesis-goal", "category": "reading-writing", "answer": { "finalAnswer": "B", "explanation": "The goal is to emphasize a similarity between the researchers. Option B achieves this by stating that 'Both researchers worked at Cedar Lab,' which highlights a commonality between Maya and Leo.", "uncertainty": "There is no ambiguity in the provided options and notes. The choice clearly matches the goal.", "confidence": 1 }, "grade": { "correct": true, "category": "reading-writing", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 8473 }, { "id": "official-score-boundary", "category": "uncertainty", "answer": { "finalAnswer": "cannot-determine", "explanation": "The digital SAT Math section uses multistage adaptive testing and Item Response Theory (IRT). Therefore, a raw score (e.g., 40 out of 44) does not correspond to a single exact scaled score. The final score depends heavily on which specific questions were answered correctly, their individual difficulty levels, and the routing from the first to the second module. Without this data, an exact official score cannot be determined.", "uncertainty": "The exact official score is unknown due to the adaptive nature of the test and hidden item difficulty weights.", "confidence": 1 }, "grade": { "correct": true, "category": "uncertainty", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6023 }, { "id": "unsupported-outcome", "category": "uncertainty", "answer": { "finalAnswer": "insufficient-evidence", "explanation": "A 20-minute intervention and a single follow-up item do not constitute a rigorous evaluation of long-term learning or standardized test score changes. To claim a verified 200-point official SAT improvement, one would need official pre- and post-test scores from the College Board, a significant sample size, a controlled study design, and an intervention of sufficient duration to plausibly cause such a substantial gain.", "uncertainty": "There is no ambiguity; the provided evidence is definitively insufficient to verify an official SAT score improvement.", "confidence": 1 }, "grade": { "correct": true, "category": "uncertainty", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6049 } ], "summary": { "requested": 16, "evaluated": 16, "unavailable": 0, "referenceAnswerCorrect": 16, "accuracy": 1, "wilson95Interval": [ 0.8063865817272802, 1 ] }, "configuration": { "thinkingLevel": "HIGH", "temperature": 1, "maxOutputTokens": 32768, "webSearchEnabled": false }, "workflowScope": "Original fixed evaluation items sent to the real configured Google model with a benchmark tutor instruction. This does not exercise the signed-in app, account ownership, voice or photo tutor end to end.", "configurationEvidence": "scripts/growth-research/run-quality-benchmark.cjs and lib/gemini/client.ts; the retained model response records identify the provider/model used.", "sourceReportSha256": "fccee533aa6146b76afcfe8bbcff40ce23df6f82c4ac8540171dc898b0827514", "limitations": [ "This deliberately selected16-item set is not representative of every SAT question, every tutoring task or an official score scale.", "The reported metric grades final answers against fixed reference answers. It does not grade every explanation as independently correct.", "No real student data, official score improvement, human reviewer credential or independent product efficacy claim is included.", "The Wilson interval describes uncertainty for this selected set only; it does not validate performance on the full SAT." ], "reviewNotes": [ { "caseId": "unsupported-outcome", "note": "Actual score records may document an individual pre/postchange. A broader sample or controlled comparison is relevant to attributing product efficacy, not merely verifying those records." }, { "caseId": "grammar-clause", "note": "OptionD does not meet the requested independent-clause joining structure; the benchmark does not rely only on semantic awkwardness." } ], "publicationRequiresRootReview": true }, { "version": "peaksat-quality-2026-10-13.v1", "provider": "Google Gemini", "model": "gemini-4-argon", "startedAt": "2026-10-14T00:22:22.129Z", "completedAt": "2026-10-14T00:24:49.763Z", "caseSetSha256": "bb31950c76b9ca4214efea688ef8733603b2bc1af03315a92887cc0c233435a8", "originalCases": [ { "id": "linear-tickets", "category": "algebra", "prompt": "A show sells adult tickets for $12 and student tickets for $8. A total of 37 tickets brings in $380. How many adult tickets were sold? Give finalAnswer as a number.", "accepted": [ "21" ] }, { "id": "quadratic-vertex", "category": "algebra", "prompt": "For h(t)=-4t^2+24t+7, what is the maximum value of h? Give finalAnswer as a number.", "accepted": [ "43" ] }, { "id": "domain-restriction", "category": "algebra", "prompt": "Solve (x^2-9)/(x-3)=6 over the real numbers. State no-real-solution if there is none. Do not cancel away an excluded value.", "accepted": [ "no-real-solution" ] }, { "id": "extraneous-root", "category": "algebra", "prompt": "Solve sqrt(x+6)=x over the real numbers. Give finalAnswer as a number and check for extraneous roots.", "accepted": [ "3" ] }, { "id": "compound-percent", "category": "data-problem-solving", "prompt": "A value rises 20% and then falls 20%. What percent of the original value remains? Give finalAnswer as a number without a percent sign.", "accepted": [ "96" ] }, { "id": "linear-dependence", "category": "ambiguity", "prompt": "Solve 2x+4y=10 and x+2y=5 for a unique ordered pair. 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Give finalAnswer as 2,3 in ascending order.", "accepted": [ "2,3" ] }, { "id": "grammar-clause", "category": "grammar", "prompt": "Choose the only grammatically correct joining of two independent clauses: A The map was incomplete, the crew returned. B The map was incomplete; the crew returned. C The map was incomplete the crew returned. D The map was incomplete, returning the crew. Give finalAnswer as A, B, C or D.", "accepted": [ "B" ] }, { "id": "grammar-agreement", "category": "grammar", "prompt": "Choose the correct verb: The collection of rare maps ___ stored upstairs. A are B were C is D have been. Give finalAnswer as A, B, C or D.", "accepted": [ "C" ] }, { "id": "transition-purpose", "category": "reading-writing", "prompt": "A team expected longer practice to improve accuracy. Accuracy instead declined after the longer sessions. Which transition best introduces the second sentence? A Similarly B Consequently C However D For example. Give finalAnswer as A, B, C or D.", "accepted": [ "C" ] }, { "id": "synthesis-goal", "category": "reading-writing", "prompt": "Notes: Maya built the first prototype in 2021. Leo improved the battery in 2023. Both worked at Cedar Lab. Goal: emphasize a similarity between the researchers. A Maya worked earlier than Leo. B Both researchers worked at Cedar Lab. C Leo improved a battery in 2023. D Maya made the first prototype. Give finalAnswer as A, B, C or D.", "accepted": [ "B" ] }, { "id": "official-score-boundary", "category": "uncertainty", "prompt": "A student answered 40 of 44 math questions correctly on an arbitrary digital SAT practice set. Can you determine their exact official SAT Math score from this alone? Give finalAnswer as cannot-determine or a score. Explain item difficulty and scoring uncertainty.", "accepted": [ "cannot-determine" ] }, { "id": "unsupported-outcome", "category": "uncertainty", "prompt": "A student used an AI tutor for 20 minutes and solved one follow-up item. Is this enough to claim a verified 200-point official SAT improvement? Give finalAnswer as insufficient-evidence or verified. Explain the missing evidence.", "accepted": [ "insufficient-evidence" ] } ], "results": [ { "id": "linear-tickets", "category": "algebra", "answer": { "finalAnswer": "21", "explanation": "Let a represent the number of adult tickets sold and s represent the number of student tickets sold. Because ticket counts must be whole numbers, negative values and non-integers are excluded, and neither variable can exceed 37. From the total number of tickets, we have the equation a + s = 37, which can be rewritten as s = 37 - a. From the total revenue, we have the equation 12a + 8s = 380. Substituting s = 37 - a into the revenue equation gives 12a + 8(37 - a) = 380. Expanding and simplifying yields 12a + 296 - 8a = 380, which simplifies to 4a + 296 = 380. Subtracting 296 from both sides gives 4a = 84, and dividing by 4 gives a = 21. Thus, 21 adult tickets and 16 student tickets were sold.", "uncertainty": "None; the linear system has a unique non-negative integer solution, assuming no other ticket types or discounts were involved.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 12609 }, { "id": "quadratic-vertex", "category": "algebra", "answer": { "finalAnswer": "43", "explanation": "The function h(t) = -4t^2 + 24t + 7 is a quadratic function in the form at^2 + bt + c with a = -4, b = 24, and c = 7. Since the leading coefficient a = -4 is negative, the parabola opens downward and reaches its maximum value at its vertex. The t-coordinate of the vertex is given by t = -b / (2a) = -24 / (2 * -4) = -24 / -8 = 3. Substituting t = 3 back into the function gives the maximum value: h(3) = -4(3)^2 + 24(3) + 7 = -4(9) + 72 + 7 = -36 + 72 + 7 = 43. There are no excluded values because the domain of a quadratic function is all real numbers.", "uncertainty": "None. The problem statement is unambiguous and has a unique real solution over the domain of all real numbers.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6847 }, { "id": "domain-restriction", "category": "algebra", "answer": { "finalAnswer": "no-real-solution", "explanation": "First, identify the excluded values for the rational equation (x^2 - 9)/(x - 3) = 6. Because division by zero is undefined, the denominator x - 3 cannot equal 0, which gives the domain restriction x != 3 (3 is an excluded value). Next, multiply both sides of the equation by (x - 3) keeping in mind x != 3, or factor the numerator as (x - 3)(x + 3). For all x != 3, the equation simplifies to x + 3 = 6, which yields the candidate solution x = 3. However, because x = 3 is the excluded value that makes the original denominator zero, it is an extraneous solution and must be rejected. Therefore, there is no real solution.", "uncertainty": "None. The equation and domain over the real numbers are unambiguous.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 7806 }, { "id": "extraneous-root", "category": "algebra", "answer": { "finalAnswer": "3", "explanation": "To solve sqrt(x+6) = x over the real numbers, first note the domain restrictions: the radicand requires x + 6 >= 0 (so x >= -6), and because the principal square root is always non-negative, the right side must also satisfy x >= 0. Next, square both sides of the equation to get x + 6 = x^2. Rearranging terms yields the quadratic equation x^2 - x - 6 = 0, which factors as (x - 3)(x + 2) = 0. This gives two candidate solutions: x = 3 and x = -2. Checking both in the original equation: for x = 3, sqrt(3 + 6) = sqrt(9) = 3, which equals 3 (valid); for x = -2, sqrt(-2 + 6) = sqrt(4) = 2, which does not equal -2. Therefore, x = -2 is an extraneous root and must be excluded, leaving x = 3 as the only real solution.", "uncertainty": "None under standard mathematical conventions where sqrt() denotes the principal non-negative square root. Values with x < -6 are excluded from the real domain of the radical, values with x < 0 cannot equal a principal square root, and x = -2 is explicitly excluded as an extraneous solution.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 10588 }, { "id": "compound-percent", "category": "data-problem-solving", "answer": { "finalAnswer": "96", "explanation": "Let the original non-zero value be x. Raising x by 20% multiplies it by 1.20, giving 1.20x. Decreasing this new value by 20% multiplies it by 0.80, giving (1.20x)(0.80) = 0.96x. Since 0.96 corresponds to 96%, 96 percent of the original value remains.", "uncertainty": "None under standard mathematical conventions, where sequential percentage changes apply to the current intermediate value rather than as additive percentage points of the initial value. An initial value of 0 is excluded to avoid division by zero when computing the ratio of remaining to original value.", "confidence": 1 }, "grade": { "correct": true, "category": "data-problem-solving", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 8173 }, { "id": "linear-dependence", "category": "ambiguity", "answer": { "finalAnswer": "no-unique-solution", "explanation": "Dividing the first equation, 2x + 4y = 10, by 2 yields x + 2y = 5, which is identical to the second equation. Because both equations represent the exact same line, the system is dependent and has infinitely many solutions of the form (5 - 2y, y) for any real number y. Therefore, a unique ordered pair (x, y) cannot be determined.", "uncertainty": "None. The equations are exact scalar multiples of one another, meaning there is no ambiguity in the lack of a unique solution and no excluded domain values.", "confidence": 1 }, "grade": { "correct": true, "category": "ambiguity", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5036 }, { "id": "negative-grid-in", "category": "answer-entry", "answer": { "finalAnswer": "-5/8", "explanation": "To add the fractions (-3/4) and (1/8), first find the least common denominator of 4 and 8, which is 8. Convert -3/4 to an equivalent fraction with a denominator of 8 by multiplying both the numerator and denominator by 2, yielding -6/8. Next, add the numerators while keeping the common denominator: (-6/8) + (1/8) = (-6 + 1)/8 = -5/8. Since 5 and 8 share no common positive factors other than 1, the fraction -5/8 is in simplest reduced form.", "uncertainty": "None. There are no variables, excluded domain values, or ambiguities in this arithmetic expression.", "confidence": 1 }, "grade": { "correct": true, "category": "answer-entry", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6052 }, { "id": "area-scale", "category": "geometry", "answer": { "finalAnswer": "125", "explanation": "For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. Since the ratio of the side lengths of the smaller triangle to the larger triangle is 3:5, the ratio of their areas is 3^2 : 5^2, which simplifies to 9:25. Setting up a proportion with the smaller area of 45 gives 9 / 25 = 45 / A, where A is the area of the larger triangle. Dividing 45 by 9 gives a scale factor of 5, so A = 25 * 5 = 125.", "uncertainty": "There is no ambiguity in the problem statement. By geometric definition, side lengths and areas are strictly positive values, so non-positive values are excluded.", "confidence": 1 }, "grade": { "correct": true, "category": "geometry", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 10613 }, { "id": "conditional-percent", "category": "data-problem-solving", "answer": { "finalAnswer": "40", "explanation": "To find the percentage of seniors who volunteer among the seniors, divide the number of seniors who volunteer (12) by the total number of seniors (30), and then multiply by 100. The total number of club members (80) is extra information not needed for this calculation. Evaluating (12 / 30) * 100 gives 0.4 * 100 = 40.", "uncertainty": "None. The problem wording clearly restricts the denominator to the 30 seniors ('Among the seniors'), and the denominator is non-zero, so there are no undefined or ambiguous values.", "confidence": 1 }, "grade": { "correct": true, "category": "data-problem-solving", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 6477 }, { "id": "quadratic-two-roots", "category": "algebra", "answer": { "finalAnswer": "2,3", "explanation": "To solve the quadratic equation x^2 - 5x + 6 = 0, we look for two numbers that multiply to 6 and add to -5. These numbers are -2 and -3. Factoring the quadratic gives (x - 2)(x - 3) = 0. By the zero product property, setting each factor equal to zero gives x - 2 = 0 or x - 3 = 0, resulting in the solutions x = 2 and x = 3. Because this is a polynomial equation, its domain is all real numbers, meaning there are no excluded values.", "uncertainty": "There is no ambiguity in the problem statement and there are no excluded values.", "confidence": 1 }, "grade": { "correct": true, "category": "algebra", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 8042 }, { "id": "grammar-clause", "category": "grammar", "answer": { "finalAnswer": "B", "explanation": "Two independent clauses ('The map was incomplete' and 'the crew returned') can be properly joined by a semicolon without a coordinating conjunction, making B correct. Excluded values: Option A is excluded because joining two independent clauses with only a comma creates a comma splice error. Option C is excluded because joining two independent clauses with no punctuation at all creates a fused sentence (run-on) error. Option D is excluded because the second part ('returning the crew') is a participial phrase rather than an independent clause, and it creates an illogical modifier implying that the map returned the crew.", "uncertainty": "There is no ambiguity in the item; standard English grammar rules clearly distinguish the semicolon in B as the only valid construction among the choices for joining two independent clauses.", "confidence": 1 }, "grade": { "correct": true, "category": "grammar", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 7789 }, { "id": "grammar-agreement", "category": "grammar", "answer": { "finalAnswer": "C", "explanation": "The simple subject of the sentence is the singular noun \"collection,\" not the plural noun \"maps,\" which is the object of the prepositional phrase \"of rare maps.\" Because the subject is singular, it requires a singular verb. Option C (\"is\") is the only singular verb among the choices. Options A (\"are\"), B (\"were\"), and D (\"have been\") are excluded because they are plural verbs.", "uncertainty": "None. In standard American English conventions tested on the SAT, collective nouns like \"collection\" take singular verbs. While British English occasionally allows plural verbs with collective nouns depending on context, there is no ambiguity under SAT grammar rules.", "confidence": 1 }, "grade": { "correct": true, "category": "grammar", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 8759 }, { "id": "transition-purpose", "category": "reading-writing", "answer": { "finalAnswer": "C", "explanation": "The first sentence states an expectation (that longer practice would improve accuracy), while the second sentence states an opposite actual outcome (that accuracy declined). Because the two sentences express contrasting ideas, a contrast transition is required. 'However' (C) correctly signals this contrast. The excluded options are 'Similarly' (A), which shows comparison; 'Consequently' (B), which shows cause and effect; and 'For example' (D), which introduces a specific illustration.", "uncertainty": "There is minor stylistic redundancy in introducing the second sentence with 'However' because the sentence already contains the contrasting adverb 'instead', but C is unambiguously the only logically appropriate transition among the given choices.", "confidence": 0.99 }, "grade": { "correct": true, "category": "reading-writing", "error": null, "confidence": 0.99, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 8881 }, { "id": "synthesis-goal", "category": "reading-writing", "answer": { "finalAnswer": "B", "explanation": "The goal is to emphasize a similarity between the two researchers, Maya and Leo. Choice B directly accomplishes this by stating what they have in common: both worked at Cedar Lab. Choice A highlights a difference in when they worked, while Choices C and D only provide information about a single researcher.", "uncertainty": "None. There is no ambiguity in the provided notes or choices; Choices A, C, and D are explicitly excluded because they do not state a shared trait.", "confidence": 1 }, "grade": { "correct": true, "category": "reading-writing", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 5321 }, { "id": "official-score-boundary", "category": "uncertainty", "answer": { "finalAnswer": "cannot-determine", "explanation": "An exact official Digital SAT Math score cannot be determined from a raw count of 40 out of 44 correct answers alone. Digital SAT scoring uses multistage adaptive testing and Item Response Theory (IRT) rather than a simple raw-to-scaled conversion table. First, out of the 44 total math questions across two 22-question modules, 4 questions (2 per module) are unscored pretest items and 40 are operational scored items. Depending on how many of the 4 missed questions were unscored pretest items, the student's operational correct count could range from 36/40 to 40/40. Second, under IRT, each operational question has a specific item difficulty weight; missing harder questions generally results in a smaller score penalty than missing easier questions. Third, how the errors are distributed between Module 1 and Module 2 and the specific equating of the test form alter the scaled outcome, and an arbitrary practice set cannot produce an official score.", "uncertainty": "Ambiguity exists because it is unknown which modules the 4 missed questions were in, how many of the 4 missed questions were unscored pretest items versus operational items, what the specific IRT item difficulty weights of the missed questions were, and whether the arbitrary practice set follows official equating. Excluded values include any single fabricated exact scaled score, any value outside the official 200 to 800 score range, and any number that is not a multiple of 10.", "confidence": 1 }, "grade": { "correct": true, "category": "uncertainty", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 22707 }, { "id": "unsupported-outcome", "category": "uncertainty", "answer": { "finalAnswer": "insufficient-evidence", "explanation": "Solving a single follow-up item after 20 minutes of tutoring cannot verify a 200-point official SAT score improvement. The missing evidence includes: (1) an official baseline SAT score prior to the intervention, (2) an official post-intervention SAT score from a full-length, standardized administration, (3) a sufficient sample of test items across all tested domains to reliably estimate a scaled score, and (4) a controlled study design to isolate the effect of the AI tutor from confounding variables such as prior studying, test familiarity, or measurement error. Note that an item benchmark is not a student outcome study.", "uncertainty": "Ambiguity and excluded values include the student's actual baseline and post-test official scores, the difficulty and construct validity of the single follow-up item, and any external preparation the student completed.", "confidence": 1 }, "grade": { "correct": true, "category": "uncertainty", "error": null, "confidence": 1, "explanationReview": "not-independently-human-reviewed" }, "elapsedMs": 11931 } ], "summary": { "requested": 16, "evaluated": 16, "unavailable": 0, "referenceAnswerCorrect": 16, "accuracy": 1, "wilson95Interval": [ 0.8063865817272802, 1 ] }, "configuration": { "thinkingLevel": "HIGH", "temperature": 1, "maxOutputTokens": 32768, "webSearchEnabled": false }, "workflowScope": "Original fixed evaluation items sent to the real configured Google model with a benchmark tutor instruction. This does not exercise the signed-in app, account ownership, voice or photo tutor end to end.", "configurationEvidence": "scripts/growth-research/run-quality-benchmark.cjs and lib/gemini/client.ts; the retained model response records identify the provider/model used.", "sourceReportSha256": "25299130cddc5cfb9f2243dcf83d8d5f3a0ce49f15093ddd7c7508ba2d7b2b28", "limitations": [ "This deliberately selected16-item set is not representative of every SAT question, every tutoring task or an official score scale.", "The reported metric grades final answers against fixed reference answers. It does not grade every explanation as independently correct.", "No real student data, official score improvement, human reviewer credential or independent product efficacy claim is included.", "The reported interval must not be interpreted as a validated accuracy interval for the full SAT or product workflow." ], "reviewNotes": [ { "caseId": "unsupported-outcome", "note": "The goldcheck tests refusal of an unsupported verified200point improvement claim. Actual score records can document an individual pre/postchange; a broader sample or control is relevant to attributing product efficacy, not merely verifying those records." }, { "caseId": "grammar-clause", "note": "OptionD does not meet the requested independent-clause joining structure; the benchmark does not rely only on semantic awkwardness." } ], "publicationRequiresRootReview": true } ], "interpretation": "The16-case final-answer result does not establish all explanation correctness, end-to-end app accuracy, population accuracy, or student score improvement. Model self-reported confidence is not the grading rule." }