# Synthetic Rule-Agreement Records without Learner Diagnosis

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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.

batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations · 2026-10-13 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-12, b=-9, response=-20. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-12, -9, -20, -21, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-12, -9, -20, -21, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0001/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 2. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-11, b=-7, response=-18. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-11, -7, -18, -18, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-11, -7, -18, -18, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0002/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 3. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-10, b=-5, response=-15. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-10, -5, -15, -15, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-10, -5, -15, -15, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0003/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 4. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-9, b=-3, response=-11. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-9, -3, -11, -12, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-9, -3, -11, -12, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0004/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 5. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-8, b=-1, response=-9. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-8, -1, -9, -9, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-8, -1, -9, -9, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0005/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 6. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-7, b=1, response=-6. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-7, 1, -6, -6, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-7, 1, -6, -6, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0006/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 7. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-6, b=3, response=-2. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-6, 3, -2, -3, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-6, 3, -2, -3, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0007/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 8. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-5, b=5, response=0. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-5, 5, 0, 0, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-5, 5, 0, 0, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0008/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 9. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-4, b=7, response=3. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-4, 7, 3, 3, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-4, 7, 3, 3, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0009/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 10. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=9, response=7. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-3, 9, 7, 6, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 9, 7, 6, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0010/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 11. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=11, response=9. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-2, 11, 9, 9, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 11, 9, 9, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0011/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 12. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=13, response=12. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(-1, 13, 12, 12, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 13, 12, 12, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0012/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 13. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=15, response=16. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(0, 15, 16, 15, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 15, 16, 15, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0013/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 14. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=17, response=18. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(1, 17, 18, 18, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 17, 18, 18, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0014/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 15. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=19, response=21. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(2, 19, 21, 21, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 19, 21, 21, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0015/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 16. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=21, response=25. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(3, 21, 25, 24, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 21, 25, 24, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0016/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 17. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=4, b=23, response=27. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(4, 23, 27, 27, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 23, 27, 27, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0017/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 18. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=5, b=25, response=30. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(5, 25, 30, 30, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (5, 25, 30, 30, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0018/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 19. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=6, b=27, response=34. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(6, 27, 34, 33, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6, 27, 34, 33, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0019/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 20. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=7, b=29, response=36. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(7, 29, 36, 36, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7, 29, 36, 36, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0020/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 21. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=8, b=31, response=39. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(8, 31, 39, 39, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8, 31, 39, 39, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0021/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 22. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=9, b=33, response=43. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(9, 33, 43, 42, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9, 33, 43, 42, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0022/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 23. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=10, b=35, response=45. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(10, 35, 45, 45, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (10, 35, 45, 45, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0023/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 24. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=11, b=37, response=48. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(11, 37, 48, 48, Yes, matches_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11, 37, 48, 48, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0024/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 25. Synthetic Integer-Sum Response and Its Rule Code

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=12, b=39, response=52. Give (a,b,response,a+b,match?,matches_rule_expected or differs_from_rule_expected).

View answer and explanation(12, 39, 52, 51, No, differs_from_rule_expected)

Recompute the exact integer sum. A mismatched response licenses only the stated rule code, not a diagnosis of its author. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12, 39, 52, 51, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0025/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-integer-sum-record · candidate





## 26. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-8, q=1≠0, r=-7, s=1≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-8, 1, -7, 1, -8, -7, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-8, 1, -7, 1, -8, -7, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0026/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 27. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-7, q=2≠0, r=-14, s=2≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-7, 2, -14, 2, -14, -28, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-7, 2, -14, 2, -14, -28, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0027/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 28. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-6, q=3≠0, r=-17, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-6, 3, -17, 3, -18, -51, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-6, 3, -17, 3, -18, -51, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0028/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 29. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-5, q=4≠0, r=-20, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-5, 4, -20, 4, -20, -80, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-5, 4, -20, 4, -20, -80, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0029/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 30. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-4, q=5≠0, r=-19, s=5≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-4, 5, -19, 5, -20, -95, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-4, 5, -19, 5, -20, -95, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0030/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 31. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-3, q=1≠0, r=-18, s=6≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-3, 1, -18, 6, -18, -18, Yes, Yes, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 1, -18, 6, -18, -18, Yes, Yes, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0031/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 32. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-2, q=2≠0, r=-13, s=7≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-2, 2, -13, 7, -14, -26, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 2, -13, 7, -14, -26, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0032/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 33. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=-1, q=3≠0, r=-1, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(-1, 3, -1, 1, -1, -3, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 3, -1, 1, -1, -3, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0033/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 34. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=0, q=4≠0, r=1, s=2≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(0, 4, 1, 2, 0, 4, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 4, 1, 2, 0, 4, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0034/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 35. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=1, q=5≠0, r=3, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(1, 5, 3, 3, 3, 15, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 5, 3, 3, 3, 15, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0035/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 36. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=2, q=1≠0, r=9, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(2, 1, 9, 4, 8, 9, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 1, 9, 4, 8, 9, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0036/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 37. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=3, q=2≠0, r=15, s=5≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(3, 2, 15, 5, 15, 30, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 2, 15, 5, 15, 30, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0037/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 38. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=4, q=3≠0, r=25, s=6≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(4, 3, 25, 6, 24, 75, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (4, 3, 25, 6, 24, 75, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0038/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 39. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=5, q=4≠0, r=35, s=7≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(5, 4, 35, 7, 35, 140, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (5, 4, 35, 7, 35, 140, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0039/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 40. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=6, q=5≠0, r=7, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(6, 5, 7, 1, 6, 35, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (6, 5, 7, 1, 6, 35, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0040/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 41. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=7, q=1≠0, r=14, s=2≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(7, 1, 14, 2, 14, 14, Yes, Yes, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (7, 1, 14, 2, 14, 14, Yes, Yes, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0041/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 42. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=8, q=2≠0, r=25, s=3≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(8, 2, 25, 3, 24, 50, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (8, 2, 25, 3, 24, 50, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0042/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 43. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=9, q=3≠0, r=36, s=4≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(9, 3, 36, 4, 36, 108, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (9, 3, 36, 4, 36, 108, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0043/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 44. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=10, q=4≠0, r=51, s=5≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(10, 4, 51, 5, 50, 204, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (10, 4, 51, 5, 50, 204, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0044/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 45. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=11, q=5≠0, r=66, s=6≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(11, 5, 66, 6, 66, 330, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (11, 5, 66, 6, 66, 330, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0045/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 46. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=12, q=1≠0, r=85, s=7≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(12, 1, 85, 7, 84, 85, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (12, 1, 85, 7, 84, 85, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0046/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 47. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=13, q=2≠0, r=13, s=1≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(13, 2, 13, 1, 13, 26, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (13, 2, 13, 1, 13, 26, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0047/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 48. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=14, q=3≠0, r=29, s=2≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(14, 3, 29, 2, 28, 87, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (14, 3, 29, 2, 28, 87, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0048/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 49. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=15, q=4≠0, r=45, s=3≠0; Boolean response=false. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(15, 4, 45, 3, 45, 180, No, No, Yes, matches_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (15, 4, 45, 3, 45, 180, No, No, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0049/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 50. Synthetic Fraction-Equivalence Response with Nonzero Denominators

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. Fractions p/q and r/s have p=16, q=5≠0, r=65, s=4≠0; Boolean response=true. Give (p,q,r,s,p*s,r*q,equivalent?,response,match?,rule code). Preserve the signed original numerator/denominator values in these fields.

View answer and explanation(16, 5, 65, 4, 64, 325, No, Yes, No, differs_from_rule_expected)

Cross products test equivalence exactly, including negative denominators; compare that truth value with the synthetic response without replacing the record’s raw fractions. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (16, 5, 65, 4, 64, 325, No, Yes, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0050/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-fraction-equivalence-record · candidate





## 51. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=-11, x=-2, response=-6. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-3, -11, -2, -6, -5, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, -11, -2, -6, -5, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0051/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 52. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=-10, x=-1, response=-8. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-2, -10, -1, -8, -8, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, -10, -1, -8, -8, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0052/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 53. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=-9, x=0, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-1, -9, 0, -9, -9, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, -9, 0, -9, -9, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0053/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 54. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=-8, x=1, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(0, -8, 1, -9, -8, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, -8, 1, -9, -8, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0054/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 55. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=-7, x=2, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(1, -7, 2, -5, -5, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, -7, 2, -5, -5, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0055/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 56. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=-6, x=-2, response=-10. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(2, -6, -2, -10, -10, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, -6, -2, -10, -10, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0056/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 57. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=-5, x=-1, response=-9. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(3, -5, -1, -9, -8, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, -5, -1, -9, -8, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0057/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 58. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=-4, x=0, response=-4. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-3, -4, 0, -4, -4, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, -4, 0, -4, -4, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0058/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 59. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=-3, x=1, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-2, -3, 1, -5, -5, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, -3, 1, -5, -5, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0059/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 60. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=-2, x=2, response=-5. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-1, -2, 2, -5, -4, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, -2, 2, -5, -4, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0060/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 61. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=-1, x=-2, response=-1. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(0, -1, -2, -1, -1, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, -1, -2, -1, -1, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0061/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 62. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=0, x=-1, response=-1. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(1, 0, -1, -1, -1, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 0, -1, -1, -1, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0062/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 63. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=1, x=0, response=0. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(2, 1, 0, 0, 1, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 1, 0, 0, 1, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0063/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 64. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=2, x=1, response=5. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(3, 2, 1, 5, 5, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 2, 1, 5, 5, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0064/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 65. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=3, x=2, response=-3. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-3, 3, 2, -3, -3, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 3, 2, -3, -3, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0065/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 66. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=4, x=-2, response=7. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-2, 4, -2, 7, 8, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 4, -2, 7, 8, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0066/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 67. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=5, x=-1, response=6. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-1, 5, -1, 6, 6, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 5, -1, 6, 6, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0067/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 68. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=6, x=0, response=6. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(0, 6, 0, 6, 6, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 6, 0, 6, 6, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0068/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 69. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=1, b=7, x=1, response=7. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(1, 7, 1, 7, 8, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (1, 7, 1, 7, 8, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0069/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 70. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=2, b=8, x=2, response=12. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(2, 8, 2, 12, 12, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (2, 8, 2, 12, 12, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0070/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 71. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=3, b=9, x=-2, response=3. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(3, 9, -2, 3, 3, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (3, 9, -2, 3, 3, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0071/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 72. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-3, b=10, x=-1, response=12. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-3, 10, -1, 12, 13, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-3, 10, -1, 12, 13, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0072/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 73. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-2, b=11, x=0, response=11. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-2, 11, 0, 11, 11, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-2, 11, 0, 11, 11, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0073/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 74. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=-1, b=12, x=1, response=11. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(-1, 12, 1, 11, 11, Yes, matches_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (-1, 12, 1, 11, 11, Yes, matches_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0074/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 75. Synthetic Response to a Declared Substitution

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. a=0, b=13, x=2, response=12. Give (a,b,x,response,a*x+b,match?,rule code).

View answer and explanation(0, 13, 2, 12, 13, No, differs_from_rule_expected)

Evaluate the declared expression, compare values and retain only a rule-agreement status. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (0, 13, 2, 12, 13, No, differs_from_rule_expected).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0075/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-linear-substitution-record · candidate





## 76. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21000; prompt_present=true, expected_present=false, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21000, Yes, No, No, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21000, Yes, No, No, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0076/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 77. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21001; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21001, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21001, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0077/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 78. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21002; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21002, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21002, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0078/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 79. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21003; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21003, Yes, Yes, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21003, Yes, Yes, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0079/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 80. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21004; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21004, Yes, Yes, No, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21004, Yes, Yes, No, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0080/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 81. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21005; prompt_present=true, expected_present=false, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21005, Yes, No, Yes, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21005, Yes, No, Yes, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0081/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 82. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21006; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21006, Yes, Yes, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21006, Yes, Yes, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0082/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 83. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21007; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21007, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21007, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0083/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 84. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21008; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21008, Yes, Yes, No, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21008, Yes, Yes, No, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0084/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 85. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21009; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21009, Yes, Yes, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21009, Yes, Yes, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0085/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 86. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21010; prompt_present=true, expected_present=false, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21010, Yes, No, Yes, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21010, Yes, No, Yes, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0086/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 87. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21011; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21011, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21011, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0087/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 88. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21012; prompt_present=true, expected_present=true, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21012, Yes, Yes, No, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21012, Yes, Yes, No, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0088/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 89. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21013; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21013, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21013, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0089/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 90. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21014; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21014, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21014, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0090/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 91. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21015; prompt_present=true, expected_present=false, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21015, Yes, No, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21015, Yes, No, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0091/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 92. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21016; prompt_present=true, expected_present=true, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21016, Yes, Yes, No, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21016, Yes, Yes, No, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0092/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 93. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21017; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21017, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21017, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0093/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 94. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21018; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21018, Yes, Yes, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21018, Yes, Yes, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0094/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 95. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21019; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21019, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21019, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0095/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 96. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21020; prompt_present=true, expected_present=false, response_present=false, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21020, Yes, No, No, Yes, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21020, Yes, No, No, Yes, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0096/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 97. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21021; prompt_present=true, expected_present=true, response_present=true, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21021, Yes, Yes, Yes, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21021, Yes, Yes, Yes, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0097/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 98. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21022; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21022, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21022, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0098/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 99. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21023; prompt_present=true, expected_present=true, response_present=true, rule_present=true. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21023, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21023, Yes, Yes, Yes, Yes, Yes, synthetic_record_complete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0099/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate





## 100. Presence Flags for a Replayable Synthetic Record

Use a synthetic response record and the explicitly declared mathematical rule. A match code reports only rule agreement, not the ability, personality, learning difficulty, cause of error or learning outcome of a real student. item_id=21024; prompt_present=true, expected_present=true, response_present=false, rule_present=false. Give (item id,prompt flag,expected flag,response flag,rule flag,all present?,synthetic_record_complete or synthetic_record_incomplete).

View answer and explanation(21024, Yes, Yes, No, No, No, synthetic_record_incomplete)

Completeness requires every explicitly Boolean field-presence flag. A complete record alone proves neither response correctness nor educational effectiveness. This explicit finite/exact slice is neither a general theorem nor a judgment about a person. The exact result, retaining the requested order, is (21024, Yes, Yes, No, No, No, synthetic_record_incomplete).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-0100/)

Diagnostic mathematical assessment records · qf-app21-diagnostic-record-completeness · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261013-advance-20261021-r02-diagnostic-mathematical-assessment-foundations/validation-report.json)