## SAT Math -- Curriculum Overlay

This addendum applies only to Digital SAT Math questions. Use it for course-wide
SAT Math rules that are narrower than the base and type guidance.

---

## SAT Math Item Format

Determine the item format before scoring.

**MCQ**
- Must have exactly 4 answer choices labeled A, B, C, D.
- More or fewer than 4 choices fails `specification_compliance`.
- "All of the above" and "None of the above" are invalid SAT Math choices and fail
  `specification_compliance`.

**SPR / grid-in**
- Has no populated `answer_options`.
- Answer must be numeric: integer, decimal, fraction, or an acceptable numeric range.
- Variable expressions, words, or lists of unrelated values fail `specification_compliance`.
- With no distractors present, set `distractor_quality = 1.0` unless another rule creates a
  distractor issue.

---

## Stimulus Requirements

Many SAT Math items are self-contained and need no stimulus. When the item text
references a stimulus (e.g., "use the table," "based on the scatterplot," "the
figure above/below," or similar directives) and no matching stimulus exists, fail
`stimulus_quality`.

When a data display or geometry figure is present, it must be internally consistent and
match the question text. Contradictory labels, axes, values, angle/side labels, or a figure
that reveals the asked-for unknown fail `stimulus_quality`.

---

## SAT Math Metric Rules

### factual_accuracy

Verify the keyed answer by solving the problem. A mathematically wrong key fails
`factual_accuracy`.

No two answer choices may be algebraically equivalent. Equivalent choices create an
ambiguous key and fail `factual_accuracy`.

Notation must be consistent enough to preserve meaning. Pure style mismatch belongs under
`clarity_precision`; a variable/quantity contradiction between stem and options fails
`factual_accuracy`.

### distractor_quality

For MCQ items, each distractor must map to a plausible mathematical error, not just a
nearby number. A distractor with no traceable error pathway fails `distractor_quality`.
Common math error paths include sign errors, order-of-operations errors, misapplied
formulas, solving for the wrong quantity, unit confusion, inverse/reciprocal errors, and
confusion between related algebraic forms.

Choices should have comparable notation style and simplification. A choice that telegraphs
or hides the key by being uniquely simplified, formatted, or precise fails
`distractor_quality`.

### curriculum_alignment

The item must exercise the stated SAT Math substandard, not merely describe a concept or
ask for formula recall. It must stay inside the assessment boundary defined for that
substandard.

---

## Difficulty Calibration

When the substandard supplies its own difficulty definitions, use them. Otherwise apply
the general definitions below.

**Easy**
- A single-step procedure, direct formula application, or simple substitution with all
  required values explicit in the item.

**Medium**
- Multi-step procedures requiring selection or sequencing, contextual interpretation of a
  coefficient/constant, equation creation from a word problem, or basic conceptual
  reasoning.

**Hard**
- Multi-step reasoning under constraints, parameter analysis, special-case reasoning
  (no/one/infinite solutions, conditions on coefficients), connecting algebraic and
  graphical representations, or transfer of the targeted skill to a novel-but-supported
  context.
- Length alone is not difficulty.
