"AlgebraicValue" (Comparison Method)
Details
 The algebra solution comparison method considers two expressions to be equivalent if they are mathematically equal without performing any solving operations, e.g. Solve, SolveValues, Fit, Reduce, etc.
 The values of the key and answer can both be specified as held expressions with Hold[expr] to maintain the values exactly as provided. However, even when the values are held, evaluation of nonalgebra functions (i.e. excluding Solve and similar functions) is performed during assessment. It is recommended to always hold the answer.
 "AlgebraicValue" assessments accept the setting "OptionalResultName" for specifying the variable of interest in a question: AssessmentFunction[key,<"ComparisonMethod""AlgebraicValue","OptionalResultName"var >]
 When "OptionalResultName"var is included, any of the following forms are accepted as correct for an answer ans:

ans Hold[var=ans] Hold[var==ans] varans  The supported options values of var include:

var accept the variable var in the submitted result False (default) only match answers provided as ans True attempt to infer var from the key
Examples
open allclose allBasic Examples (1)
Create an AssessmentFunction for an algebra question:
Scope (4)
Create an assessment function to find where a line intersects a circle:
Define code that finds a solution:
The code is not marked as correct because it contains algebraic solving code:
Allowing the code to evaluate to a correct answer before assessment gives a correct marking:
Calculate a solution to an equation:
Create an assessment that accepts alternate forms of answers containing the variable x as the result name:
The regular answer does not need to include the variable name that is searched for:
The alternate forms accepted are:
The use of any other variable name results in a false assessment:
The variable name can be inferred from the answer key if it uses any of the allowed alternate forms:
The variable name needs not to figure in the answer:
Compute the solution to an equation reduction problem:
Define an assessment function:
Applications (3)
Create a QuestionObject for an algebra problem with multiple correct answers:
Create a QuestionObject for a geometry question:
Create a polynomial solving problem including a plot to help find values. Setting "OptionalResultName" allows flexibility in the accepted answer forms:
Properties & Relations (3)
Evaluation for operations not considered to be algebra occurs even when the answer is held:
When values are held, global definitions are ignored during assessment:
Global definitions may also conflict with the name specified for the "OptionalResultName", if the variable is not held:
Wrap the variable into Hold or HoldPattern to ignore the global definition:
"AlgebraicValue" method allows functions, like Plus, that do not solve algebraic problems to evaluate:
Functions that do solve algebraic problems do not evaluate and are marked incorrect:
"CalculusResult" allows the algebraic solving functions to evaluate:
Possible Issues (1)
Create an answer key using Solve for multiple variables:
Creating an AssessmentFunction with the default "ListAssessment" setting treats each list in the key as a single answer:
Only answers identical to the keys are considered as correct:
Even with the setting "OptionalResultName"True, values without variable names are marked as incorrect:
Instead, use "AllElementsOrderless" or "AllElementsOrdered" as the "ListAssessment" setting to assess each subvalue independently:
Each individual element of the key and answer is matched separately, and the "OptionalResultName" setting works as expected:
Mathematically equivalent results that differ only by arithmetic are accepted:
To provide answers using an equal sign, use Hold to prevent setting values: