Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true, destructiveHint=false and idempotentHint=false, but the description adds real substance beyond them: the adaptive selection rule (missed problems first, weak heavily weighted topics get more), the exact return shape, the count bounds, and the warning that each call may return a different set — which independently corroborates idempotentHint=false.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Front-loaded with the core purpose and the answerless distinction, and each later sentence carries distinct information (selection logic, return fields, topic filter, side-effect status, variability). Minor weakness: the '(1 to 20 per call, default 5)' parenthetical is attached to 'lettered options', which momentarily misreads as a bound on option count.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description takes on the burden of describing returns and does so precisely (id, topic, text, lettered options). Combined with the selection behavior, default count, topic filter and the read-only guarantee, an agent has everything needed to call this correctly in one shot.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so all three parameters are already documented in the schema, including the exam id source, the 1-20 count range and the domain topic id source. The description largely restates 'one exam (grade)', '1 to 20 per call, default 5' and 'limit to one topic by its id from get_exam_overview' rather than adding new semantics, so it lands at the baseline.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Get a set of math practice problems WITHOUT their answers') and immediately scopes it to one exam/grade for this learner. The 'WITHOUT their answers' clause cleanly separates it from check_answer, so an agent can distinguish the fetch step from the grading step without opening a schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives clear routing context: use it to fetch problems, use get_exam_overview for topic ids, and nothing is recorded until check_answer. It does not explicitly exclude alternatives such as get_study_plan or the mock-exam tools, so the when-not guidance is incomplete, but the positive usage path is unambiguous.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.