The test questions for grades 7-10 are designed to assess your ability to explain mathematical reasoning clearly.

Click here to view examples and instructions.

• Why Clear Write-Ups Are Crucial
In advanced mathematics, the final answer is often less important than the process used to reach it. Proofs are not just derivations; they are arguments intended to persuade a reader of the truth of a statement.
• Communication of Ideas: Mathematics is a social endeavor. To be useful, discoveries must be understood, verified, and built upon by others. Writing clearly trains students to communicate their complex ideas to their peers and to the wider mathematical community.
• Self-Correction and Rigor: The act of writing down a proof forces the student to slow down and check every logical jump. A poorly written proof often reveals flaws in the student's own reasoning that they missed while thinking the problem through mentally.
• Building Intuition: Clearly articulated proofs help solidify the underlying mathematical intuition and general principles, which is more valuable than memorizing specific solution steps.




• What the Write-Ups Test (Content and Structure)
Instructors look for several specific elements in a student's proof or solution write-up:



Component Tested	Description
Clarity of Notation	Are variables defined? Are standard mathematical symbols used correctly? Is the notation consistent throughout?
Logical Flow	Does the proof proceed step-by-step? Are the transitions between ideas smooth? Does the conclusion logically follow from the premises?
Rigor and Completeness	Are all cases considered? Are all necessary conditions stated? Is the proof self-contained (does it rely on unstated facts)?
Grammar and Exposition	Is the prose clear, grammatically correct, and easy to read? Proofs should read like concise essays, not lists of equations.
Justification	Is every non-trivial step explicitly justified by a theorem, definition, or previously established fact? (e.g., "By the Pigeonhole Principle...", "By the combination formula...")
Structure	Does the write-up start with a clear statement of what is being proved? Is the structure (e.g., proof by induction, contradiction, or case analysis) clearly articulated?





• Abilities the Write-Ups Are Designed to Test
The requirement for clear writing is an indirect test of several high-level intellectual abilities necessary for success in mathematical research and beyond:



Ability Tested	Description
Analytical Thinking	The ability to break down a complex problem into smaller, manageable, and logically ordered steps.
Precision and Attention to Detail	The need to ensure every word, symbol, and statement is exact, reflecting the non-negotiable standards of mathematical truth.
Synthesizing Information	The capacity to take disparate concepts (theorems, definitions, lemmas) and combine them into a coherent and convincing whole.
Self-Correction and Reflection	The necessity of reviewing one's work for omissions and errors, demonstrating the ability to rigorously critique one's own arguments.
Mathematical Maturity	This is the overall goal: moving beyond merely calculating answers to understanding why mathematics works, embracing definitions, and recognizing the essential role of proof in establishing truth.