Mathematics I Exam Rescue Sheet

Use this when you need the fastest clean recall for the normal assignment track.

Concepts

• Weeks 1 and 2 are about objects, definitions, and algebraic structure.
• Weeks 3 to 7 are about calculus behavior, limits, derivatives, and integrals.
• Week 8 is about linear algebra form, dimensions, and transformation thinking.
• Weeks 9 to 12 are about mixed application, graph-style thinking, and final consolidation.

Facts

• A limit is about local behavior, not the whole graph.
• A derivative is a rate rule, not just arithmetic.
• An integral is accumulation or signed area depending on the question.
• Matrix multiplication depends on dimensions.
• Graph questions reward clean counting and careful structure.

Procedure

1. Name the topic family first.
2. Write the governing rule or theorem.
3. Reduce the expression or case.
4. Check dimensions, sign, or interval constraints.
5. Compare the result with the expected shape.

Duration / path / outcome

• Short path: identify theorem, compute, simplify.
• Medium path: transform the expression, then verify.
• Long path: mixed questions with algebra plus calculus or graph reasoning.
• Outcome should match the exact symbolic form and any sign or domain conditions.

Stages / phases / spectrum

• Setup phase: what object am I working on?
• Simplification phase: which identity or rule collapses the problem?
• Validation phase: does the answer obey constraints?
• Interpretation phase: what does the result mean geometrically or algebraically?

Jargon

• Continuity, differentiability, antiderivative, signed area, adjacency, tree, matrix, basis, constraint.

Refresher

• Weeks 1 to 2: sets and polynomial structure.
• Weeks 3 to 5: limits, continuity, derivatives, optimization.
• Weeks 6 to 7: integration and area logic.
• Weeks 8 to 12: linear algebra and mixed consolidation.

Handbook

• Draw the object if it helps.
• Write dimensions beside every matrix.
• Keep sign conventions visible.
• If the question looks easy, still check the domain.