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University of Waterloo · Waterloo · honours mathematics

University of Waterloo MATH137 — Calculus 1 for Honours Mathematics

Practise limits, continuity, polynomial derivatives and linear approximation. MATH137’s honours-level reasoning and theorem proofs remain outside this practice bank.

44 original question families · 132 parameter instances

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Course alignment and coverage

2026–2027 Undergraduate Studies Academic Calendar, effective September 2026–August 2027, checked on 25 October 2026 through Waterloo’s public catalogue. A catalogue description is not a section syllabus.

Across this collection: 140 distinct original families and 420 parameter instances. Courses share topic banks; translations and shared mappings are not extra questions.

Supported learning objectives

  • Limits

    Evaluate a limit using substitution, factoring or rationalization.

  • Continuity

    Find missing values and compare one-sided limits.

  • Polynomial derivatives

    Apply the power rule and interpret a derivative.

  • Product rule

    Differentiate polynomial products and identify missing terms.

  • Chain rule

    Differentiate composite polynomial functions.

  • Tangent lines

    Connect slope, point and tangent-line equation.

  • Implicit differentiation

    Differentiate a curve and evaluate a local slope.

  • Related rates

    Relate changing lengths, areas, volumes and distances.

  • Linear approximation

    Use a tangent model and estimate a differential.

  • Optimization

    Locate and check a maximum or minimum in a stated domain.

  • Algebra essentials

    Solve linear equations, expand products, factor a quadratic and identify an inequality boundary.

What is not covered

Not a replacement for the honours course. Sequence limits, absolute-value case analysis, IVT/MVT proofs, Newton’s method, error bounds and software work are missing. No claim of preparation for proof-based assessments. Selected single-variable and polynomial foundations only. Trigonometric/logarithmic derivatives, quotient-rule exercises, formal proofs, complete curve sketching and long modelling tasks are not covered. Elementary function evaluation is not equivalent to differentiating those functions.

An original worked example

Solve 2x+3=9. Enter x.

Worked solution

Answer: 3

  1. 2x=6.
  2. Divide by 2: x=3.
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Official course sources

Independent, original, free self-study practice. Not affiliated with or endorsed by this university; these are not official exam questions. Topic alignment does not establish transfer credit, a current section’s weekly syllabus, full course coverage or a grade prediction. Follow your instructor’s rules and use official course materials for assessed work. No live AI chat or paid access is required.