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University of New Brunswick · Fredericton

University of New Brunswick MATH1003 — Calculus I: Differential Calculus

Review functions, limits and polynomial derivative applications for UNB’s differential-calculus course. Integral calculus belongs to the separate MATH1013 route.

56 original question families · 168 parameter instances

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Course alignment and coverage

Official public course description checked on 25 October 2026. Current section syllabus and weekly order have not been verified.

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.

  • Functions and domains

    Evaluate and compose functions, invert a linear function and find a square-root domain endpoint.

  • Powers and logarithms

    Evaluate integer powers and logarithms, apply a doubling model and solve an equal-base equation.

  • Trigonometry foundations

    Convert degrees to radians, use a right-triangle ratio and find a sine period. Numeric answers only.

What is not covered

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.