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University of British Columbia · Vancouver campus · A / B / C streams

MATH100 Differential calculus: common foundations

Start with the common foundations of MATH100 A (physical sciences / engineering), B (life sciences) or C (commerce / social sciences). The stream selector shows what this pilot leaves for later.

40 original question families · 120 parameter instances

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Course alignment and coverage

Aligned to the public 2026 Winter Term 1 course outline and current Vancouver calendar, checked 25 October 2026. The outline’s weekly schedule is tentative; this tool organizes by skill rather than promising a weekly match.

The four pathways share topic families. Across the whole pilot there are 80 distinct families and 240 parameter instances, presented in English and French; translations and shared course 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.

What this pilot does not cover

Only the shared differential foundations are covered. A: Taylor/Newton and differential equations are not included. B: logistic models, phase lines and numerical differential equations are not included. C: partial derivatives, multivariable and constrained optimization are not included. Trigonometric/logarithmic differentiation and l’Hôpital are also not included.

An original worked example

Find lim as x→2 of (x² + 3x - 1).

Worked solution

Answer: 9

  1. Polynomials are continuous everywhere.
  2. 2² + 3(2) - 1 = 9.
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Official course sources

Original independent self-study only. This is not a university service, an official exam, an assignment-solving service or a prediction of your course grade. Follow your instructor’s rules. No live language model is used. The MATH100 outline restricts AI assistance on course assignments. These original practice questions do not reproduce assessed work.