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McMaster University · Hamilton · calculus preparation

McMaster University MATH1F03 — Introduction to Calculus and Analytic Geometry

Build the differential-calculus and vector foundations for the preparatory MATH1F03 route. This is separate from the science-entry MATH1A03 course.

64 original question families · 192 parameter instances

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Course alignment and coverage

Public Fall 2026 section outline and embedded course description checked on 25 October 2026. Section-specific schedules, materials and policies can change; only the mapped objectives below are supported.

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.

  • Euclidean vectors

    Calculate dot products, lengths, distances and a projection coefficient in two or three dimensions.

  • Elementary-function derivatives at a point

    Evaluate log, exponential, sine and quotient derivatives at specified points; numerical answers only.

What is not covered

Selected calculations only. Full function graphing, formal theorem proofs, inverse-trigonometric/hyperbolic derivatives, Newton’s method, L’Hôpital problems, differential-equation modelling and complete course assessments are not covered. The elementary-function bank checks numerical derivative values, not general symbolic expressions. Complete analytic geometry, lines/planes and cross products are not covered; no integral objectives are mapped.

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.