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Toronto Metropolitan University · Toronto · undergraduate
Toronto Metropolitan University MTH140 — Calculus I
Practise selected calculus foundations for TMU’s engineering route, including related rates and local curve behaviour. The official course is available only to Engineering and Engineering Special students.
56 original question families · 168 parameter instances
Practise this course →Course alignment and coverage
Current official public course description checked 25 October 2026. No current section-level or weekly syllabus was publicly verified; topic alignment below does not claim a teaching sequence or assessment coverage.
Across this collection: 156 distinct original families and 468 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.
Polynomial antiderivatives
Reverse the power rule and use a stated constant or initial value. Exact fractional coefficients are supported.
Definite integrals and average value
Evaluate elementary polynomial integrals, distinguish signed accumulation and compute an average value.
Elementary-function derivatives at a point
Evaluate log, exponential, sine and quotient derivatives at specified points; numerical answers only.
Local extrema and inflections
Locate selected polynomial extrema, inflections and concavity boundaries; distinguish x-coordinates from function values.
What is not covered
Selected numerical and polynomial calculations only. No complete graph sketches, theorem proofs, inverse-trigonometric/hyperbolic differentiation, L’Hôpital exercises or full modelling/assessment tasks. Elementary-function derivatives are checked at specified points, not as general symbolic formulas. No volumes, complete area applications or inverse/hyperbolic function coverage. Engineering access and antirequisites are set by TMU.
An original worked example
Find lim as x→2 of (x² + 3x - 1).
Worked solution
Answer: 9
- Polynomials are continuous everywhere.
- 2² + 3(2) - 1 = 9.
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.