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York University · Keele · applied calculus I
York University SC/MATH1013 — Applied Calculus I
Practise York’s differential-calculus foundations, with a small introduction to integration. The applied route is distinct from MATH1300 and the life-sciences sequence.
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. Integral practice is elementary; this is not Applied Calculus II. Check prerequisite and exclusion rules.
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.