MATH-10 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Calculus I: Limits and Derivatives
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Sign in to save this learning pathPractical outcome: Estimate speed from progressively shorter journey intervals.
Explain average versus instantaneous change using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain numerical limits using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain one-sided limits using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain limit laws using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Use the first concepts from this section. Estimate speed from progressively shorter journey intervals. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain infinite limits using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain continuity at a point using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain intermediate value theorem using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Explain epsilon-delta meaning using a visual and one worked real-world example. Context: Estimate speed from progressively shorter journey intervals. End with a prediction or check-for-understanding.
Estimate speed from progressively shorter journey intervals. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Average versus instantaneous change, Numerical limits, One-sided limits and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Optimise the dimensions of a fixed-perimeter enclosure.
Explain derivative from first principles using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain power rule using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain product rule using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain quotient rule using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Use the first concepts from this section. Optimise the dimensions of a fixed-perimeter enclosure. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain chain rule using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain trigonometric derivatives using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain exponential derivatives using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain logarithmic derivatives using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Explain implicit differentiation using a visual and one worked real-world example. Context: Optimise the dimensions of a fixed-perimeter enclosure. End with a prediction or check-for-understanding.
Optimise the dimensions of a fixed-perimeter enclosure. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Derivative from first principles, Power rule, Product rule and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Explain a turning point in an observed cost curve.
Explain tangent approximation using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain related rates using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain critical points using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain first-derivative test using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Use the first concepts from this section. Explain a turning point in an observed cost curve. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain second-derivative test using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain constrained optimisation in one variable using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain mean value theorem using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain l'hopital's rule using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain newton's method using a visual and one worked real-world example. Context: Explain a turning point in an observed cost curve. End with a prediction or check-for-understanding.
Explain a turning point in an observed cost curve. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Tangent approximation, Related rates, Critical points and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Explain a turning point in an observed cost curve. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Calculus I: Limits and Derivatives, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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