MATH-09 · Secondary · 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 | Trigonometry and Precalculus
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Sign in to save this learning pathPractical outcome: Estimate a building height from a scale diagram.
Explain right-triangle sine using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain right-triangle cosine using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain right-triangle tangent using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain inverse trigonometric functions using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Use the first concepts from this section. Estimate a building height from a scale diagram. 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 degrees and radians using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain unit circle using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain sine graph using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain cosine graph using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Explain tangent graph using a visual and one worked real-world example. Context: Estimate a building height from a scale diagram. End with a prediction or check-for-understanding.
Estimate a building height from a scale diagram. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Right-triangle sine, Right-triangle cosine, Right-triangle tangent and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Model the height of a rotating wheel.
Explain pythagorean identity using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain angle-addition identities using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain double-angle identities using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain trigonometric equations using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Use the first concepts from this section. Model the height of a rotating wheel. 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 sine rule using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain cosine rule using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain polar coordinates using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Explain complex numbers in polar form using a visual and one worked real-world example. Context: Model the height of a rotating wheel. End with a prediction or check-for-understanding.
Model the height of a rotating wheel. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Pythagorean identity, Angle-addition identities, Double-angle identities and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Fit a seasonal pattern and state its limitations.
Explain function composition using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain inverse functions using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain polynomial end behaviour using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain conic sections using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Use the first concepts from this section. Fit a seasonal pattern and state its limitations. 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 parametric curves using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain sequence limits intuitively using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain summation notation using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Explain mathematical models and residuals using a visual and one worked real-world example. Context: Fit a seasonal pattern and state its limitations. End with a prediction or check-for-understanding.
Fit a seasonal pattern and state its limitations. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Function composition, Inverse functions, Polynomial end behaviour and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Fit a seasonal pattern and state its limitations. 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 Trigonometry and Precalculus, 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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