Calculus 1

1. Limits

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   Evaluate a limit from a graph, a table, and algebra, including a one-sided and infinite case.

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2. The derivative

   After Limits — test out to unlock

   Use the definition on a simple function, and say what f′(a) means as a slope and a rate.

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3. Differentiation rules

   After The derivative — test out to unlock

   Differentiate polynomials, products, quotients, and compositions without mixing the rules.

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4. Applications of derivatives

   After Differentiation rules — test out to unlock

   Do related rates, linearisation, and a max/min word problem, with a check that the critical point is the right kind.

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5. Integrals

   After Applications of derivatives — test out to unlock

   Write a Riemann sum, evaluate a simple definite integral, and antiderive a polynomial.

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6. Fundamental theorem

   After Integrals — test out to unlock

   Use both parts of the FTC: evaluate a definite integral, and differentiate an integral with a variable limit.

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Why a path, not a playlist

Limits, derivatives, applications, integrals. Later headings open after the one before.

Each heading is its own course with a tutor. Later headings open when you finish — or test out of — the one before.

After you sign in

• •You land on this map — every heading is already there.
• •Take the open class, or test out of a later heading to unlock it.
• •Each heading is one shared course — same syllabus and first class for everyone. Later classes continue on your copy.