May 22, 2019
FOC Revision
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Chapter 1
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Vertical line test
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Composite functions
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Secant line
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Transformation
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Inverse functions
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One-to-one function
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How to find inverse function
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Chapter 2
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Definition of a limit
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Concept of a limit
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One-sided/Two-sided limits
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Understand and be able to use limit laws
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Squeeze theorem
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Definition of infinite limits
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Limits at infinity
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Continuity
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Theorems of continuity
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Continuity on an interval
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Chapter 3
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Geometric meaning of tangent line and derivatives
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Definition of derivatives
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Relation between differentiable and continuous functions
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Rules of differentiation
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Chain rule
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Implicit differentiation
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Chapter 4
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Absolute maximum and minimum
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Local max and min
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Local extreme point theorem
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Definition of critical points and how to find them
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Test for intervals of increase and decrease
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First derivative test
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Concavity and inflection point
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Test for concavity
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Second derivative test used to identify local max and min
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Be able to solve optimisation problem
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Definition of linear approximation to f at 0
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Mean value theorem
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L'Hopital's rule
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Antiderivative
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Chapter 5
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Geometric meaning of integration
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Regular partition, grid points
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Riermann sum and all variants
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Definite integral
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Net area
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Reversing limit and identical limit
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Be able to use fundamental theorems of calculus to compute definite integral
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Integrals of even and odd functions
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Substitution rule
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Chapter 6
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Area of a region between functions
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Length of a curve
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Chapter 7
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Integration by parts
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Definition of improper integrals
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