Topic 5 Calculus

SL 5.1—Concept of a limit

Introduction to the concept of a limit.
Derivative interpreted as gradient function and as rate of change.

SL 5.2—Increasing and decreasing functions

SL 5.3—Differentiating polynomials, n E Z

SL 5.4—Tangents and normal

SL 5.5—Integration introduction, areas between curve and x axis

SL 5.6A—Differentiating polynomials n E Q. [A] Product rules

SL 5.6B—Differentiating polynomials n E Q. [B]Quotient rules

SL 5.6C—Differentiating polynomials n E Q. [C] Chain rules

SL 5.7—The second derivative

SL 5.8—Testing for max and min, optimisation. Points of inflexion

SL 5.9—Kinematics problems

SL 5.10a—Indefinite integration

SL 5.10b—Indefinite integration, reverse chain, by substitution

SL 5.11a—Definite integrals

SL 5.11b—Areas under curve onto x-axis and areas between curves

AHL 5.12a—AROC, First principles
b. Higher derivatives

AHL 5.13—Limits and L’Hopitals

AHL 5.14A—Implicit functions

AHL 5.14B—Related Rates

AHL 5.14C—Optimisation

AHL 5.15A—Further derivatives

AHL 5.15B—Indefinite integration of these, partial fractions

AHL 5.16—Integration by substitution, parts and repeated parts

AHL 5.17—Areas under curve onto y-axis, volume of revolution (about x and y axes)

AHL 5.18—1st order DE’s – Euler method, variables separable, integrating factor, homogeneous DE using sub y=vx

AHL 5.19—Maclaurin series

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