IB Mathematics Analysis and Approaches Topic Calculus (SL/HL) covers syllabus content. Use these notes, questionbank, videos, flashcards, and lessons to review the topic, practise exam questions, and move between notes, videos, flashcards, and lessons where available.
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What this topic covers
SL 5.1—Introduction of differential calculus
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 5.6—Differentiating polynomials n E Q. Chain, product and quotient 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 5.10—Indefinite integration, reverse chain, by substitution
SL 5.11—Definite integrals, areas under curve onto x-axis and areas between curves
AHL 5.12—First principles, higher derivatives
AHL 5.13—Limits and L’Hopitals
AHL 5.14—Implicit functions, related rates, optimisation
AHL 5.15—Further derivatives and 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