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Analysis & Approaches
Calculus
Contents: Click to skip to subtopic
5.9
5.10
5.11
5.13
5.16
5.19
5.1
5.1: Limits, slopes of curves
5.2
5.2: Increasing & decreasing regions
5.3
5.3: Derivatives of polynomials
Problems:
-
If f(x) = 4x², find f'(x):
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If g(x) = 5x³ - 2x, find g'(x):
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If f(x) = x⁻ ² + 7, find f'(x):
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If y = x + 12 - 2x, find dy/dx:
Answer
Answer
8x
Answer
Answer
15x² - 2
Answer
Answer
-2x⁻³
Answer
Answer
-1
5.4
5.4: Equations of tangents and normals
Exercises
Solutions
5.5
5.5: Introduction to integration
Problems:
-
Find ∫2xdx:
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Find ∫(4t³-2)dt:
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Find ∫9x²dx:
Answer
Answer
x²
Answer
Answer
t⁴ - 2t
Answer
Answer
3x³
5.6
5.6: Given derivatives
Videos
Exercises
Solutions
5.7
5.7: Second derivatives and derivative graphs
5.8
5.8: Stationary points & inflection points
Exercises
Solutions
5.9
5.9: Kinematics
5.10
5.10: Integral rules
5.11
5.11: Definite integrals & area
Standard Level content
Additional Higher Level content
5.12
5.12: Limits & first principles [AHL]
5.13
5.13: L'Hôpitals's rule [AHL]
5.14
5.14: Implicit diff. & related rates [AHL]
5.15
5.15: More given derivatives [AHL]
5.16
5.16: Int by substitution & parts [AHL]
5.17
5.17: Volume of revolution [AHL]
5.18
5.18: Differential equations [AHL]
5.19
5.19: Maclaurin series [AHL]
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