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Applications & Interpretation
Calculus
Contents: Click to skip to subtopic
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.12
5.13
5.15
5.16
5.17
AI5.1
5.1: Limits, slopes of curves
AI5.2
5.2: Increasing & decreasing regions
AI5.3
5.3: Derivatives of polynomials
Problems:
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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
AI5.4
5.4: Equations of tangents and normals
Exercises
Solutions
AI5.5
5.5: Introduction to integration
Problems:
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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
AI5.6
5.6: Turning Points
AI5.7
5.7: Optimisation
AI5.8
5.8: Trapezoidal Rule
AI5.9
Standard Level content
Additional Higher Level content
5.9: Differentiation Rules (HL)
AI5.10
5.10: Second Derivatives (HL)
AI5.11
5.11: Integration Methods (HL)
AI5.12
5.12: Area & Volume (HL)
AI5.13
5.13: Kinematics (HL)
AI5.14
5.14: Separable Differential Equations (HL)
AI5.15
5.15: Slope Fields (HL)
AI5.16
5.16: Euler's Method (HL)
AI5.17
5.17: Phase Portraits & Coupled Systems (HL)
AI5.18
5.18: 2nd Order Differential Equations (HL)
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