Analysis & Approaches

Calculus

Contents: Click to skip to subtopic

 

5.1: Limits, slopes of curves

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5.2: Increasing & decreasing regions

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5.3: Derivatives of polynomials

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Problems:

  1. If f(x) = 4x², find f'(x):

  2. If g(x) = 5x³ - 2x, find g'(x):

  3. If f(x) = x⁻ ² + 7, find f'(x):

  4. If yx + 12 - 2x, find dy/dx:

Answer
      8     
Answer
      15x² - 2      
Answer
    -2x³    
Answer
      -1     
 

5.4: Equations of tangents and normals

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Exercises

2 - Tangent:Normal Revision Sheet.jpg

Solutions

 

5.5: Introduction to integration

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Problems:

  1. Find 2xdx:

  2. Find (4t³-2)dt:

  3. Find 9x²dx:

Answer
      x²      
Answer
      t - 2t      
Answer
    3x³    
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5.6: Given derivatives

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Exercises

1 - Derivatives Revision Sheet.jpg

Solutions

 

5.7: Second derivatives and derivative graphs

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5.8: Stationary points & inflection points 

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Exercises

3 - Stationary:Inflexion Revision Sheet.

Solutions

Revision Sheet Answers 3.jpg
 

5.9: Kinematics

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5.10: Integral rules

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5.11: Definite integrals & area

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Standard Level content

Additional Higher Level content

 

5.12: Limits & first principles [AHL]

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5.13: L'Hôpitals's rule [AHL]

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5.14: Implicit diff. & related rates [AHL]

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5.15: More given derivatives [AHL]

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5.16: Int by substitution & parts [AHL]

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5.17: Volume of revolution [AHL]

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5.18: Differential equations [AHL]

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5.19: Maclaurin series [AHL]

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