Analysis & Approaches

Calculus

Contents: Click to skip to subtopic

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

  kinematics  

5.10

5.11

5.12

5.13

5.14

5.15

5.16

5.17

5.18

5.19

 

5.1: Limits, slopes of curves

 

5.2: Increasing & decreasing regions

 

5.3: Derivatives of polynomials

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
Answer
Answer
Answer
 

5.4: Equations of tangents and normals

Exercises

Solutions

 

5.5: Introduction to integration

Problems:

  1. Find 2xdx:

  2. Find (4t³-2)dt:

  3. Find 9x²dx:

Answer
Answer
Answer
 

5.6: Given derivatives

Exercises

Solutions

 

5.7: Second derivatives and derivative graphs

 

5.8: Stationary points & inflection points 

Exercises

Solutions

 

5.9: Kinematics

 

5.10: Integral rules

 

5.11: Definite integrals & area

Standard Level content

Additional Higher Level content

 

5.12: Limits & first principles [AHL]

 

5.13: L'Hôpitals's rule [AHL]

 

5.14: Implicit diff. & related rates [AHL]

 

5.15: More given derivatives [AHL]

 

5.16: Int by substitution & parts [AHL]

 

5.17: Volume of revolution [AHL]

 

5.18: Differential equations [AHL]

 

5.19: Maclaurin series [AHL]

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