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AI5.1

5.1: Limits, slopes of curves

pg1 A&A HL - Topic 5 - Calculus Notes.jp
AI5.2

5.2: Increasing & decreasing regions

pg2 A&A HL - Topic 5 - Calculus Notes.jp
AI5.3

5.3: Derivatives of polynomials

pg3 A&A HL - Topic 5 - Calculus Notes.jp

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
      8     
Answer
Answer
      15x² - 2      
Answer
Answer
    -2x³    
Answer
Answer
      -1     
AI5.4

5.4: Equations of tangents and normals

pg4 A&A HL - Topic 5 - Calculus Notes.jp

Exercises

2 - Tangent:Normal Revision Sheet.jpg

Solutions

Revision Sheet Answers 2.jpg
AI5.5

5.5: Introduction to integration

pg5 A&A HL - Topic 5 - Calculus Notes.jp

Problems:

  1. Find 2xdx:

  2. Find (4t³-2)dt:

  3. Find 9x²dx:

Answer
Answer
      x²      
Answer
Answer
      t - 2t      
Answer
Answer
    3x³    
pg6 A&A HL - Topic 5 - Calculus Notes.jp
AI5.6

5.6: Turning Points

pg7 A&I SL - Topic 5 - Calculus Notes.jp
AI5.7

5.7: Optimisation

pg8 A&I SL - Topic 5 - Calculus Notes.jp
AI5.8

5.8: Trapezoidal Rule 

pg9 A&I SL - Topic 5 - Calculus Notes.jp
AI5.9

Standard Level content

Additional Higher Level content

5.9: Differentiation Rules (HL) 

AHL5.9a jpg.jpg
AHL5.9b jpg.jpg
AI5.10

5.10: Second Derivatives (HL) 

AHL5.10 jpg.jpg
AI5.11

5.11: Integration Methods (HL) 

AHL5.11 jpg.jpg
AI5.12

5.12: Area & Volume (HL) 

AHL5.12a jpg.jpg
AHL5.12b jpg.jpg
AI5.13

5.13: Kinematics (HL) 

AHL5.13 jpg.jpg
AI5.14

5.14: Separable Differential Equations (HL) 

AHL5.14 jpg.jpg
AI5.15

5.15: Slope Fields (HL) 

AHL5.15 jpg.jpg
AI5.16

5.16: Euler's Method (HL) 

AHL5.16a jpg.jpg
AHL5.16b jpg.jpg
AI5.17

5.17: Phase Portraits & Coupled Systems (HL) 

AHL5.17a jpg.jpg
AHL5.17b jpg.jpg
AI5.18

5.18: 2nd Order Differential Equations (HL) 

AHL5.18 jpg.jpg
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