Past exam of the mathematics course of the University of Cambridge / 2007 / ib

Table of contents
- Paper 1 ib
  - 1G Paper 1
    - Solution 1G
  - 2A Paper 1
    - Solution 2A
  - 3F Paper 1
    - Solution 3F
  - 4B Paper 1
    - Solution 4B
  - 5D Paper 1
    - i 5D
      - Solution i
    - ii 5D
      - Solution ii
    - iii 5D
      - Solution iii
    - iv 5D
      - Solution iv
  - 6F Paper 1
    - Solution 6F
  - 7C Paper 1
    - Solution 7C
  - 8C Paper 1
    - Solution 8C
  - 9G Paper 1
    - Solution 9G
  - 10G Paper 1
    - i 10G
      - Solution i
    - ii 10G
      - Solution ii
    - iii 10G
      - Solution iii
  - 11H Paper 1
    - Solution 11H
  - 12A Paper 1
    - i 12A
      - Solution i
    - ii 12A
      - Solution ii
    - iii 12A
      - Solution iii
  - 13F Paper 1
    - Solution 13F
  - 14D Paper 1
    - i 14D
      - Solution i
  - 15B Paper 1
    - Solution 15B
  - 16E Paper 1
    - Solution 16E
  - 17D Paper 1
    - i 17D
      - Solution i
    - ii 17D
      - Solution ii
    - iii 17D
      - Solution iii
  - 18C Paper 1
    - i 18C
      - Solution i
    - ii 18C
      - Solution ii
    - iii 18C
      - Solution iii
  - 19C Paper 1
    - Solution 19C
- Paper 2 ib
  - 1G Paper 2
    - Solution 1G
  - 2G Paper 2
    - Solution 2G
  - 3H Paper 2
    - Solution 3H
  - 4A Paper 2
    - i 4A
      - Solution i
    - ii 4A
      - Solution ii
    - iii 4A
      - Solution iii
  - 5D Paper 2
    - Solution 5D
  - 6E Paper 2
    - Solution 6E
  - 7B Paper 2
    - Solution 7B
  - 8D Paper 2
    - Solution 8D
  - 9C Paper 2
    - Solution 9C
  - 10G Paper 2
    - i 10G
      - Solution i
    - ii 10G
      - Solution ii
    - iii 10G
      - Solution iii
  - 11G Paper 2
    - i 11G
      - Solution i
    - ii 11G
      - Solution ii
  - 12A Paper 2
    - i 12A
      - Solution i
    - ii 12A
      - Solution ii
  - 13H Paper 2
    - Solution 13H
  - 14F Paper 2
    - Solution 14F
  - 15D Paper 2
    - Solution 15D
  - 16B Paper 2
    - Solution 16B
  - 17E Paper 2
    - Solution 17E
  - 18F Paper 2
    - Solution 18F
  - 19C Paper 2
    - Solution 19C
  - 20C Paper 2
    - Solution 20C
- Paper 3 ib
  - 1G Paper 3
    - Solution 1G
  - 2A Paper 3
    - Solution 2A
  - 3H Paper 3
    - i 3H
      - Solution i
    - ii 3H
      - Solution ii
  - 4A Paper 3
    - a 4A
      - Solution a
    - b 4A
      - Solution b
  - 5F Paper 3
    - Solution 5F
  - 6E Paper 3
    - Solution 6E
  - 7B Paper 3
    - Solution 7B
  - 8C Paper 3
    - Solution 8C
  - 9C Paper 3
    - Solution 9C
  - 10G Paper 3
    - i 10G
      - Solution i
    - ii 10G
      - Solution ii
  - 11G Paper 3
    - i 11G
      - Solution i
    - ii 11G
      - Solution ii
  - 12A Paper 3
    - Solution 12A
  - 13H Paper 3
    - Solution 13H
  - 14H Paper 3
    - Solution 14H
  - 15E Paper 3
    - Solution 15E
  - 16B Paper 3
    - Solution 16B
  - 17E Paper 3
    - Solution 17E
  - 18D Paper 3
    - Solution 18D
  - 19F Paper 3
    - Solution 19F
  - 20C Paper 3
    - Solution 20C
- Paper 4 ib
  - 1G Paper 4
    - Solution 1G
  - 2G Paper 4
    - Solution 2G
  - 3H Paper 4
    - i 3H
      - Solution i
    - ii 3H
      - Solution ii
  - 4H Paper 4
    - Solution 4H
  - 5B Paper 4
    - Solution 5B
  - 6B Paper 4
    - Solution 6B
  - 7E Paper 4
    - Solution 7E
  - 8F Paper 4
    - Solution 8F
  - 9C Paper 4
    - i 9C
      - Solution i
    - ii 9C
      - Solution ii
  - 10G Paper 4
    - i 10G
      - Solution i
    - ii 10G
      - Solution ii
  - 11G Paper 4
    - i 11G
      - Solution i
    - ii 11G
      - Solution ii
  - 12A Paper 4
    - Solution 12A
  - 13H Paper 4
    - Solution 13H
  - 14A Paper 4
    - a 14A
      - Solution a
    - b 14A
      - Solution b
  - 15F Paper 4
    - i 15F
      - Solution i
    - ii 15F
      - Solution ii
    - iii 15F
      - Solution iii
    - iv 15F
      - Solution iv
  - 16E Paper 4
    - Solution 16E
  - 17B Paper 4
    - a 17B
      - Solution a
    - b 17B
      - Solution b
  - 18D Paper 4
    - Solution 18D
  - 19C Paper 4
    - i 19C
      - Solution i
    - ii 19C
      - Solution ii
    - iii 19C
      - Solution iii
    - iv 19C
      - Solution iv
  - 20C Paper 4
    - i 20C
      - Solution i
    - ii 20C
      - Solution ii
    - iii 20C
      - Solution iii

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperIB_1.pdf

1G (Linear Algebra)

Solution

2A (Geometry)

Solution

3F (Complex Analysis or Complex Methods)

Solution

4B (Special Relativity)

Solution

5D (Fluid Dynamics)

i

Solution

ii

Solution

iii

Solution

iv

Solution

6F (Numerical Analysis)

Solution

7C (Statistics)

Solution

8C (Optimization)

Solution

9G (Linear Algebra)

Solution

10G (Groups, Rings and Modules)

i

Solution

ii

Solution

iii

Solution

11H (Analysis II)

Solution

12A (Metric and Topological Spaces)

i

Solution

ii

Solution

iii

Solution

13F (Complex Analysis or Complex Methods)

Solution

14D (Methods)

i

Solution

15B (Quantum Mechanics)

Solution

16E (Electromagnetism)

Solution

17D (Fluid Dynamics)

i

Solution

ii

Solution

iii

Solution

18C (Statistics)

i

Solution

ii

Solution

iii

Solution

19C (Markov Chains)

Solution

Paper 2

www.maths.cam.ac.uk/undergrad/pastpapers/files/2007/PaperIB_2.pdf

1G (Linear Algebra)

Solution

2G (Groups, Rings and Modules)

Solution

3H (Analysis II)

Solution

4A (Metric and Topological Spaces)

i

Solution

ii

Solution

iii

Solution

5D (Methods)

Solution

6E (Electromagnetism)

Solution

7B (Special Relativity)

Solution

8D (Fluid Dynamics)

Solution

9C (Optimization)

Solution

10G (Linear Algebra)

i

Solution

ii

Solution

iii

Solution

11G (Groups, Rings and Modules)

i

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