Past exam of the mathematics course of the University of Cambridge / 2008 / ib

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

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2008/PaperIB_1.pdf

1E (Linear Algebra)

i

Solution

ii

Solution

iii

Solution

iv

Solution

2G (Geometry)

Solution

3C (Complex Analysis or Complex Methods)

a

Solution

b

Solution

4C (Special Relativity)

Solution

5B (Fluid Dynamics)

Solution

6D (Numerical Analysis)

Solution

7H (Statistics)

Solution

8H (Optimization)

Solution

9E (Linear Algebra)

Solution

10G (Groups, Rings and Modules)

i

Solution

ii

Solution

iii

Solution

11F (Analysis II)

Solution

12F (Metric and Topological Spaces)

a

Solution

b

Solution

c

Solution

d

Solution

13C (Complex Analysis or Complex Methods)

a

Solution

b

Solution

14D (Methods)

Solution

15A (Quantum Mechanics)

Solution

16B (Electromagnetism)

i

Solution

ii

Solution

iii

Solution

iv

Solution

17B (Fluid Dynamics)

i

Solution

ii

Solution

iii

Solution

18H (Statistics)

i

Solution

ii

Solution

19H (Markov Chains)

Solution

Paper 2

www.maths.cam.ac.uk/undergrad/pastpapers/files/2008/PaperIB_2.pdf

1E (Linear Algebra)

Solution

2G (Groups, Rings and Modules)

Solution

3F (Analysis II)

Solution

4F (Metric and Topological Spaces)

Solution

5D (Methods)

Solution

6B (Electromagnetism)

Solution

7C (Special Relativity)

Solution

8B (Fluid Dynamics)

i

Solution

ii

Solution

9H (Optimization)

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