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Past exam of the mathematics course of the University of Cambridge / 2009

Table of contents 967
- ia 2009 172
  - Paper 1 ia 59
    - 1C Paper 1 6
      - a 1C 1
        Solution a
      - b 1C 1
        Solution b
      - c 1C 1
        Solution c
    - 2B Paper 1 6
      - a 2B 1
        Solution a
      - b 2B 1
        Solution b
      - c 2B 1
        Solution c
    - 3F Paper 1 4
      - a 3F 1
        Solution a
      - b 3F 1
        Solution b
    - 4E Paper 1 1
      - Solution 4E
    - 5C Paper 1 1
      - Solution 5C
    - 6B Paper 1 1
      - Solution 6B
    - 7A Paper 1 8
      - a 7A 1
        Solution a
      - b 7A 1
        Solution b
      - c 7A 1
        Solution c
      - d 7A 1
        Solution d
    - 8A Paper 1 6
      - a 8A 1
        Solution a
      - b 8A 1
        Solution b
      - c 8A 1
        Solution c
    - 9F Paper 1 6
      - a 9F 1
        Solution a
      - b 9F 1
        Solution b
      - c 9F 1
        Solution c
    - 10D Paper 1 1
      - Solution 10D
    - 11D Paper 1 1
      - Solution 11D
    - 12E Paper 1 6
      - a 12E 1
        Solution a
      - b 12E 1
        Solution b
      - c 12E 1
        Solution c
  - Paper 2 ia 36
    - 1C Paper 2 1
      - Solution 1C
    - 2C Paper 2 1
      - Solution 2C
    - 3F Paper 2 4
      - a 3F 1
        Solution a
      - b 3F 1
        Solution b
    - 4F Paper 2 1
      - Solution 4F
    - 5C Paper 2 1
      - Solution 5C
    - 6C Paper 2 1
      - Solution 6C
    - 7C Paper 2 1
      - Solution 7C
    - 8C Paper 2 4
      - a 8C 1
        Solution a
      - b 8C 1
        Solution b
    - 9F Paper 2 4
      - a 9F 1
        Solution a
      - b 9F 1
        Solution b
    - 10F Paper 2 4
      - a 10F 1
        Solution a
      - b 10F 1
        Solution b
    - 11F Paper 2 1
      - Solution 11F
    - 12F Paper 2 1
      - Solution 12F
  - Paper 3 ia 24
    - 1D Paper 3 1
      - Solution 1D
    - 2D Paper 3 1
      - Solution 2D
    - 3B Paper 3 1
      - Solution 3B
    - 4B Paper 3 1
      - Solution 4B
    - 5D Paper 3 1
      - Solution 5D
    - 6D Paper 3 1
      - Solution 6D
    - 7D Paper 3 1
      - Solution 7D
    - 8D Paper 3 1
      - Solution 8D
    - 9B Paper 3 1
      - Solution 9B
    - 10B Paper 3 1
      - Solution 10B
    - 11B Paper 3 1
      - Solution 11B
    - 12B Paper 3 1
      - Solution 12B
  - Paper 4 ia 49
    - 1E Paper 4 1
      - Solution 1E
    - 2E Paper 4 4
      - a 2E 1
        Solution a
      - b 2E 1
        Solution b
    - 3A Paper 4 1
      - Solution 3A
    - 4A Paper 4 6
      - a 4A 1
        Solution a
      - b 4A 1
        Solution b
      - c 4A 1
        Solution c
    - 5E Paper 4 4
      - a 5E 1
        Solution a
      - b 5E 1
        Solution b
    - 6E Paper 4 7
      - a 6E 1
        Solution a
      - b 6E 4
        i b 1
        Solution i
        ii b 1
        Solution ii
    - 7E Paper 4 1
      - Solution 7E
    - 8E Paper 4 1
      - Solution 8E
    - 9A Paper 4 1
      - Solution 9A
    - 10A Paper 4 6
      - a 10A 1
        Solution a
      - b 10A 1
        Solution b
      - c 10A 1
        Solution c
    - 11A Paper 4 1
      - Solution 11A
    - 12A Paper 4 4
      - a 12A 1
        Solution a
      - b 12A 1
        Solution b
- ib 2009 205
  - Paper 1 ib 53
    - 1G Paper 1 1
      - Solution 1G
    - 2G Paper 1 1
      - Solution 2G
    - 3D Paper 1 1
      - Solution 3D
    - 4C Paper 1 1
      - Solution 4C
    - 5D Paper 1 1
      - Solution 5D
    - 6C Paper 1 1
      - Solution 6C
    - 7H Paper 1 1
      - Solution 7H
    - 8H Paper 1 1
      - Solution 8H
    - 9G Paper 1 1
      - Solution 9G
    - 10F Paper 1 1
      - Solution 10F
    - 11E Paper 1 1
      - Solution 11E
    - 12F Paper 1 6
      - i 12F 1
        Solution i
      - ii 12F 1
        Solution ii
      - iii 12F 1
        Solution iii
    - 13D Paper 1 1
      - Solution 13D
    - 14B Paper 1 1
      - Solution 14B
    - 15B Paper 1 1
      - Solution 15B
    - 16A Paper 1 6
      - a 16A 1
        Solution a
      - b 16A 1
        Solution b
      - c 16A 1
        Solution c
    - 17D Paper 1 6
      - i 17D 1
        Solution i
      - ii 17D 1
        Solution ii
      - iii 17D 1
        Solution iii
    - 18H Paper 1 1
      - Solution 18H
    - 19H Paper 1 1
      - Solution 19H
  - Paper 2 ib 54
    - 1G Paper 2 1
      - Solution 1G
    - 2F Paper 2 1
      - Solution 2F
    - 3E Paper 2 1
      - Solution 3E
    - 4F Paper 2 1
      - Solution 4F
    - 5B Paper 2 1
      - Solution 5B
    - 6A Paper 2 4
      - a 6A 1
        Solution a
      - b 6A 1
        Solution b
    - 7C Paper 2 1
      - Solution 7C
    - 8D Paper 2 1
      - Solution 8D
    - 9H Paper 2 1
      - Solution 9H
    - 10G Paper 2 1
      - Solution 10G
    - 11F Paper 2 1
      - Solution 11F
    - 12G Paper 2 4
      - i 12G 1
        Solution i
      - ii 12G 1
        Solution ii
    - 13E Paper 2 1
      - Solution 13E
    - 14D Paper 2 4
      - i 14D 1
        Solution i
      - ii 14D 1
        Solution ii
    - 15B Paper 2 1
      - Solution 15B
    - 16B Paper 2 1
      - Solution 16B
    - 17A Paper 2 1
      - Solution 17A
    - 18C Paper 2 1
      - Solution 18C
    - 19H Paper 2 1
      - Solution 19H
    - 20H Paper 2 6
      - a 20H 1
        Solution a
      - b 20H 1
        Solution b
      - c 20H 1
        Solution c
  - Paper 3 ib 51
    - 1F Paper 3 1
      - Solution 1F
    - 2G Paper 3 1
      - Solution 2G
    - 3E Paper 3 1
      - Solution 3E
    - 4F Paper 3 6
      - i 4F 1
        Solution i
      - ii 4F 1
        Solution ii
      - iii 4F 1
        Solution iii
    - 5D Paper 3 2
      - i 5D 1
        Solution i
    - 6A Paper 3 1
      - Solution 6A
    - 7B Paper 3 1
      - Solution 7B
    - 8H Paper 3 1
      - Solution 8H
    - 9H Paper 3 1
      - Solution 9H
    - 10G Paper 3 1
      - Solution 10G
    - 11F Paper 3 1
      - Solution 11F
    - 12G Paper 3 1
      - Solution 12G
    - 13E Paper 3 1
      - Solution 13E
    - 14E Paper 3 1
      - Solution 14E
    - 15A Paper 3 1
      - Solution 15A
    - 16B Paper 3 1
      - Solution 16B
    - 17A Paper 3 6
      - a 17A 1
        Solution a
      - b 17A 1
        Solution b
      - c 17A 1
        Solution c
    - 18D Paper 3 1
      - Solution 18D
    - 19C Paper 3 1
      - Solution 19C
    - 20H Paper 3 1
      - Solution 20H
  - Paper 4 ib 43
    - 1G Paper 4 1
      - Solution 1G
    - 2F Paper 4 1
      - Solution 2F
    - 3E Paper 4 1
      - Solution 3E
    - 4E Paper 4 1
      - Solution 4E
    - 5B Paper 4 1
      - Solution 5B
    - 6B Paper 4 1
      - Solution 6B
    - 7A Paper 4 1
      - Solution 7A
    - 8C Paper 4 1
      - Solution 8C
    - 9H Paper 4 1
      - Solution 9H
    - 10G Paper 4 1
      - Solution 10G
    - 11F Paper 4 1
      - Solution 11F
    - 12G Paper 4 1
      - Solution 12G
    - 13E Paper 4 1
      - Solution 13E
    - 14F Paper 4 1
      - Solution 14F
    - 15D Paper 4 1
      - Solution 15D
    - 16A Paper 4 1
      - Solution 16A
    - 17C Paper 4 1
      - Solution 17C
    - 18D Paper 4 4
      - i 18D 1
        Solution i
      - ii 18D 1
        Solution ii
    - 19H Paper 4 1
      - Solution 19H
    - 20H Paper 4 1
      - Solution 20H
- ii 2009 587
  - Paper 1 ii 156
    - 1G Paper 1 1
      - Solution 1G
    - 2F Paper 1 4
      - i 2F 1
        Solution i
      - ii 2F 1
        Solution ii
    - 3F Paper 1 1
      - Solution 3F
    - 4H Paper 1 6
      - i 4H 1
        Solution i
      - ii 4H 1
        Solution ii
      - iii 4H 1
        Solution iii
    - 5I Paper 1 1
      - Solution 5I
    - 6A Paper 1 1
      - Solution 6A
    - 7E Paper 1 1
      - Solution 7E
    - 8B Paper 1 1
      - Solution 8B
    - 9E Paper 1 1
      - Solution 9E
    - 10D Paper 1 1
      - Solution 10D
    - 11F Paper 1 1
      - Solution 11F
    - 12H Paper 1 6
      - i 12H 1
        Solution i
      - ii 12H 1
        Solution ii
      - iii 12H 1
        Solution iii
    - 13I Paper 1 1
      - Solution 13I
    - 14B Paper 1 1
      - Solution 14B
    - 15D Paper 1 4
      - i 15D 1
        Solution i
      - ii 15D 1
        Solution ii
    - 16G Paper 1 1
      - Solution 16G
    - 17F Paper 1 6
      - i 17F 1
        Solution i
      - ii 17F 1
        Solution ii
      - iii 17F 1
        Solution iii
    - 18H Paper 1 1
      - Solution 18H
    - 19F Paper 1 1
      - Solution 19F
    - 20H Paper 1 6
      - i 20H 1
        Solution i
      - ii 20H 1
        Solution ii
      - iii 20H 1
        Solution iii
    - 21G Paper 1 1
      - Solution 21G
    - 22H Paper 1 6
      - a 22H 1
        Solution a
      - b 22H 1
        Solution b
      - c 22H 1
        Solution c
    - 23G Paper 1 4
      - a 23G 1
        Solution a
      - b 23G 1
        Solution b
    - 24G Paper 1 1
      - Solution 24G
    - 25H Paper 1 8
      - i 25H 1
        Solution i
      - ii 25H 1
        Solution ii
      - iii 25H 1
        Solution iii
      - iv 25H 1
        Solution iv
    - 26J Paper 1 1
      - Solution 26J
    - 27J Paper 1 6
      - a 27J 1
        Solution a
      - b 27J 1
        Solution b
      - c 27J 1
        Solution c
    - 28I Paper 1 6
      - i 28I 1
        Solution i
      - ii 28I 1
        Solution ii
      - iii 28I 1
        Solution iii
    - 29J Paper 1 6
      - a 29J 1
        Solution a
      - b 29J 1
        Solution b
      - c 29J 1
        Solution c
    - 30B Paper 1 8
      - i 30B 1
        Solution i
      - ii 30B 1
        Solution ii
      - iii 30B 1
        Solution iii
      - iv 30B 1
        Solution iv
    - 31A Paper 1 1
      - Solution 31A
    - 32B Paper 1 1
      - Solution 32B
    - 33C Paper 1 1
      - Solution 33C
    - 34D Paper 1 1
      - Solution 34D
    - 35C Paper 1 6
      - i 35C 1
        Solution i
      - ii 35C 1
        Solution ii
      - iii 35C 1
        Solution iii
    - 36D Paper 1 1
      - Solution 36D
    - 37E Paper 1 4
      - i 37E 1
        Solution i
      - ii 37E 1
        Solution ii
    - 38A Paper 1 1
      - Solution 38A
    - 39B Paper 1 8
      - i 39B 1
        Solution i
      - ii 39B 1
        Solution ii
      - iii 39B 1
        Solution iii
      - iv 39B 1
        Solution iv
  - Paper 2 ii 149
    - 1G Paper 2 1
      - Solution 1G
    - 2F Paper 2 4
      - a 2F 1
        Solution a
      - b 2F 1
        Solution b
    - 3F Paper 2 1
      - Solution 3F
    - 4H Paper 2 1
      - Solution 4H
    - 5I Paper 2 1
      - Solution 5I
    - 6A Paper 2 1
      - Solution 6A
    - 7E Paper 2 4
      - i 7E 1
        Solution i
      - ii 7E 1
        Solution ii
    - 8B Paper 2 4
      - i 8B 1
        Solution i
      - ii 8B 1
        Solution ii
    - 9E Paper 2 1
      - Solution 9E
    - 10D Paper 2 4
      - a 10D 1
        Solution a
      - b 10D 1
        Solution b
    - 11F Paper 2 6
      - a 11F 1
        Solution a
      - b 11F 1
        Solution b
      - c 11F 1
        Solution c
    - 12H Paper 2 1
      - Solution 12H
    - 13A Paper 2 1
      - Solution 13A
    - 14C Paper 2 4
      - i 14C 1
        Solution i
      - ii 14C 1
        Solution ii
    - 15E Paper 2 4
      - i 15E 1
        Solution i
      - ii 15E 1
        Solution ii
    - 16G Paper 2 4
      - i 16G 1
        Solution i
      - ii 16G 1
        Solution ii
    - 17F Paper 2 4
      - i 17F 1
        Solution i
      - ii 17F 1
        Solution ii
    - 18H Paper 2 1
      - Solution 18H
    - 19F Paper 2 6
      - i 19F 1
        Solution i
      - ii 19F 1
        Solution ii
      - iii 19F 1
        Solution iii
    - 20H Paper 2 6
      - i 20H 1
        Solution i
      - ii 20H 1
        Solution ii
      - iii 20H 1
        Solution iii
    - 21G Paper 2 1
      - Solution 21G
    - 22H Paper 2 6
      - a 22H 1
        Solution a
      - b 22H 1
        Solution b
      - c 22H 1
        Solution c
    - 23G Paper 2 4
      - a 23G 1
        Solution a
      - b 23G 1
        Solution b
    - 24G Paper 2 1
      - Solution 24G
    - 25H Paper 2 6
      - a 25H 1
        Solution a
      - b 25H 1
        Solution b
      - c 25H 1
        Solution c
    - 26J Paper 2 1
      - Solution 26J
    - 27J Paper 2 4
      - a 27J 1
        Solution a
      - b 27J 1
        Solution b
    - 28I Paper 2 1
      - Solution 28I
    - 29I Paper 2 1
      - Solution 29I
    - 30J Paper 2 1
      - Solution 30J
    - 31B Paper 2 7
      - a 31B 1
        Solution a
      - b 31B 1
        Solution b
      - c 31B 2
        x c 1
        Solution x
    - 32B Paper 2 1
      - Solution 32B
    - 33C Paper 2 1
      - Solution 33C
    - 34D Paper 2 1
      - Solution 34D
    - 35D Paper 2 6
      - i 35D 1
        Solution i
      - ii 35D 1
        Solution ii
      - iii 35D 1
        Solution iii
    - 36D Paper 2 1
      - Solution 36D
    - 37E Paper 2 1
      - Solution 37E
    - 38A Paper 2 1
      - Solution 38A
    - 39B Paper 2 6
      - i 39B 1
        Solution i
      - ii 39B 1
        Solution ii
      - iii 39B 1
        Solution iii
  - Paper 3 ii 148
    - 1G Paper 3 1
      - Solution 1G
    - 2F Paper 3 4
      - a 2F 1
        Solution a
      - b 2F 1
        Solution b
    - 3F Paper 3 1
      - Solution 3F
    - 4H Paper 3 1
      - Solution 4H
    - 5I Paper 3 1
      - Solution 5I
    - 6A Paper 3 1
      - Solution 6A
    - 7E Paper 3 1
      - Solution 7E
    - 8B Paper 3 1
      - Solution 8B
    - 9E Paper 3 4
      - a 9E 1
        Solution a
      - b 9E 1
        Solution b
    - 10D Paper 3 4
      - a 10D 1
        Solution a
      - b 10D 1
        Solution b
    - 11G Paper 3 1
      - Solution 11G
    - 12F Paper 3 6
      - a 12F 1
        Solution a
      - b 12F 1
        Solution b
      - c 12F 1
        Solution c
    - 13A Paper 3 1
      - Solution 13A
    - 14E Paper 3 6
      - i 14E 1
        Solution i
      - ii 14E 1
        Solution ii
      - iii 14E 1
        Solution iii
    - 15D Paper 3 4
      - i 15D 1
        Solution i
      - ii 15D 1
        Solution ii
    - 16G Paper 3 1
      - Solution 16G
    - 17F Paper 3 6
      - a 17F 1
        Solution a
      - b 17F 1
        Solution b
      - c 17F 1
        Solution c
    - 18H Paper 3 1
      - Solution 18H
    - 19F Paper 3 6
      - i 19F 1
        Solution i
      - ii 19F 1
        Solution ii
      - iii 19F 1
        Solution iii
    - 20G Paper 3 4
      - i 20G 1
        Solution i
      - ii 20G 1
        Solution ii
    - 21H Paper 3 6
      - a 21H 1
        Solution a
      - b 21H 1
        Solution b
      - c 21H 1
        Solution c
    - 22G Paper 3 4
      - i 22G 1
        Solution i
      - ii 22G 1
        Solution ii
    - 23G Paper 3 1
      - Solution 23G
    - 24H Paper 3 4
      - a 24H 1
        Solution a
      - b 24H 1
        Solution b
    - 25J Paper 3 1
      - Solution 25J
    - 26J Paper 3 6
      - a 26J 1
        Solution a
      - b 26J 1
        Solution b
      - c 26J 1
        Solution c
    - 27I Paper 3 1
      - Solution 27I
    - 28I Paper 3 1
      - Solution 28I
    - 29J Paper 3 1
      - Solution 29J
    - 30B Paper 3 8
      - a 30B 1
        Solution a
      - b 30B 1
        Solution b
      - c 30B 1
        Solution c
      - d 30B 1
        Solution d
    - 31A Paper 3 1
      - Solution 31A
    - 32B Paper 3 4
      - i 32B 1
        Solution i
      - ii 32B 1
        Solution ii
    - 33C Paper 3 4
      - i 33C 1
        Solution i
      - ii 33C 1
        Solution ii
    - 34D Paper 3 1
      - Solution 34D
    - 35D Paper 3 6
      - i 35D 1
        Solution i
      - ii 35D 1
        Solution ii
      - iii 35D 1
        Solution iii
    - 36C Paper 3 1
      - Solution 36C
    - 37E Paper 3 1
      - Solution 37E
    - 38A Paper 3 1
      - Solution 38A
    - 39B Paper 3 2
      - k 39B 1
        Solution k
  - Paper 4 ii 130
    - 1G Paper 4 1
      - Solution 1G
    - 2F Paper 4 1
      - Solution 2F
    - 3F Paper 4 1
      - Solution 3F
    - 4H Paper 4 8
      - i 4H 1
        Solution i
      - ii 4H 1
        Solution ii
      - iii 4H 1
        Solution iii
      - iv 4H 1
        Solution iv
    - 5I Paper 4 1
      - Solution 5I
    - 6A Paper 4 1
      - Solution 6A
    - 7E Paper 4 1
      - Solution 7E
    - 8D Paper 4 1
      - Solution 8D
    - 9E Paper 4 4
      - a 9E 1
        Solution a
      - b 9E 1
        Solution b
    - 10D Paper 4 4
      - a 10D 1
        Solution a
      - b 10D 1
        Solution b
    - 11G Paper 4 1
      - Solution 11G
    - 12F Paper 4 2
      - ii 12F 1
        Solution ii
    - 13I Paper 4 1
      - Solution 13I
    - 14E Paper 4 1
      - Solution 14E
    - 15E Paper 4 1
      - Solution 15E
    - 16G Paper 4 1
      - Solution 16G
    - 17F Paper 4 1
      - Solution 17F
    - 18H Paper 4 6
      - a 18H 1
        Solution a
      - b 18H 1
        Solution b
      - c 18H 1
        Solution c
    - 19F Paper 4 6
      - a 19F 1
        Solution a
      - b 19F 1
        Solution b
      - c 19F 1
        Solution c
    - 20H Paper 4 1
      - Solution 20H
    - 21G Paper 4 1
      - Solution 21G
    - 22H Paper 4 8
      - a 22H 1
        Solution a
      - b 22H 1
        Solution b
      - c 22H 1
        Solution c
      - d 22H 1
        Solution d
    - 23G Paper 4 1
      - Solution 23G
    - 24H Paper 4 6
      - a 24H 1
        Solution a
      - b 24H 1
        Solution b
      - c 24H 1
        Solution c
    - 25J Paper 4 1
      - Solution 25J
    - 26J Paper 4 4
      - a 26J 1
        Solution a
      - b 26J 1
        Solution b
    - 27I Paper 4 1
      - Solution 27I
    - 28I Paper 4 4
      - a 28I 1
        Solution a
      - b 28I 1
        Solution b
    - 29J Paper 4 1
      - Solution 29J
    - 30B Paper 4 1
      - Solution 30B
    - 31A Paper 4 1
      - Solution 31A
    - 32C Paper 4 1
      - Solution 32C
    - 33D Paper 4 1
      - Solution 33D
    - 34D Paper 4 8
      - i 34D 1
        Solution i
      - ii 34D 1
        Solution ii
      - iii 34D 1
        Solution iii
      - iv 34D 1
        Solution iv
    - 35C Paper 4 1
      - Solution 35C
    - 36D Paper 4 1
      - Solution 36D
    - 37E Paper 4 1
      - Solution 37E
    - 38A Paper 4 1
      - Solution 38A
    - 39B Paper 4 4
      - a 39B 1
        Solution a
      - b 39B 1
        Solution b

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ib

Articles: 205

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ii

Articles: 587

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 Ancestors (6)