Past exam of the mathematics course of the University of Cambridge / 2011

Table of contents
- ia 2011
  - Paper 1 ia
    - 1C Paper 1
      - i 1C
        Solution i
      - ii 1C
        Solution ii
    - 2A Paper 1
      - Solution 2A
    - 3F Paper 1
      - a 3F
        Solution a
      - b 3F
        Solution b
      - c 3F
        Solution c
      - d 3F
        Solution d
    - 4D Paper 1
      - i 4D
        Solution i
      - ii 4D
        Solution ii
    - 5C Paper 1
      - Solution 5C
    - 6A Paper 1
      - a 6A
        Solution a
      - b 6A
        Solution b
      - c 6A
        Solution c
      - d 6A
        Solution d
    - 7B Paper 1
      - a 7B
        Solution a
      - b 7B
        Solution b
      - c 7B
        Solution c
    - 8B Paper 1
      - a 8B
        i a
        Solution i
        ii a
        Solution ii
        iii a
        Solution iii
      - b 8B
        Solution b
    - 9F Paper 1
      - a 9F
        Solution a
      - b 9F
        Solution b
      - c 9F
        Solution c
    - 10E Paper 1
      - i 10E
        Solution i
      - ii 10E
        Solution ii
      - iii 10E
        Solution iii
      - iv 10E
        Solution iv
    - 11E Paper 1
      - i 11E
        Solution i
      - ii 11E
        Solution ii
    - 12D Paper 1
      - Solution 12D
  - Paper 2 ia
    - 1A Paper 2
      - a 1A
        Solution a
      - b 1A
        Solution b
    - 2A Paper 2
      - a 2A
        Solution a
      - b 2A
        Solution b
    - 3F Paper 2
      - a 3F
        Solution a
      - b 3F
        Solution b
      - c 3F
        Solution c
    - 4F Paper 2
      - Solution 4F
    - 5A Paper 2
      - a 5A
        Solution a
      - b 5A
        Solution b
    - 6A Paper 2
      - a 6A
        Solution a
      - b 6A
        i b
        Solution i
        ii b
        Solution ii
        iii b
        Solution iii
        iv b
        Solution iv
    - 7A Paper 2
      - a 7A
        Solution a
      - b 7A
        Solution b
      - c 7A
        Solution c
    - 8A Paper 2
      - a 8A
        Solution a
      - b 8A
        Solution b
    - 9F Paper 2
      - a 9F
        Solution a
      - b 9F
        Solution b
    - 10F Paper 2
      - a 10F
        Solution a
      - b 10F
        Solution b
    - 11F Paper 2
      - a 11F
        Solution a
      - b 11F
        Solution b
      - c 11F
        Solution c
      - d 11F
        Solution d
      - e 11F
        Solution e
    - 12F Paper 2
      - a 12F
        Solution a
      - b 12F
        i b
        Solution i
        ii b
        Solution ii
        iii b
        Solution iii
  - Paper 3 ia
    - 1D Paper 3
      - a 1D
        Solution a
      - b 1D
        Solution b
    - 2D Paper 3
      - Solution 2D
    - 3C Paper 3
      - Solution 3C
    - 4C Paper 3
      - Solution 4C
    - 5D Paper 3
      - a 5D
        Solution a
      - b 5D
        Solution b
      - c 5D
        Solution c
      - d 5D
        Solution d
    - 6D Paper 3
      - a 6D
        Solution a
      - b 6D
        Solution b
    - 7D Paper 3
      - a 7D
        Solution a
      - b 7D
        Solution b
    - 8D Paper 3
      - a 8D
        Solution a
      - b 8D
        Solution b
    - 9C Paper 3
      - Solution 9C
    - 10C Paper 3
      - Solution 10C
    - 11C Paper 3
      - a 11C
        Solution a
      - b 11C
        Solution b
      - c 11C
        Solution c
    - 12C Paper 3
      - Solution 12C
  - Paper 4 ia
    - 1E Paper 4
      - i 1E
        Solution i
      - ii 1E
        Solution ii
    - 2E Paper 4
      - Solution 2E
    - 3B Paper 4
      - Solution 3B
    - 4B Paper 4
      - Solution 4B
    - 5E Paper 4
      - a 5E
        Solution a
      - b 5E
        Solution b
    - 6E Paper 4
      - a 6E
        Solution a
      - b 6E
        Solution b
      - c 6E
        Solution c
      - d 6E
        Solution d
    - 7E Paper 4
      - Solution 7E
    - 8E Paper 4
      - Solution 8E
    - 9B Paper 4
      - a 9B
        Solution a
      - b 9B
        Solution b
      - c 9B
        Solution c
    - 10B Paper 4
      - a 10B
        Solution a
      - b 10B
        Solution b
    - 11B Paper 4
      - a 11B
        Solution a
      - b 11B
        Solution b
    - 12B Paper 4
      - a 12B
        Solution a
      - b 12B
        Solution b
- ii 2011
  - Paper 1 ii
    - 1I Paper 1
      - Solution 1I
    - 2F Paper 1
      - i 2F
        Solution i
      - ii 2F
        Solution ii
    - 3G Paper 1
      - Solution 3G
    - 4G Paper 1
      - Solution 4G
    - 5J Paper 1
      - Solution 5J
    - 6B Paper 1
      - Solution 6B
    - 7C Paper 1
      - Solution 7C
    - 8E Paper 1
      - Solution 8E
    - 9C Paper 1
      - i 9C
        Solution i
      - ii 9C
        Solution ii
    - 10E Paper 1
      - Solution 10E
    - 11G Paper 1
      - Solution 11G
    - 12G Paper 1
      - Solution 12G
    - 13J Paper 1
      - Solution 13J
    - 14E Paper 1
      - i 14E
        Solution i
      - ii 14E
        Solution ii
    - 15E Paper 1
      - i 15E
        Solution i
      - ii 15E
        Solution ii
    - 16H Paper 1
      - i 16H
        Solution i
      - ii 16H
        Solution ii
      - iii 16H
        Solution iii
      - iv 16H
        Solution iv
    - 17F Paper 1
      - Solution 17F
    - 18H Paper 1
      - i 18H
        Solution i
      - ii 18H
        Solution ii
    - 19I Paper 1
      - i 19I
        Solution i
      - ii 19I
        Solution ii
      - iii 19I
        Solution iii
    - 20F Paper 1
      - Solution 20F
    - 21H Paper 1
      - i 21H
        Solution i
      - ii 21H
        Solution ii
      - iii 21H
        Solution iii
      - iv 21H
        Solution iv
    - 22G Paper 1
      - Solution 22G
    - 23G Paper 1
      - Solution 23G
    - 24H Paper 1
      - i 24H
        Solution i
      - ii 24H
        Solution ii
      - iii 24H
        Solution iii
    - 25I Paper 1
      - Solution 25I
    - 26K Paper 1
      - i 26K
        Solution i
      - ii 26K
        Solution ii
      - iii 26K
        Solution iii
      - iv 26K
        Solution iv
    - 27J Paper 1
      - i 27J
        Solution i
      - ii 27J
        Solution ii
      - iii 27J
        Solution iii
      - iv 27J
        Solution iv
      - v 27J
        Solution v
    - 28K Paper 1
      - Solution 28K
    - 29J Paper 1
      - i 29J
        Solution i
      - ii 29J
        Solution ii
      - iii 29J
        Solution iii
    - 30A Paper 1
      - i 30A
        Solution i
      - ii 30A
        Solution ii
      - iii 30A
        Solution iii
      - iv 30A
        Solution iv
    - 31A Paper 1
      - Solution 31A
    - 32A Paper 1
      - Solution 32A
    - 33D Paper 1
    - 34E Paper 1
      - Solution 34E
    - 35D Paper 1
      - Solution 35D
    - 36C Paper 1
      - Solution 36C
    - 37D Paper 1
      - Solution 37D
    - 38B Paper 1
      - Solution 38B
    - 39B Paper 1
      - Solution 39B
    - 40A Paper 1
      - i 40A
        Solution i
      - ii 40A
        Solution ii
      - iii 40A
        Solution iii
  - Paper 3 ii
    - 1I Paper 3
      - i 1I
        Solution i
      - ii 1I
        Solution ii
    - 2F Paper 3
      - i 2F
        Solution i
      - ii 2F
        Solution ii
    - 3G Paper 3
      - Solution 3G
    - 4G Paper 3
      - Solution 4G
    - 5J Paper 3
      - Solution 5J
    - 6B Paper 3
      - Solution 6B
    - 7C Paper 3
      - i 7C
        Solution i
      - ii 7C
        Solution ii
      - iii 7C
        Solution iii
      - iv 7C
        Solution iv
    - 8E Paper 3
      - Solution 8E
    - 9C Paper 3
      - Solution 9C
    - 10E Paper 3
      - i 10E
        Solution i
      - ii 10E
        Solution ii
    - 11I Paper 3
      - i 11I
        Solution i
      - ii 11I
        Solution ii
    - 12F Paper 3
      - i 12F
        Solution i
      - ii 12F
        Solution ii
      - iii 12F
        Solution iii
    - 13B Paper 3
      - i 13B
        Solution i
      - ii 13B
        Solution ii
      - iii 13B
        Solution iii
      - iv 13B
        Solution iv
    - 14C Paper 3
      - i 14C
        Solution i
      - ii 14C
        Solution ii
      - iii 14C
        Solution iii
      - iv 14C
        Solution iv
    - 15E Paper 3
      - i 15E
        Solution i
      - ii 15E
        Solution ii
    - 16H Paper 3
      - i 16H
        Solution i
      - ii 16H
        Solution ii
      - iii 16H
        Solution iii
      - iv 16H
        Solution iv
    - 17F Paper 3
      - Solution 17F
    - 18H Paper 3
      - i 18H
        Solution i
      - ii 18H
        Solution ii
      - iii 18H
        Solution iii
    - 19I Paper 3
      - Solution 19I
    - 20H Paper 3
      - i 20H
        Solution i
      - ii 20H
        Solution ii
      - iii 20H
        Solution iii
    - 21G Paper 3
      - Solution 21G
    - 22G Paper 3
      - Solution 22G
    - 23H Paper 3
      - i 23H
        Solution i
      - ii 23H
        Solution ii
    - 24I Paper 3
      - Solution 24I
    - 25K Paper 3
      - i 25K
        Solution i
      - ii 25K
        Solution ii
      - iii 25K
        Solution iii
      - iv 25K
        Solution iv
    - 26J Paper 3
      - i 26J
        Solution i
      - ii 26J
        Solution ii
      - iii 26J
        Solution iii
      - iv 26J
        Solution iv
    - 27K Paper 3
      - Solution 27K
    - 28K Paper 3
      - Solution 28K
    - 29J Paper 3
      - i 29J
        Solution i
      - ii 29J
        Solution ii
    - 30A Paper 3
      - a 30A
        Solution a
      - b 30A
        Solution b
    - 31A Paper 3
      - Solution 31A
    - 32A Paper 3
      - i 32A
        Solution i
      - ii 32A
        Solution ii
    - 33D Paper 3
      - i 33D
        Solution i
      - ii 33D
        Solution ii
      - iii 33D
        Solution iii
    - 34E Paper 3
      - Solution 34E
    - 35D Paper 3
      - Solution 35D
    - 36C Paper 3
      - Solution 36C
    - 37B Paper 3
      - Solution 37B
    - 38B Paper 3
      - Solution 38B
    - 39A Paper 3
      - i 39A
        Solution i
      - ii 39A
        Solution ii
      - iii 39A
        Solution iii
  - Paper 4 ii
    - 1I Paper 4
      - i 1I
        Solution i
      - ii 1I
        Solution ii
    - 2F Paper 4
      - a 2F
        Solution a
      - b 2F
        i b
        Solution i
        ii b
        Solution ii
    - 3G Paper 4
      - Solution 3G
    - 4G Paper 4
      - Solution 4G
    - 5J Paper 4
      - Solution 5J
    - 6B Paper 4
      - Solution 6B
    - 7C Paper 4
      - i 7C
        Solution i
      - ii 7C
        Solution ii
    - 8E Paper 4
      - Solution 8E
    - 9C Paper 4
      - i 9C
        Solution i
      - ii 9C
        Solution ii
    - 10E Paper 4
      - Solution 10E
    - 11I Paper 4
      - i 11I
        Solution i
      - ii 11I
        Solution ii
    - 12G Paper 4
      - Solution 12G
    - 13J Paper 4
      - Solution 13J
    - 14C Paper 4
      - i 14C
        Solution i
      - ii 14C
        Solution ii
    - 15C Paper 4
      - Solution 15C
    - 16H Paper 4
      - Solution 16H
    - 17F Paper 4
      - i 17F
        Solution i
      - ii 17F
        Solution ii
    - 18H Paper 4
      - i 18H
        Solution i
      - ii 18H
        Solution ii
      - iii 18H
        Solution iii
      - iv 18H
        Solution iv
    - 19I Paper 4
      - i 19I
        Solution i
      - ii 19I
        Solution ii
      - iii 19I
        Solution iii
    - 20F Paper 4
      - i 20F
        Solution i
      - ii 20F
        Solution ii
      - iii 20F
        Solution iii
    - 21H Paper 4
      - Solution 21H
    - 22G Paper 4
      - Solution 22G
    - 23H Paper 4
      - Solution 23H
    - 24I Paper 4
      - Solution 24I
    - 25K Paper 4
      - i 25K
        Solution i
      - ii 25K
        Solution ii
      - iii 25K
        Solution iii
    - 26J Paper 4
      - i 26J
        Solution i
      - ii 26J
        Solution ii
      - iii 26J
        Solution iii
      - iv 26J
        Solution iv
    - 27K Paper 4
      - Solution 27K
    - 28K Paper 4
      - Solution 28K
    - 29J Paper 4
      - Solution 29J
    - 30A Paper 4
      - i 30A
        Solution i
      - ii 30A
        Solution ii
    - 31A Paper 4
      - Solution 31A
    - 32D Paper 4
      - Solution 32D
    - 33E Paper 4
      - Solution 33E
    - 34D Paper 4
      - i 34D
        Solution i
      - ii 34D
        Solution ii
      - iii 34D
        Solution iii
      - iv 34D
        Solution iv
    - 35C Paper 4
      - Solution 35C
    - 36D Paper 4
      - Solution 36D
    - 37B Paper 4
      - Solution 37B
    - 38B Paper 4
      - Solution 38B
    - 39A Paper 4
      - i 39A
        Solution i
      - ii 39A
        Solution ii

ia

Paper 1

www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperIA_1.pdf

1C (Vectors and Matrices)

i

Solution

ii

Solution

2A (Vectors and Matrices)

Solution

3F (Analysis I)

a

Solution

b

Solution

c

Solution

d

Solution

4D (Analysis I)

i

Solution

ii

Solution

5C (Vectors and Matrices)

Solution

6A (Vectors and Matrices)

a

Solution

b

Solution

c

Solution

d

Solution

7B (Vectors and Matrices)

a

Solution

b

Solution

c

Solution

8B (Vectors and Matrices)

a

i

Solution

ii

Solution

iii

Solution

b

Solution

9F (Analysis I)

a

Solution

b

Solution

c

Solution

10E (Analysis I)

i

Solution

ii

Solution

iii

Solution

iv

Solution

11E (Analysis I)

i

Solution

ii

Solution

12D (Analysis I)

Solution

Paper 2

www.maths.cam.ac.uk/undergrad/pastpapers/files/2011/PaperIA_2.pdf

1A (Differential Equations)

a

Solution

b

Solution

2A (Differential Equations)

a

Solution

b

Solution

3F (Probability)

a

Solution

b

Solution

c

Solution

4F (Probability)

Solution

5A (Differential Equations)

a

Solution

b

Solution

6A (Differential Equations)

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