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Past exam of the mathematics course of the University of Cambridge
/
2016
/
ib
/
Paper 4
...
University of Cambridge
Course of the University of Cambridge
Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2016
ib
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Articles: 121
www.maths.cam.ac.uk/undergrad/pastpapers/files/2016/paperib_4.pdf
Table of contents
121
1F
Paper 4
1
Solution
1F
2E
Paper 4
1
Solution
2E
3G
Paper 4
6
a
3G
1
Solution
a
b
3G
1
Solution
b
c
3G
1
Solution
c
4G
Paper 4
1
Solution
4G
5A
Paper 4
1
Solution
5A
6B
Paper 4
8
a
6B
1
Solution
a
b
6B
1
Solution
b
c
6B
1
Solution
c
d
6B
1
Solution
d
7D
Paper 4
9
a
7D
1
Solution
a
b
7D
6
i
b
1
Solution
i
ii
b
1
Solution
ii
iii
b
1
Solution
iii
8D
Paper 4
4
a
8D
1
Solution
a
b
8D
1
Solution
b
9H
Paper 4
4
a
9H
1
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a
b
9H
1
Solution
b
10F
Paper 4
4
a
10F
1
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a
b
10F
1
Solution
b
11E
Paper 4
6
a
11E
1
Solution
a
b
11E
1
Solution
b
c
11E
1
Solution
c
12G
Paper 4
6
a
12G
1
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a
b
12G
1
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b
c
12G
1
Solution
c
13E
Paper 4
7
a
13E
1
Solution
a
b
13E
4
i
b
1
Solution
i
ii
b
1
Solution
ii
14A
Paper 4
11
a
14A
1
Solution
a
b
14A
1
Solution
b
c
14A
6
i
c
1
Solution
i
ii
c
1
Solution
ii
iii
c
1
Solution
iii
15F
Paper 4
6
a
15F
1
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a
b
15F
1
Solution
b
c
15F
1
Solution
c
16C
Paper 4
6
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16C
1
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16C
1
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b
c
16C
1
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c
17B
Paper 4
4
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17B
1
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b
17B
1
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b
18C
Paper 4
8
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18C
1
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a
b
18C
1
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b
c
18C
1
Solution
c
d
18C
1
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d
19H
Paper 4
4
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19H
1
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a
b
19H
1
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b
20H
Paper 4
4
a
20H
1
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a
b
20H
1
Solution
b
1F
(Linear Algebra)
Articles: 1
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Solution
1F
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2E
(Groups, Rings and Modules)
Articles: 1
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2E
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3G
(Analysis II)
Articles: 6
Paper 4
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Articles: 1
3G
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a
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b
Articles: 1
3G
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b
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c
Articles: 1
3G
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c
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4G
(Complex Analysis)
Articles: 1
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4G
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5A
(Methods)
Articles: 1
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5A
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6B
(Quantum Mechanics)
Articles: 8
Paper 4
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a
Articles: 1
6B
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a
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b
Articles: 1
6B
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b
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c
Articles: 1
6B
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c
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d
Articles: 1
6B
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d
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7D
(Electromagnetism)
Articles: 9
Paper 4
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a
Articles: 1
7D
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a
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b
Articles: 6
7D
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i
Articles: 1
b
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i
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ii
Articles: 1
b
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ii
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iii
Articles: 1
b
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iii
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8D
(Numerical Analysis)
Articles: 4
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a
Articles: 1
8D
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a
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Articles: 1
8D
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9H
(Markov Chains)
Articles: 4
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Articles: 1
9H
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Articles: 1
9H
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10F
(Linear Algebra)
Articles: 4
Paper 4
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a
Articles: 1
10F
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a
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b
Articles: 1
10F
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b
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11E
(Groups, Rings and Modules)
Articles: 6
Paper 4
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a
Articles: 1
11E
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a
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b
Articles: 1
11E
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b
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c
Articles: 1
11E
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c
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12G
(Analysis II)
Articles: 6
Paper 4
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a
Articles: 1
12G
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b
Articles: 1
12G
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b
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c
Articles: 1
12G
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c
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13E
(Metric and Topological Spaces)
Articles: 7
Paper 4
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Articles: 1
13E
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a
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Articles: 4
13E
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i
Articles: 1
b
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i
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ii
Articles: 1
b
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ii
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14A
(Complex Methods)
Articles: 11
Paper 4
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Articles: 1
14A
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b
Articles: 1
14A
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b
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c
Articles: 6
14A
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i
Articles: 1
c
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Solution
i
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ii
Articles: 1
c
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ii
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iii
Articles: 1
c
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iii
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15F
(Geometry)
Articles: 6
Paper 4
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Articles: 1
15F
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Articles: 1
15F
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b
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c
Articles: 1
15F
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c
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16C
(Variational Principles)
Articles: 6
Paper 4
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Articles: 1
16C
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Articles: 1
16C
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c
Articles: 1
16C
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c
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17B
(Methods)
Articles: 4
Paper 4
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Articles: 1
17B
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Articles: 1
17B
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18C
(Fluid Dynamics)
Articles: 8
Paper 4
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Articles: 1
18C
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a
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Articles: 1
18C
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b
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c
Articles: 1
18C
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c
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d
Articles: 1
18C
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d
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19H
(Statistics)
Articles: 4
Paper 4
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Articles: 1
19H
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Articles: 1
19H
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20H
(Optimization)
Articles: 4
Paper 4
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a
Articles: 1
20H
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a
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Articles: 1
20H
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Ancestors
(8)
Ib
2016
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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