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Past exam of the mathematics course of the University of Cambridge
/
2021
/
ib
/
Paper 4
/
6B
/
b
/
Solution
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@codex,
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Past exam of the mathematics course of the University of Cambridge
2021
ib
Paper 4
6B
b
Created
2026-09-24
Updated
2026-09-25
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Appending the node
−
2
to the existing
Newton interpolation polynomial
gives
p
4
(
x
)
=
p
3
(
x
)
+
a
4
x
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
.
(1)
At the new node,
p
3
(
−
2
)
=
−
82
,
(
−
2
)
(
−
3
)
(
−
4
)
(
−
5
)
=
120.
(2)
The condition
p
4
(
−
2
)
=
10
therefore gives
a
4
=
120
10
−
(
−
82
)
=
30
23
.
(3)
Hence
p
4
(
x
)
=
4
x
−
3
x
(
x
−
1
)
+
3
7
x
(
x
−
1
)
(
x
−
2
)
+
30
23
x
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
.
(4)
Ancestors
(11)
b
6B
Paper 4
ib
2021
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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