Mathematics · Oct / Nov 2022 · Paper 31 · Question 1
YMA01
As printed in the paper
The question as text
1. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. x − x − f(x) = 2 3 4 15 x + 3 x + 4 2
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[4]
2 ...
x
x
2
+
3
x
+
4 2
x
3
+
0
x
−
4
x
−
15
2
x
3
+
...
A =
2
B
= −
6,
C
=
3
x
2
1(b)[5]
(
)
f
( )
x
d
x
=
" "
A
+
" "
B x
+
"
C
"l
n
x
2
+
3
x
+
4
2
(
)
f
(
x
)
d
x
=
x
2
−
6
x
+
3
l
n
x
2
+
3
x
+
4
5
(
)
(
)
(
)
(
)
f
( ) d
x
x =
5
2
−
6
×+
5
3ln 5
2
+
3
×+
5
4
−
3
2
−
6
×+
3
3l
n
3
2
+
3
×+
3
4
=
.
.
3
44
= −+
5
3ln 44
+
9
−
3ln 22
=
4
+
3ln 22
=
4
+
ln8
Notes:
(a)
M1: A correct method leading to at least one of the constants. May attempt long division getting the term A,
or multiply through and compare coefficients or substitute values. Note that achieving A = 2 implies this
mark.
A =
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