Mathematics · May / June 2021 · Paper 11 · Question 4
YMA01
As printed in the paper
The question as text
4. Find ∫ ( 3 x + 2 )( x − 5 ) x d x 4 writing each term in simplest form. (6)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3
1
3
x
15
x
2
x
10
3
15
1
1
5
1
2
−
2
+
−
−
∫
d
x
=
∫
x
−
+
x
−
x
d
x
2
2
4
4
4
2
2
x
x
n
→
x +
n
1
3
15
1
3
1
x
2
x
x
5
x
C
−
+
2
−
2
+
8
4
3
M1
Attempts to write as a sum of terms using correct index laws at least once.
Award for any term with a correct index.
Score for any one of:
3
1
1
1
"3
x
2
"
" 15
−
x
2
"
+
"2 "
x
" 10"
−
−
→
...
x
→
const
→
...
x
→
...
x
2
2
4
x
4
x
4
x
4
x
Cannot be scored for a term with a correct index arising from incorrect work
" 10"
−
1
eg
→
...
x
2
4
x
3
15
1
1
5
1
−
A1
Two correct terms of
x
−
+
x
2
−
x
2
(oe). They do not need to be seen on
4
4
2
2
1
−
3
−
10
x
2
the same line for this mark and they do not need to be simplified. Eg
4 x ,
1
4
acceptable.
3
3
x
3
2
Indices must be processed though. Eg
→
x
1.5 0.5
−
is not acceptable.
4
x
4
1
1
3
15
1
5
−
A1
All four correct terms of
x
−
+
x
−
x
(oe) Terms do not need to be simplified for
2
2
4
4
2
2
this mark and do not need to be on one line.
dM1
Increases the power of any of their terms by 1. (
x
n
→
x +
n
1
). It is dependent on the first
method mark.
A1
Any two terms correct unsimplified (see below) but the indices must be processed. Condone
15
−
4 x
1
as a correct term for this mark only.
3
1
3
15
1
A1
x
2
−
x
+
x
−
5
x
+
C
o.e. all on one line (including the constant C and all simplified).
2
2
8
4
3
15
4 x
1
Do not accept
−
as a correct simplified term.
3
15
1
3
Accept alternative correct simplified forms such as
x
2
−
x
+
x
2
−
5
x
+
C
or
8
4
3
3
1
1
(
)
(
)
x x
−
10
+
x
2
x
−
15
+
C
8
3
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