Mathematics · May / June 2022 · Paper 21 · Question 1
YMA01
As printed in the paper
The question as text
1. Find the first four terms, in ascending powers of x, of the binomial expansion of 10 3 2 + x 8 Give each coefficient as an integer. (4)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
+
10
C
×+
x
10
C
×
x
2
+
10
C
×
x
3
+
1
2
3
3
3
2
3
3
+
10 2
×
9
×
x
+
45 2
×
8
×
x
+
120 2
×
7
×
x
8
8
8
Or two of
+
1920
x
+
1620
x
2
+
810
x
3
1920
x
1620
x
2
810
x
3
+
+
+
Notes:
B1: Correct constant term of 1024 as an integer.
M1: Correct binomial coefficient multiplied by the correct powers of x for at least 2 terms in x, x2
or x3.
C or 10
10
10
10
C
,
10
C
,
10
Allow e.g.
,
,
or evaluated coefficients and condone missing
1
2
3
1
2
3
3
2
3
3
3
3
brackets e.g.
8 x for
2
8 x
or
8 x for
3
8 x
May take out a common factor of 210 first, but again look for correct binomial coefficients
multiplied by the correct powers of x for at least 2 terms in x, x2 or x3.
10
10
3
3
(
)
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