Mathematics · Oct / Nov 2025 · Paper 21 · Question 2
YMA01
As printed in the paper
The question as text
2. The first 4 terms, in ascending powers of x, in the binomial expansion of 10 (1 + px) are 2+ rx 3 1 + 15x + qx where p, q and r are constants. Find the value of p, the value of q and the value of r. (6)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
×
××
10 9
10 9 8
(
)
10
1
+
px
= +
1 10
px
+
p x
2
2
+
p x
3
3
+
...
2
6
Sets 10
p
=
15
p
=
1.5
o.e.
Finds the value of
2
=
o.e.
45
p
q
101.25
Finds the value of
3
=
120
p
r
405
M1: Sets 10
=
=
or 10
=
=
p
15
p
...
px
15
x
p
...
Alternatively score for a correct simplified expansion of
(
)
10
1
+
px
= +
1 10
px
+
45
p x
2
2
+
120
p x
3
3
+
...
A1:
o.e. Candidates who simply state that
can be awarded M1, A1
p =
1.5
p =
1.5
10 9
×
M1: Finds a value for
45p or
2
2
2
or equivalent using their value of p which may or
p x
2
may not have been found via a correct method.
A1: States a correct value for
q =
o.e following the award of M1
101.25
××
10 9 8
3
M1: Finds the value for
120p or
p x
3
3
or equivalent using their value of p which
3!
may or may not have been found via a correct method.
A1: States a correct value for
following the award of M1
r =
405
Special Case I: Candidates who leave the x2 AND x3 in their answer
2
3
Candidates who show a correct method but state
=
AND
=
q
101.25
x
r
405
x
M1, A1 can score SC 1,1,1,1,1,0
3
Special Case II: Candidates who find the value of p and then expand
1
+
2 x
Candidates who show a correct method to find p then expand
10
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