Mathematics · May / June 2023 · Paper 31 · Question 1
YMA01
As printed in the paper
The question as text
1. g(x) = x 6 + 2x – 1000
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
1(a)[2]
States change of sign, continuous and hence root in [
]
3,4
x =
1000
2
×
3
=
3.1591
1(b)[3]
6
−
2
(
)3.1589
α=
Notes
(a)
M1
Attempts the value of g at 3 and 4 with one correct (accept any value for the other as an attempt).
Note narrower ranges are possible but must contain the root and lies in [3,4].
A1
Both values correct with reason (Sign change (stated or indicated) and continuous function) and
minimal conclusion (root)
(b)
M1
Attempts to substitute
x =
3
into the formula. Implied by sight of expression, awrt 3.159
1
A1
awrt 3.1591
A1
(
)3.1589
cao must be to 4 d.p. Do not be concerned about the labelling of the root (x or α
α=
etc), mark the final answer of (b)(ii). (Note sight of this value implies the M1 even if
seen).
log
T
=
4
−
2log
x
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