Mathematics · Oct / Nov 2022 · Paper 21 · Question 6
YMA01
As printed in the paper
The question as text
6. The curve C1 has equation y = f(x). A table of values of x and y for y = f(x) is shown below, with the y values rounded to 4 decimal places where appropriate. 0 0.5 1 1.5 2 x y 3 2.6833 2.4 2.1466 1.92
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
6(a)[3]
h =
0.5
1 "0.5"
[
]
2 ×
×
3 1.92
+
+
2(2.6833
+
2.4
+
2.1466)
4.845
6(b)[4]
2
2
1
3
10
x
2
−
x
2
d
x
=
2
x
−
=
4
12
3
0
0
10
"4.845" "
−
"
3
% of logo shaded
=
6
=
25.2 %
(
)
(a)
B1:
h =
0.5
seen or implied.
M1: A full attempt at the trapezium rule.
their
h
Look for
3 1.92
+
+
2(2.6833
+
2.4
+
2.1466)
but condone copying slips.
2
Note that their
h +
3 1.92
+
2(2.6833
+
2.4
+
2.1466)
scores M0 unless the missing brackets are
2
recovered or implied by their answer. (You may need to check)
Allow this mark if they add the areas of individual trapezia e.g.
their
h
their
h
their
h
their
h
3
+
2.6833
+
2.6833
+
2.4
+
2.4
+
2.1466
+
2.1466 1.92
+
2
2
2
2
Condone copying slips but must be a complete method using all the trapezia.
A1: awrt 4.845. Apply isw once awrt 4.845 is seen.
(b)
1
M1: Attempts to integrate
2
−
4 x
2
.
Award for either 2x or …x3.
A1: 10
3 seen or implied.
dM1: Attempts to find the difference (either way round) between their answer to part (a)
and their attempt at the area under C2 which must be positive and divides by 6
(Must follow an attempt to integrate C2 and not an attempt to use the trapezium rule again)
A1: awrt 25.2(%) (the % symbol is not required). Do not allow −25.2% or e.g. 0.252
Allow 907
36 (%)
Some candidates are not doing the integration and are using their calculators for the area under C2.
If they then go on and use the 10/3 to get awrt 25.2% then we will allow a Special Case of
M0A0dM0A1
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