Mathematics · May / June 2023 · Paper 21 · Question 1
YMA01
As printed in the paper
The question as text
1. The continuous curve C has equation y = f(x). A table of values of x and y for y = f(x) is shown below. 4.0 4.2 4.4 4.6 4.8 5.0 x y 9.2 8.4556 3.8512 5.0342 7.8297 8.6 Use the trapezium rule with all the values of y in the table to find an approximation for 5∫f(x) dx 4 giving your answer to 3 decimal places. (3)
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
h =
0.2
1
[
]
2 ×
"0.2"
×
9.2
+
8.6
+
2(8.4556
+
3.8512
+
5.0342
+
7.8297)
6.814
o.e. (including 5
4
) seen or implied by sight of e.g. 0.2
2 or 1
−
B1
h =
0.2
10 in front of the bracket.
5
May also be implied by a correct answer if no incorrect working seen.
h = −
0.2
is B0
M1
Correct application of the trapezium rule with their h (which may be 1 or h).
Look for a correct inner bracket structure 9.2
+
8.6
+
2(8.4556
+
3.8512
+
5.0342
+
7.8297)
condoning slips copying values from the table or the omission of the final brackets on the
rhs
e.g. 1
2 ×
"0.2"(9.2
+
8.6
+
2(8.4556
+
3.8512
+
5.0342
+
7.8297
is M1
but 1
2 ×
"0.2" 9.2
×
+
8.6
+
2(8.4556
+
3.8512
+
5.0342
+
7.8297)
is M0 unless the brackets are
recovered or implied by the correct answer (you may need to check this)
Also allow for a correct method adding individual trapezia using their h condoning copying
errors but the brackets must be correct (or recovered or implied by later work)
e.g. 1
1
1
×
"0.2"(9.2
+
8.4556)
+
×
"0.2"(8.4556
+
3.8512)
+
×
"0.2"(3.8512
+
5.0342)
+
2
2
2
1
1
×
"0.2"(5.0342
+
7.8297)
+
×
"0.2"(7.8297
+
2
2
A1
awrt 6.814 isw once a correct answer is seen. Correct answer with no working scores
B1M1A1 but if there is evidence of using
h = −
0.2
then maximum awarded is B0M1A0
The A mark cannot be awarded without both B1M1 being awarded on this question.
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