Easy -1.2 This is a straightforward application of the trapezium rule with all coordinates provided in the diagram. Students simply substitute the given values into the standard formula with no problem-solving, interpretation challenges, or multi-step reasoning required—purely mechanical execution of a standard numerical method.
Fig. 7 shows a curve and the coordinates of some points on it.
\includegraphics{figure_7}
Use the trapezium rule with 6 strips to estimate the area of the region bounded by the curve and the positive \(x\)- and \(y\)-axes. [4]
\(h = 1.5\); \(\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2 + 3) + 0)\); all y-values correct and correctly placed in formula; \(29.775\) to 3 sf or better; isw
B1, M1, B1, A1
allow if used with 6 separate trapazia; basic shape of formula correct, omission of brackets may be recovered later; condone omission of outer brackets and/or omission of 0; at least 4 y-values in middle bracket, eg \(\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2) + 3)\); M0 if any x values used; or B1 + B3 if 6 separate trapzia calculated to give correct answer; answer only does not score
$h = 1.5$; $\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2 + 3) + 0)$; all y-values correct and correctly placed in formula; $29.775$ to 3 sf or better; isw | B1, M1, B1, A1 | allow if used with 6 separate trapazia; basic shape of formula correct, omission of brackets may be recovered later; condone omission of outer brackets and/or omission of 0; at least 4 y-values in middle bracket, eg $\frac{1.5}{2} \times (2.3 + 2(2.9 + 4 + 4.6 + 4.2) + 3)$; M0 if any x values used; or B1 + B3 if 6 separate trapzia calculated to give correct answer; answer only does not score
Fig. 7 shows a curve and the coordinates of some points on it.
\includegraphics{figure_7}
Use the trapezium rule with 6 strips to estimate the area of the region bounded by the curve and the positive $x$- and $y$-axes. [4]
\hfill \mbox{\textit{OCR MEI C2 2013 Q7 [4]}}