Moderate -0.5 This is a straightforward application of the trapezium rule with the added step of handling absolute values. Students need to evaluate |3^x - 10| at four points (x = 0, 1, 2, 3), apply the standard trapezium rule formula, and perform arithmetic. While the absolute value requires identifying where 3^x = 10 occurs (between x = 2 and 3), the trapezium rule itself doesn't require this analysis—students simply evaluate the function at given points. This is slightly easier than average because it's a direct application of a standard numerical method with minimal problem-solving required.
2 Use the trapezium rule with three intervals to find an approximation to
$$\int _ { 0 } ^ { 3 } \left| 3 ^ { x } - 10 \right| \mathrm { d } x$$
\hfill \mbox{\textit{CAIE P3 2015 Q2 [4]}}