Moderate -0.5 This question requires recognizing that absolute values create regions where the integrand changes sign, then applying the trapezium rule with 3 intervals—a straightforward numerical method. While it combines two concepts (absolute values and trapezium rule), both are standard A-level techniques with no novel insight required. The calculation is routine once the setup is understood, making it slightly easier than average.
These and no more. Accept in unsimplified form \(\
Use correct formula, or equivalent, with \(h = 1\) and four ordinates
M1
Obtain answer \(5.5\)
A1
Total
3
**Question 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply ordinates $3, 2, 0, 4$ | B1 | These and no more. Accept in unsimplified form $\|2^0 - 4\|$ etc. |
| Use correct formula, or equivalent, with $h = 1$ and four ordinates | M1 | |
| Obtain answer $5.5$ | A1 | |
| **Total** | **3** | |
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1 Use the trapezium rule with 3 intervals to estimate the value of
$$\int _ { 0 } ^ { 3 } \left| 2 ^ { x } - 4 \right| \mathrm { d } x$$
\hfill \mbox{\textit{CAIE P3 2019 Q1 [3]}}