| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Numerical integration |
| Type | Simpson's rule application |
| Difficulty | Standard +0.3 This question involves finding where ln(2 + cos x) = 0 (straightforward algebra giving cos x = -1, so x = π) and then applying Simpson's rule with 4 strips, which is a standard procedural application of a formula. Both parts require routine techniques with no novel problem-solving, making it slightly easier than average. |
| Spec | 1.05a Sine, cosine, tangent: definitions for all arguments1.06d Natural logarithm: ln(x) function and properties1.09f Trapezium rule: numerical integration |
1.
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The diagram shows the curve with equation $y = \ln ( 2 + \cos x ) , x \geq 0$.\\
The smallest value of $x$ for which the curve meets the $x$-axis is $a$ as shown.\\
(i) Find the value of $a$.\\
(ii) Use Simpson's rule with four strips of equal width to estimate the area of the region bounded by the curve in the interval $0 \leq x \leq a$ and the coordinate axes.\\
\hfill \mbox{\textit{OCR C3 Q1 [5]}}