Edexcel C2 — Question 3 6 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAreas by integration
TypeArea under polynomial curve
DifficultyModerate -0.8 This is a straightforward C2 integration question requiring students to find roots (factorising to x=0 and x=5), set up a definite integral, and evaluate. It's a standard textbook exercise with no conceptual challenges beyond basic technique, making it easier than average but not trivial since it requires multiple routine steps.
Spec1.08d Evaluate definite integrals: between limits1.08e Area between curve and x-axis: using definite integrals
3. Find the area of the finite region enclosed by the curve \(y = 5 x - x ^ { 2 }\) and the \(x\)-axis.
AnswerMarks
\(5x - x^2 = 0\)B1
\(x(5 - x) = 0\)
crosses x-axis at (0, 0) and (5, 0)
\(\text{area} = \int_0^5 (5x - x^2) \, dx\)M1 A2
\(= \left[\frac{5}{2}x^2 - \frac{1}{4}x^3\right]_0^5\)
\(= \left(\frac{125}{2} - \frac{125}{4}\right) - (0) = 20\frac{5}{6}\)M1 A1 
$5x - x^2 = 0$ | B1 |
$x(5 - x) = 0$ |
crosses x-axis at (0, 0) and (5, 0) |
$\text{area} = \int_0^5 (5x - x^2) \, dx$ | M1 A2 |
$= \left[\frac{5}{2}x^2 - \frac{1}{4}x^3\right]_0^5$ |
$= \left(\frac{125}{2} - \frac{125}{4}\right) - (0) = 20\frac{5}{6}$ | M1 A1 |

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3. Find the area of the finite region enclosed by the curve $y = 5 x - x ^ { 2 }$ and the $x$-axis.\\

\hfill \mbox{\textit{Edexcel C2  Q3 [6]}}
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