Edexcel C1 2008 January — Question 1 4 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2008
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeBasic indefinite integration
DifficultyEasy -1.2 This is a straightforward application of the power rule for integration with no problem-solving required. It's a routine C1 question testing basic recall of integration formulas, making it easier than average but not trivial since students must correctly apply the rule to multiple terms and remember the constant of integration.
Spec1.08b Integrate x^n: where n != -1 and sums

Find \(\int \left( 3 x ^ { 2 } + 4 x ^ { 5 } - 7 \right) d x\).

AnswerMarks Guidance
\(3x^2 \to kx^3\) or \(4x^5 \to kx^6\) or \(-7 \to kx\) (where \(k\) is a non-zero constant)M1 Given for increasing by one the power of \(x\) in one of the three terms
\(\frac{3x^3}{3}\) or \(\frac{4x^6}{6}\) (Either of these, simplified or unsimplified)A1
\(x^3 + \frac{2x^6}{3} - 7x\) or equivalent unsimplified, such as \(\frac{3x^3}{3} + \frac{4x^6}{6} - 7x^1\)A1
\(+ C\) (or any other constant, e.g. \(+ K\))B1 Allow the mark (independently) for an integration constant appearing at any stage (even if it appears, then disappears from the final answer)
Total: 4 marks
$3x^2 \to kx^3$ or $4x^5 \to kx^6$ or $-7 \to kx$ (where $k$ is a non-zero constant) | M1 | Given for increasing by one the power of $x$ in one of the three terms

$\frac{3x^3}{3}$ or $\frac{4x^6}{6}$ (Either of these, simplified or unsimplified) | A1 | 

$x^3 + \frac{2x^6}{3} - 7x$ or equivalent unsimplified, such as $\frac{3x^3}{3} + \frac{4x^6}{6} - 7x^1$ | A1 | 

$+ C$ (or any other constant, e.g. $+ K$) | B1 | Allow the mark (independently) for an integration constant appearing at any stage (even if it appears, then disappears from the final answer)

**Total: 4 marks**

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Find $\int \left( 3 x ^ { 2 } + 4 x ^ { 5 } - 7 \right) d x$.\\

\hfill \mbox{\textit{Edexcel C1 2008 Q1 [4]}}