Edexcel C1 2011 January — Question 2 5 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2011
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeBasic indefinite integration
DifficultyEasy -1.3 This is a straightforward application of the power rule for integration with no problem-solving required. Students simply increase each power by 1 and divide by the new power, then add the constant of integration. This is a routine C1 exercise testing basic recall of integration techniques with simple algebraic manipulation.
Spec1.08b Integrate x^n: where n != -1 and sums

Find $$\int \left( 12 x ^ { 5 } - 3 x ^ { 2 } + 4 x ^ { \frac { 1 } { 3 } } \right) \mathrm { d } x$$ giving each term in its simplest form.

Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{12x^6}{6},\ -\frac{3x^3}{3},\ +\frac{4x^{\frac{4}{3}}}{\frac{4}{3}},\ (+c)\)M1, A1, A1, A1 M1 for some attempt to integrate: \(x^n \to x^{n+1}\). 1st A1 for \(\frac{12x^6}{6}\) or better. 2nd A1 for \(-\frac{3x^3}{3}\) or better. 3rd A1 for \(\frac{4x^{\frac{4}{3}}}{\frac{4}{3}}\) or better
\(= 2x^6 - x^3 + 3x^{\frac{4}{3}} + c\)A1 4th A1 for each term correct and simplified and the \(+c\) occurring in the final answer
(5)
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{12x^6}{6},\ -\frac{3x^3}{3},\ +\frac{4x^{\frac{4}{3}}}{\frac{4}{3}},\ (+c)$ | M1, A1, A1, A1 | M1 for some attempt to integrate: $x^n \to x^{n+1}$. 1st A1 for $\frac{12x^6}{6}$ or better. 2nd A1 for $-\frac{3x^3}{3}$ or better. 3rd A1 for $\frac{4x^{\frac{4}{3}}}{\frac{4}{3}}$ or better |
| $= 2x^6 - x^3 + 3x^{\frac{4}{3}} + c$ | A1 | 4th A1 for each term correct and simplified and the $+c$ occurring in the final answer |
| | **(5)** | |

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Find

$$\int \left( 12 x ^ { 5 } - 3 x ^ { 2 } + 4 x ^ { \frac { 1 } { 3 } } \right) \mathrm { d } x$$

giving each term in its simplest form.\\

\hfill \mbox{\textit{Edexcel C1 2011 Q2 [5]}}