Edexcel AS Paper 1 2018 June — Question 1 4 marks

Exam BoardEdexcel
ModuleAS Paper 1 (AS Paper 1)
Year2018
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind indefinite integral of polynomial/power
DifficultyEasy -1.3 This is a straightforward application of basic integration rules for polynomials and powers. It requires only direct recall of the power rule for integration (increase power by 1, divide by new power) with no problem-solving, manipulation, or conceptual insight needed. The presence of a fractional coefficient and square root adds minimal complexity to what remains a routine AS-level exercise.
Spec2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles
  1. Find
$$\int \left( \frac { 2 } { 3 } x ^ { 3 } - 6 \sqrt { x } + 1 \right) \mathrm { d } x$$ giving your answer in its simplest form.
Question 1:
\[\int\left(\frac{2}{3}x^3 - 6\sqrt{x} + 1\right)dx\]
AnswerMarks Guidance
Working/AnswerMark Guidance
Attempts to integrate - any correct power raised by oneM1 Award for any correct power including sight of \(1x\)
\(\frac{2}{3} \times \frac{x^4}{4} + \ldots + x\)A1 Correct two non-fractional power terms (may be unsimplified)
\(\ldots - 6\frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \ldots\)A1 Correct fractional power term (may be unsimplified)
\(\frac{1}{6}x^4 - 4x^{\frac{3}{2}} + x + c\)A1 Completely correct, simplified, including constant of integration on one line
Accept: \(\frac{x^4}{6} - 4x\sqrt{x} + 1x^1 + c\) or \(\frac{x^4 - 24x^{\frac{3}{2}} + 6x}{6} + c\)
# Question 1:

$$\int\left(\frac{2}{3}x^3 - 6\sqrt{x} + 1\right)dx$$

| Working/Answer | Mark | Guidance |
|---|---|---|
| Attempts to integrate - any correct power raised by one | M1 | Award for any correct power including sight of $1x$ |
| $\frac{2}{3} \times \frac{x^4}{4} + \ldots + x$ | A1 | Correct two non-fractional power terms (may be unsimplified) |
| $\ldots - 6\frac{x^{\frac{3}{2}}}{\frac{3}{2}} + \ldots$ | A1 | Correct fractional power term (may be unsimplified) |
| $\frac{1}{6}x^4 - 4x^{\frac{3}{2}} + x + c$ | A1 | Completely correct, simplified, including constant of integration on one line |

Accept: $\frac{x^4}{6} - 4x\sqrt{x} + 1x^1 + c$ or $\frac{x^4 - 24x^{\frac{3}{2}} + 6x}{6} + c$

---
\begin{enumerate}
  \item Find
\end{enumerate}

$$\int \left( \frac { 2 } { 3 } x ^ { 3 } - 6 \sqrt { x } + 1 \right) \mathrm { d } x$$

giving your answer in its simplest form.

\hfill \mbox{\textit{Edexcel AS Paper 1 2018 Q1 [4]}}
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