Moderate -0.3 This is a straightforward integration question requiring the student to integrate a polynomial and a power of x (x^{-2}), then apply limits. The setup is given clearly, and the techniques are standard AS-level calculus with no conceptual challenges—slightly easier than average due to its routine nature, though the algebraic manipulation with parameter 'a' adds minor complexity.
A curve has equation \(y = 6x^2 + \frac{8}{x^2}\) and is sketched below for \(x > 0\)
\includegraphics{figure_6}
Find the area of the region bounded by the curve, the \(x\)-axis and the lines \(x = a\) and \(x = 2a\), where \(a > 0\), giving your answer in terms of \(a\)
[4 marks]
Question 6:
6 | States a correct integral expression
(ignore limits at this stage) | AO1.1a | M1 | 2a 8
Area = ∫ 6x2 + dx
a x2
2a
8
= 2x3 −
x
a
4 8
= (16a3 − )−(2a3 − )
a a
4
= 14a3 +
a
Integrates at least one term correctly | AO1.1b | A1
Substitutes 2a and a into ‘their’
integrated expression | AO1.1a | M1
States correct final answer with terms
collected
FT correct substitution into incorrect
integral provided both M1 marks
awarded | AO1.1b | A1F
Total | 4
Q | Marking Instructions | AO | Marks | Typical Solution
A curve has equation $y = 6x^2 + \frac{8}{x^2}$ and is sketched below for $x > 0$
\includegraphics{figure_6}
Find the area of the region bounded by the curve, the $x$-axis and the lines $x = a$ and $x = 2a$, where $a > 0$, giving your answer in terms of $a$
[4 marks]
\hfill \mbox{\textit{AQA AS Paper 2 Q6 [4]}}