AQA AS Paper 1 Specimen — Question 12 9 marks

Exam BoardAQA
ModuleAS Paper 1 (AS Paper 1)
SessionSpecimen
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeEquation of tangent line
DifficultyModerate -0.3 This is a straightforward differentiation and tangent line question. Part (a) requires rewriting terms as powers and applying standard rules (9x^{1/2} - 32x^{-2}). Part (b) involves evaluating the derivative at x=4, finding the tangent equation, and solving for the x-intercept. All steps are routine AS-level techniques with no conceptual challenges, though the multi-step nature and 9 total marks make it slightly more substantial than the most basic exercises.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations
A curve has equation \(y = 6x\sqrt{x} + \frac{32}{x}\) for \(x > 0\)
  1. Find \(\frac{dy}{dx}\) [4 marks]
  2. The point \(A\) lies on the curve and has \(x\)-coordinate 4 Find the coordinates of the point where the tangent to the curve at \(A\) crosses the \(x\)-axis. [5 marks]
Question 12:
AnswerMarks
12(a)Rewrites given expression with a
fractional power and negative power –
at least one index form must be
AnswerMarks Guidance
correctAO1.1a M1
y 6x2 32x1
dy 3 1
6 x2 32x2
dx 2
32
9 x
x2
AnswerMarks Guidance
Both terms correctAO1.1b A1
Differentiates ‘their’ rewritten
AnswerMarks Guidance
expression – at least one term correctAO1.1a M1
Both terms correct for ‘their’
AnswerMarks Guidance
expressionAO1.1b A1F
(b)Finds the equation of the tangent, a
clear attempt must be seenAO3.1a M1
dy 32
92 16
dx 16
and
32
y 642 56
4
Tangent:
y5616(x4)
When y = 0,
56
x = 4  =0.5
16
(0.5, 0)
dy
Evaluates ‘their’ (from part (a))
dx
correctly
AnswerMarks Guidance
(when x = 4)AO1.1b A1F
Obtains correct y value
AnswerMarks Guidance
(when x = 4)AO1.1b A1
Obtains correct form of the equation
of a straight line using ‘their’ values for
dy
y and
AnswerMarks Guidance
dxAO1.1b A1F
Deduces value required at x-axis is
when y equals 0
(follow through from ‘their’ equation)
AnswerMarks Guidance
Both coordinates needed, any formAO2.2a A1F
Total9
QMarking Instructions AO 
Question 12:
--- 12(a) ---
12(a) | Rewrites given expression with a
fractional power and negative power –
at least one index form must be
correct | AO1.1a | M1 | 3
y 6x2 32x1
dy 3 1
6 x2 32x2
dx 2
32
9 x
x2
Both terms correct | AO1.1b | A1
Differentiates ‘their’ rewritten
expression – at least one term correct | AO1.1a | M1
Both terms correct for ‘their’
expression | AO1.1b | A1F
(b) | Finds the equation of the tangent, a
clear attempt must be seen | AO3.1a | M1 | When x = 4,
dy 32
92 16
dx 16
and
32
y 642 56
4
Tangent:
y5616(x4)
When y = 0,
56
x = 4  =0.5
16
(0.5, 0)
dy
Evaluates ‘their’ (from part (a))
dx
correctly
(when x = 4) | AO1.1b | A1F
Obtains correct y value
(when x = 4) | AO1.1b | A1
Obtains correct form of the equation
of a straight line using ‘their’ values for
dy
y and
dx | AO1.1b | A1F
Deduces value required at x-axis is
when y equals 0
(follow through from ‘their’ equation)
Both coordinates needed, any form | AO2.2a | A1F
Total | 9
Q | Marking Instructions | AO | Marks | Typical Solution
A curve has equation $y = 6x\sqrt{x} + \frac{32}{x}$ for $x > 0$

\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$ [4 marks]

\item The point $A$ lies on the curve and has $x$-coordinate 4

Find the coordinates of the point where the tangent to the curve at $A$ crosses the $x$-axis.
[5 marks]
\end{enumerate}

\hfill \mbox{\textit{AQA AS Paper 1  Q12 [9]}}
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Q1 1 Q2 1 Q3 4 Q4 3 Q5 2 Q6 4 Q7 4 Q8 6 Q9 5 Q10 7 Q11 7 Q12 9 Q13 2 Q14 3 Q15 5 Q16 8 Q17 9