AQA Paper 2 2024 June — Question 5 3 marks

Exam BoardAQA
ModulePaper 2 (Paper 2)
Year2024
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProduct & Quotient Rules
TypeFind derivative of quotient
DifficultyModerate -0.3 This is a straightforward application of the quotient rule with standard derivatives (x³ and sin x). While it requires careful algebraic manipulation to avoid sign errors, it's a routine calculus exercise with no conceptual difficulty or problem-solving required—slightly easier than the average A-level question due to its mechanical nature.
Spec1.07q Product and quotient rules: differentiation

Given that $$y = \frac{x^3}{\sin x}$$ find \(\frac{dy}{dx}\) [3 marks]

Question 5:
AnswerMarks
5Differentiates x3 and sinx
to obtain 3x2 and cosx
AnswerMarks Guidance
OE1.1b B1
=
dx sin2 x
Uses the quotient rule and
obtains numerator
Ax2sinx±Bx3cosx
Condone any denominator
Or
Writes as a product and applies
the product rule to obtain
AnswerMarks Guidance
Ax2cosec(x)±x3cosec(x)cot(x)3.1a M1
3x2sinx−x3cosx
Obtains
sin2 x
ACF
AnswerMarks Guidance
No ISW1.1b A1
Question 5 Total3
QMarking instructions AO
Question 5:
5 | Differentiates x3 and sinx
to obtain 3x2 and cosx
OE | 1.1b | B1 | dy 3x2sinx−x3cosx
=
dx sin2 x
Uses the quotient rule and
obtains numerator
Ax2sinx±Bx3cosx
Condone any denominator
Or
Writes as a product and applies
the product rule to obtain
Ax2cosec(x)±x3cosec(x)cot(x) | 3.1a | M1
3x2sinx−x3cosx
Obtains
sin2 x
ACF
No ISW | 1.1b | A1
Question 5 Total | 3
Q | Marking instructions | AO | Marks | Typical solution
Given that
$$y = \frac{x^3}{\sin x}$$

find $\frac{dy}{dx}$
[3 marks]

\hfill \mbox{\textit{AQA Paper 2 2024 Q5 [3]}}