AQA Paper 3 2021 June — Question 3 1 marks

Exam BoardAQA
ModulePaper 3 (Paper 3)
Year2021
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferentiation from First Principles
TypeFirst principles: x² terms
DifficultyEasy -1.8 This is a 1-mark multiple choice question testing recognition of the derivative from first principles. Students only need to identify the correct limit expression (which simplifies to 6x), requiring minimal calculation or conceptual understanding beyond basic differentiation recall.
Spec1.07a Derivative as gradient: of tangent to curve1.07g Differentiation from first principles: for small positive integer powers of x
\(f(x) = 3x^2\) Obtain \(\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\) Circle your answer. [1 mark] \(\frac{3h^2}{h}\) \quad \(x^3\) \quad \(\frac{3(x + h)^2 - 3x^2}{h}\) \quad \(6x\)
Question 3:
AnswerMarks Guidance
3Circles correct answer 1.1b
Total1
QMarking instructions AO 
Question 3:
3 | Circles correct answer | 1.1b | B1 | 6x
Total | 1
Q | Marking instructions | AO | Marks | Typical solution
$f(x) = 3x^2$

Obtain $\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$

Circle your answer.
[1 mark]

$\frac{3h^2}{h}$ \quad $x^3$ \quad $\frac{3(x + h)^2 - 3x^2}{h}$ \quad $6x$

\hfill \mbox{\textit{AQA Paper 3 2021 Q3 [1]}}
This paper (18 questions)
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Q1 1 Q2 1 Q3 1 Q4 5 Q5 13 Q6 4 Q7 10 Q8 6 Q9 9 Q10 1 Q11 1 Q12 3 Q13 6 Q14 7 Q15 7 Q16 4 Q17 11 Q18 10