Edexcel AS Paper 1 — Question 10

Exam BoardEdexcel
ModuleAS Paper 1 (AS Paper 1)
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Mark schemeDownload PDF ↗
TopicDifferentiation from First Principles
TypeFirst principles: x² terms
DifficultyEasy -1.2 This is a straightforward first principles differentiation question requiring only the standard limit definition and basic algebraic manipulation. While it tests understanding of the derivative definition, it's a routine textbook exercise with no problem-solving required—students simply substitute into the formula and simplify, making it easier than average.
Spec1.07g Differentiation from first principles: for small positive integer powers of x
Prove, from the first principles, that the derivative of \(5x^2\) is \(10x\).
AnswerMarks Guidance
\(f'(x) = \lim_{h \to 0} \frac{5(x+h)^2 - 5x^2}{h} = \lim_{h \to 0} \frac{10xh + 5h^2}{h} = \lim_{h \to 0}(10x + 5h) = 10x\)B1, M1, A1, A1 Substitutes the function; Attempts to expand \(5(x + h)^2\) looking for two correct terms; Simplifies correctly; Correctly computes the limit 
$f'(x) = \lim_{h \to 0} \frac{5(x+h)^2 - 5x^2}{h} = \lim_{h \to 0} \frac{10xh + 5h^2}{h} = \lim_{h \to 0}(10x + 5h) = 10x$ | B1, M1, A1, A1 | Substitutes the function; Attempts to expand $5(x + h)^2$ looking for two correct terms; Simplifies correctly; Correctly computes the limit
Prove, from the first principles, that the derivative of $5x^2$ is $10x$.

\hfill \mbox{\textit{Edexcel AS Paper 1  Q10}}
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