Moderate -0.8 This is a straightforward differentiation exercise requiring two applications of the power rule. All terms follow standard patterns (x^n becomes nx^(n-1)), with no product/quotient/chain rule needed. It's purely procedural with no problem-solving element, making it easier than average, though not trivial since it requires careful handling of negative powers and a second derivative.
Question 3:
3 | Differentiates once, at least one
term correct | 1.1a | M1 | 𝑑𝑑𝑑𝑑 3 2 1
= 12𝑑𝑑 − 2 −
𝑑𝑑𝑑𝑑 𝑑𝑑 4
= 36x2 +
2
𝑑𝑑 𝑦𝑦 4
2 3
𝑑𝑑𝑥𝑥 𝑥𝑥
Differentiates twice, both powers of
x correct at least one coefficient
correct (ACF)
Condone one extra term from error
differentiating twice | 1.1a | M1
𝑥𝑥
Obtains completely correct
−4
expression with no errors | 1.1b | A1
Total | 3
Q | Marking Instructions | AO | Marks | Typical Solution
It is given that
$$y = 3x^4 + \frac{2}{x} - \frac{x}{4} + 1$$
Find an expression for $\frac{d^2y}{dx^2}$
[3 marks]
\hfill \mbox{\textit{AQA AS Paper 2 2020 Q3 [3]}}