AQA Paper 1 2022 June — Question 5 3 marks

Exam BoardAQA
ModulePaper 1 (Paper 1)
Year2022
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyEasy -1.2 This is a straightforward single-step differentiation problem requiring the chain rule to find dy/dx, evaluate at x=0, find the y-coordinate, then write the tangent equation using y-y₁=m(x-x₁). It's simpler than average A-level questions as it involves only basic differentiation and no problem-solving insight.
Spec1.07m Tangents and normals: gradient and equations1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates

5 Find an equation of the tangent to the curve $$y = ( x - 2 ) ^ { 4 }$$ at the point where \(x = 0\)

Question 5:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{dy}{dx} = 4(x-2)^3\) or \(4x^3 - 24x^2 + 48x - 32\)B1 Correct derivative; PI by \(-32\) obtained with no errors in evaluating \(\frac{dy}{dx}\)
When \(x = 0\), \(\frac{dy}{dx} = -32\); \(y = 16\)M1 Substitutes \(x = 0\) into \(\frac{dy}{dx}\) to obtain numerical value; or PI by constant from \(\frac{dy}{dx}\); or PI by \(-32\) with no errors
\(y = -32x + 16\)A1 ACF; award at first opportunity; ISW incorrect rearrangement; no errors seen
## Question 5:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{dy}{dx} = 4(x-2)^3$ or $4x^3 - 24x^2 + 48x - 32$ | B1 | Correct derivative; PI by $-32$ obtained with no errors in evaluating $\frac{dy}{dx}$ |
| When $x = 0$, $\frac{dy}{dx} = -32$; $y = 16$ | M1 | Substitutes $x = 0$ into $\frac{dy}{dx}$ to obtain numerical value; or PI by constant from $\frac{dy}{dx}$; or PI by $-32$ with no errors |
| $y = -32x + 16$ | A1 | ACF; award at first opportunity; ISW incorrect rearrangement; no errors seen |

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5 Find an equation of the tangent to the curve

$$y = ( x - 2 ) ^ { 4 }$$

at the point where $x = 0$\\

\hfill \mbox{\textit{AQA Paper 1 2022 Q5 [3]}}