OCR MEI C3 — Question 2 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicChain Rule
TypeChain rule with single composition
DifficultyModerate -0.8 This is a straightforward single application of the chain rule with a simple power function composition. It requires recognizing √(1+x³) as (1+x³)^(1/2) and applying the chain rule mechanically: dy/dx = (1/2)(1+x³)^(-1/2) × 3x². This is a routine textbook exercise testing basic chain rule recall with minimal problem-solving, making it easier than average.
Spec1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates
2 Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) when \(y = \sqrt { 1 + x ^ { 3 } }\).
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\(y = \sqrt{1+x^3}\), Let \(u = 1+x^3 \Rightarrow \frac{du}{dx} = 3x^2\)M1 Chain rule
\(y = u^{\frac{1}{2}} \Rightarrow \frac{dy}{du} = \frac{1}{2}u^{-\frac{1}{2}}\)A1 \(\frac{dy}{du}\)
\(\Rightarrow \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx} = \frac{1}{2}u^{-\frac{1}{2}} \times 3x^2 = \frac{3}{2}\frac{x^2}{\sqrt{1+x^3}}\)A1 Answer
Total: 3 
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| $y = \sqrt{1+x^3}$, Let $u = 1+x^3 \Rightarrow \frac{du}{dx} = 3x^2$ | M1 | Chain rule |
| $y = u^{\frac{1}{2}} \Rightarrow \frac{dy}{du} = \frac{1}{2}u^{-\frac{1}{2}}$ | A1 | $\frac{dy}{du}$ |
| $\Rightarrow \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx} = \frac{1}{2}u^{-\frac{1}{2}} \times 3x^2 = \frac{3}{2}\frac{x^2}{\sqrt{1+x^3}}$ | A1 | Answer |
| **Total: 3** | | |

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2 Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ when $y = \sqrt { 1 + x ^ { 3 } }$.

\hfill \mbox{\textit{OCR MEI C3  Q2 [3]}}
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Q1 2 Q2 3 Q3 7 Q4 7 Q5 5 Q6 6 Q7 6 Q8 18 Q9 18