Standard +0.3 This is a separable variables question requiring standard technique (separate, integrate both sides, solve for y). The main challenge is factorising the cubic and partial fractions for integration, but these are routine A-level skills. Slightly above average due to the algebraic manipulation required, but still a standard textbook-style question.
12 Find the general solution of the differential equation
\(\left( 2 x ^ { 3 } - 3 x ^ { 2 } - 11 x + 6 \right) \frac { \mathrm { d } y } { \mathrm {~d} x } = y ( 20 x - 35 )\).
Give your answer in the form \(y = \mathrm { f } ( x )\).
\section*{END OF QUESTION PAPER}
\section*{OCR
Oxford Cambridge and RSA}
Obtain correct equation; any correct form not involving ln; may be \(e^c\) not \(A\), but A0 if fraction \(+c\); could have \((x+2)^{-3}\) in a product
[9]
The image you've shared appears to be only the contact/back page of an OCR document, containing just the OCR address, customer contact details, and Cambridge Assessment logo.
There is no mark scheme content visible in this image.
To extract mark scheme content, please share the actual mark scheme pages containing the questions, answers, mark allocations, and guidance notes. Could you upload those pages instead?
## Question 12
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\int \frac{1}{y}\,dy = \int \frac{20x-35}{2x^3 - 3x^2 - 11x + 6}\,dx$ | M1 | Separate variables; correct process to deal with algebraic fractions with BOD on integral notation |
| $f(x) = 2x^3 - 3x^2 - 11x + 6 = (x-3)(2x^2+3x-2)$ | M1 | Attempt to factorise cubic; possibly BC, so correct factorised cubic implies M1A1 |
| $= (x-3)(x+2)(2x-1)$ | A1 | Correct factorised cubic |
| $\frac{20x-35}{2x^3-3x^2-11x+6} = \frac{A}{x+2} + \frac{B}{x-3} + \frac{C}{2x-1}$ | M1 | Attempt partial fractions using their 3 linear factors; must be correct structure, attempting at least one numerator |
| $= \frac{-3}{x+2} + \frac{1}{x-3} + \frac{4}{2x-1}$ | A1 | Obtain any one correct fraction www |
| | A1 | Obtain fully correct partial fractions |
| $\int \frac{1}{y}\,dy = \ln|y|$ | B1 | Correct integration of $\frac{1}{y}$; condone no modulus sign |
| $-3\ln|x+2| + \ln|x-3| + 2\ln|2x-1| + \ln A$ | A1FT | Obtain correct integral following their 3 linear partial fractions; condone no constant of integration; condone brackets and not modulus; FT from point that partial fractions were credited |
| $y = \frac{A(x-3)(2x-1)^2}{(x+2)^3}$ | A1 | Obtain correct equation; any correct form not involving ln; may be $e^c$ not $A$, but A0 if fraction $+c$; could have $(x+2)^{-3}$ in a product |
| | **[9]** | |
The image you've shared appears to be only the **contact/back page** of an OCR document, containing just the OCR address, customer contact details, and Cambridge Assessment logo.
**There is no mark scheme content visible in this image.**
To extract mark scheme content, please share the actual mark scheme pages containing the questions, answers, mark allocations, and guidance notes. Could you upload those pages instead?
12 Find the general solution of the differential equation\\
$\left( 2 x ^ { 3 } - 3 x ^ { 2 } - 11 x + 6 \right) \frac { \mathrm { d } y } { \mathrm {~d} x } = y ( 20 x - 35 )$.\\
Give your answer in the form $y = \mathrm { f } ( x )$.
\section*{END OF QUESTION PAPER}
\section*{OCR \\
Oxford Cambridge and RSA}
\hfill \mbox{\textit{OCR H240/01 2020 Q12 [9]}}