Moderate -0.3 This is a straightforward application of the quotient rule to find dy/dx, followed by standard tangent line procedure. While it requires multiple steps (differentiation, substitution, point-slope form, rearrangement), each step is routine and the question type is a common textbook exercise with no conceptual challenges.
1 Find the equation of the tangent to the curve \(y = \frac { 2 x + 1 } { 3 x - 1 }\) at the point \(\left( 1 , \frac { 3 } { 2 } \right)\), giving your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
Allow for numerator 'wrong way round'; or attempt use of product rule
Obtain \(\frac{2(3x-1)-3(2x+1)}{(3x-1)^2}\)
A1
or equiv
Obtain \(-\frac{5}{4}\) for gradient
A1
or equiv
Attempt equation of straight line with numerical gradient
M1
Obtained from their \(\frac{dy}{dx}\); tangent not normal
Obtain \(5x + 4y - 11 = 0\)
A1
5 or similar equiv
# Question 1:
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt use of quotient rule to find derivative | M1 | Allow for numerator 'wrong way round'; or attempt use of product rule |
| Obtain $\frac{2(3x-1)-3(2x+1)}{(3x-1)^2}$ | A1 | or equiv |
| Obtain $-\frac{5}{4}$ for gradient | A1 | or equiv |
| Attempt equation of straight line with numerical gradient | M1 | Obtained from their $\frac{dy}{dx}$; tangent not normal |
| Obtain $5x + 4y - 11 = 0$ | A1 | **5** or similar equiv |
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1 Find the equation of the tangent to the curve $y = \frac { 2 x + 1 } { 3 x - 1 }$ at the point $\left( 1 , \frac { 3 } { 2 } \right)$, giving your answer in the form $a x + b y + c = 0$, where $a$, $b$ and $c$ are integers.
\hfill \mbox{\textit{OCR C3 2007 Q1 [5]}}