| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Rational curve sketching with asymptotes and inequalities |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths curve sketching question with standard techniques: finding y-intercept, identifying vertical asymptotes from denominators and horizontal asymptote from degree comparison, sketching based on asymptotic behavior, and solving a rational inequality. While it's Further Maths content, all parts are routine applications of well-practiced methods with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02n Sketch curves: simple equations including polynomials |
(i) Write down the value of $y$ when $x = 0$. [1]
(ii) Write down the equations of the three asymptotes. [3]
(iii) Sketch the curve. [3]
(iv) Find the values of $x$ for which $\frac{5}{(x-2)(4-x)} = 1$ and hence solve the inequality $\frac{5}{(x-2)(4-x)} \geq 1$. [5]7 A curve has equation $y = \frac { 5 } { ( x + 2 ) ( 4 - x ) }$.\\
(i) Write down the value of $y$ when $x = 0$.\\
(ii) Write down the equations of the three asymptotes.\\
(iii) Sketch the curve.\\
(iv) Find the values of $x$ for which $\frac { 5 } { ( x + 2 ) ( 4 - x ) } = 1$ and hence solve the inequality
$$\frac { 5 } { ( x + 2 ) ( 4 - x ) } < 1 .$$
\hfill \mbox{\textit{OCR MEI FP1 2007 Q7 [12]}}