| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2009 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Difficulty | Standard +0.3 This is a straightforward Further Pure 1 question on rational functions requiring standard techniques: finding intercepts by substitution, identifying vertical asymptote from denominator, and polynomial division for oblique asymptote. While it's Further Maths content, the methods are routine and well-practiced, making it slightly easier than average overall but harder than typical Core questions. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
| Answer | Marks |
|---|---|
| (i) \((1.0), (4,0)\) | B1 |
| \((0,4)\) | B1 |
| (ii) One asymptote is \(x = -1\) | B1 |
| \(y = x - 6 + 10/(x+1)\) | M1 |
| Other asymptote: \(y = x - 6\) | A1 |
| (iii) Sketch: | |
| Axes and asymptotes | B1 |
| Upper branch: Correct location and orientation | B1 |
| Lower branch correctly located and orientated | B1 |
(i) $(1.0), (4,0)$ | B1 |
$(0,4)$ | B1 |
(ii) One asymptote is $x = -1$ | B1 |
$y = x - 6 + 10/(x+1)$ | M1 |
Other asymptote: $y = x - 6$ | A1 |
(iii) Sketch: | |
Axes and asymptotes | B1 |
Upper branch: Correct location and orientation | B1 |
Lower branch correctly located and orientated | B1 |3 The curve $C$ has equation
$$y = \frac { x ^ { 2 } - 5 x + 4 } { x + 1 }$$
(i) Obtain the coordinates of the points of intersection of $C$ with the axes.\\
(ii) Obtain the equation of each of the asymptotes of $C$.\\
(iii) Draw a sketch of $C$.
\hfill \mbox{\textit{CAIE FP1 2009 Q3 [8]}}