| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 8 |
| Topic | Curve Sketching |
| Type | Reflection or vertical transformation |
| Difficulty | Easy -1.3 This is a straightforward multi-part question requiring basic algebraic expansion, identifying roots from factored form, and sketching cubic curves with known intercepts. Part (i) is routine bracket expansion, part (ii) requires plotting given roots and y-intercept with no calculus needed, and part (iii) is a simple reflection. All steps are mechanical with no problem-solving or novel insight required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
\begin{enumerate}[label=(\roman*)]
\item By expanding the brackets, show that
$(x - 4)(x - 3)(x + 1) = x^3 - 6x^2 + 5x + 12$. [3]
\item Sketch the curve
$y = x^3 - 6x^2 + 5x + 12$,
giving the coordinates of the points where the curve meets the axes. Label the curve $C_1$. [3]
\item On the same diagram as in part (ii), sketch the curve
$y = -x^3 + 6x^2 - 5x - 12$.
Label this curve $C_2$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q4 [8]}}