| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2019 |
| Session | Specimen |
| Marks | 1 |
| Topic | Factor & Remainder Theorem |
| Type | Fully specified polynomial: verify factor and solve |
| Difficulty | Moderate -0.8 This is a straightforward application of the factor theorem requiring substitution to verify x=2 is a root, then polynomial division to find the quadratic factor, followed by solving a simple quadratic. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires multiple standard techniques. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
(a) $\text{f}(-2) = 0$ clearly shown — **B1**
**Total: 1**
(b) Method shown e.g. division — **M1**
Obtain $2x^2 + 3x - 9$ — **A1**
Attempt to solve quadratic $((2x-3)(x+3))$ — **M1**
$x = \frac{3}{2}$ — **B1** (B1ft)
$x = 2$ and $x = -3$ — **B1** (B1ft)
**Total: 5**4
\begin{enumerate}[label=(\alph*)]
\item Show that $x = 2$ is a root of the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.
\item Hence solve the equation $2 x ^ { 3 } - x ^ { 2 } - 15 x + 18 = 0$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2019 Q4 [1]}}