| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Remainder condition then further work |
| Difficulty | Moderate -0.8 This is a straightforward polynomial question testing the Remainder Theorem and Factor Theorem with standard techniques. Part (a) requires direct substitution (x=3), part (b)(i) uses f(-2)=0 to find a constant, and part (b)(ii) involves factoring a cubic after finding one root—all routine AS-level procedures with no problem-solving insight required. The 10 marks reflect multiple steps rather than conceptual difficulty. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
\begin{enumerate}[label=(\alph*)]
\item Find the remainder when the polynomial $3x^3 + 2x^2 + x - 1$ is divided by $(x - 3)$. [3]
\item The polynomial $f(x) = 2x^3 - 3x^2 + ax + 6$ is divisible by $(x + 2)$, where $a$ is a real constant.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $a$. [3]
\item Showing all your working, solve the equation $f(x) = 0$. [4]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q4 [10]}}