| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Verify factor then sketch or analyse curve |
| Difficulty | Moderate -0.3 This is a standard C1 question testing routine application of the factor theorem, polynomial factorization, and basic transformations. Part (i) involves straightforward verification by substitution, factorizing by inspection or division (yielding (x-1)(x-4)(x+2)), and a basic cubic sketch. Part (ii) tests understanding of horizontal translation (replacing x with x+3) and finding a y-intercept by substitution. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-part nature and 12 total marks. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
A cubic polynomial is given by $f(x) = x^3 + x^2 - 10x + 8$.
\begin{enumerate}[label=(\roman*)]
\item Show that $(x - 1)$ is a factor of $f(x)$.
Factorise $f(x)$ fully.
Sketch the graph of $y = f(x)$. [7]
\item The graph of $y = f(x)$ is translated by $\begin{pmatrix} -3 \\ 0 \end{pmatrix}$.
Write down an equation for the resulting graph. You need not simplify your answer.
Find also the intercept on the $y$-axis of the resulting graph. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q11 [12]}}