| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Line intersection verification |
| Difficulty | Standard +0.3 Part (ii) is a standard verification that two lines are skew by showing no common solution exists for their parametric equations—a routine C4 technique requiring algebraic manipulation but no novel insight. This is slightly above average difficulty due to the algebraic work involved, but remains a textbook exercise. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
9
\end{array} \right) + t \left( \begin{array} { c }
2 \\
- 3 \\
1
\end{array} \right)$$
(ii) Show that lines $l _ { 1 }$ and $l _ { 2 }$ do not intersect.\\
(iii) Find the position vector of the point $C$ on $l _ { 2 }$ such that $\angle A B C = 90 ^ { \circ }$.\\
8. $f ( x ) = \frac { 5 - 8 x } { ( 1 + 2 x ) ( 1 - x ) ^ { 2 } }$.\\
\begin{enumerate}[label=(\roman*)]
\item Express $\mathrm { f } ( x )$ in partial fractions.
\item Find the series expansion of $\mathrm { f } ( x )$ in ascending powers of $x$ up to and including the term in $x ^ { 3 }$, simplifying each coefficient.
\item State the set of values of $x$ for which your expansion is valid.
\end{enumerate}
\hfill \mbox{\textit{OCR C4 Q9}}