| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | 3x3 Matrices |
| Type | Consistency conditions for systems |
| Difficulty | Standard +0.8 Part (i) is a routine 3×3 system solved by Gaussian elimination or matrix methods. Part (ii) requires understanding consistency conditions for infinitely many solutions—recognizing that the third equation must be a linear combination of the first two, which involves finding specific values of p and k. This conceptual step elevates it above standard Further Maths exercises but remains within expected syllabus material. |
| Spec | 4.03r Solve simultaneous equations: using inverse matrix4.03s Consistent/inconsistent: systems of equations |
8 (i) Find the solution to the following simultaneous equations.
$$\begin{array} { r r r }
x + y + & z = & 3 \\
2 x + 4 y + 5 z = & 9 \\
7 x + 11 y + 12 z = & 20
\end{array}$$
(ii) Determine the values of $p$ and $k$ for which there are an infinity of solutions to the following simultaneous equations.
$$\begin{array} { r r r r }
x + & y + & z = & 3 \\
2 x + & 4 y + & 5 z = & 9 \\
7 x + & 11 y + & p z = & k
\end{array}$$
\hfill \mbox{\textit{OCR Further Pure Core 1 2017 Q8 [8]}}