| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve |linear| < constant with sketch or follow-up application |
| Difficulty | Standard +0.3 Part (i) is a routine modulus inequality requiring simple manipulation to get 0.17 < x < 0.23. Part (ii) requires substituting x = 0.95^n and solving logarithmically, which adds a modest step beyond standard textbook exercises but remains straightforward application of techniques. |
| Spec | 1.02h Express solutions: using 'and', 'or', set and interval notation1.02l Modulus function: notation, relations, equations and inequalities |
\begin{enumerate}
\item (i) Solve the inequality
\end{enumerate}
$$| x - 0.2 | < 0.03$$
(ii) Hence, find all integers $n$ such that
$$\left| 0.95 ^ { n } - 0.2 \right| < 0.03$$
\hfill \mbox{\textit{OCR C3 Q1 [5]}}