| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Substitution in inequality |
| Difficulty | Standard +0.3 Part (i) is a routine quadratic inequality requiring factorisation and sign analysis. Part (ii) adds a straightforward substitution step (letting u = 2^y) followed by solving an exponential inequality using logarithms. This is a standard C2 technique with clear structure, slightly above average due to the two-part nature and exponential manipulation, but still well within typical exam expectations. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02g Inequalities: linear and quadratic in single variable1.06g Equations with exponentials: solve a^x = b |
4. (i) Solve the inequality
$$x ^ { 2 } - 13 x + 30 < 0$$
(ii) Hence find the set of values of $y$ such that
$$2 ^ { 2 y } - 13 \left( 2 ^ { y } \right) + 30 < 0 .$$
\hfill \mbox{\textit{OCR C2 Q4 [6]}}