| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | September |
| Marks | 5 |
| Topic | Inequalities |
| Type | Compound inequality with double bound |
| Difficulty | Easy -1.8 This is a very routine question testing basic algebraic manipulation of inequalities. Part (i) requires simple linear operations (subtract 1, divide by 3), and part (ii) requires rearranging to standard form and solving a quadratic inequality. Both are standard textbook exercises with no problem-solving or conceptual challenge beyond direct application of learned procedures. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| (i) | \(-6 < 3x < 13\) | M1 |
| (i) | \(-2 < x < \frac{13}{3}\) | A1 |
| (ii) | \(4x^2 > 25\) | M1 |
| (ii) | \(-\frac{5}{2}, \frac{5}{2}\) | M1 |
| (ii) | \(x < -\frac{5}{2}\) or \(x > \frac{5}{2}\) | A1IFT |
Total: [3]
(i) | $-6 < 3x < 13$ | M1 | Attempt to solve two equations/inequalities each involving all three terms
(i) | $-2 < x < \frac{13}{3}$ | A1 | Obtain correct inequality
(ii) | $4x^2 > 25$ | M1 | Rearrange to useable form (or $4x^2 - 25 > 0$)
(ii) | $-\frac{5}{2}, \frac{5}{2}$ | M1 | Attempt to find critical values
(ii) | $x < -\frac{5}{2}$ or $x > \frac{5}{2}$ | A1IFT | Choose 'outside' region for inequality FT their critical values
Total: [3]1 Solve the following inequalities.\\
(i) $- 5 < 3 x + 1 < 14$\\
(ii) $4 x ^ { 2 } + 3 > 28$
\hfill \mbox{\textit{OCR H240/01 2018 Q1 [5]}}