| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Inequalities |
| Type | Perimeter or area constraint inequality |
| Difficulty | Moderate -0.3 This is a straightforward inequality problem requiring students to translate verbal constraints into algebraic inequalities (x+3 ≥ 14.5 and x(x+3) < 180), then solve a quadratic inequality. While it involves multiple steps and a quadratic, the setup is routine and the solving techniques are standard A-level fare, making it slightly easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(x + 3 \geq 14.5\) | M1 3.1b | Accept any inequality or equals and any letter for the width |
| \(x \geq 11.5\) | A1 1.1 | Correct inequality (seen or implied); M1A1 correct answer with no working |
| \(x(x+3) < 180\) | M1 3.1b | Accept any inequality or equals |
| \(x^2 + 3x - 180 (< 0) \Rightarrow (x-12)(x+15)(< 0)\) | M1 1.1 | Correct expansion and attempt to solve three-term quadratic; SC B1: \(x < \sqrt{60}\) |
| \(-15 < x < 12\) | A1 1.1 | Correct inequalities (seen or implied); B1: \(x \geq 29/6\) |
| \(11.5 \leq x < 12\) | B1 1.1 [6] | — |
## Question 3:
**DR**
$x + 3 \geq 14.5$ | M1 3.1b | Accept any inequality or equals and any letter for the width
$x \geq 11.5$ | A1 1.1 | Correct inequality (seen or implied); M1A1 correct answer with no working
$x(x+3) < 180$ | M1 3.1b | Accept any inequality or equals
$x^2 + 3x - 180 (< 0) \Rightarrow (x-12)(x+15)(< 0)$ | M1 1.1 | Correct expansion and attempt to solve three-term quadratic; **SC** B1: $x < \sqrt{60}$
$-15 < x < 12$ | A1 1.1 | Correct inequalities (seen or implied); B1: $x \geq 29/6$
$11.5 \leq x < 12$ | B1 1.1 [6] | —
---3 In this question you must show detailed reasoning.
A gardener is planning the design for a rectangular flower bed. The requirements are:
\begin{itemize}
\item the length of the flower bed is to be 3 m longer than the width,
\item the length of the flower bed must be at least 14.5 m ,
\item the area of the flower bed must be less than $180 \mathrm {~m} ^ { 2 }$.
\end{itemize}
The width of the flower bed is $x \mathrm {~m}$.\\
By writing down and solving appropriate inequalities in $x$, determine the set of possible values for the width of the flower bed.
\hfill \mbox{\textit{OCR H240/03 2018 Q3 [6]}}