| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Perimeter or area constraint inequality |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic inequality formation and solving. Part (a) involves simple perimeter formula manipulation, part (b) uses area formula, and part (c) requires solving a linear inequality and a quadratic inequality—all standard techniques with no novel problem-solving required. The multi-part structure adds some length but each step is routine. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x + 2(x + 20) < 300\) | M1 A1 | Using \(x - 20\) is A0 |
| Answer | Marks | Guidance |
|---|---|---|
| \(x(x + 20) > 4800\) | M1 A1 | Using \(x - 20\) is A0 |
| Answer | Marks |
|---|---|
| \(65\) (allow wrong inequality sign or \(x = 65\)) | B1ft |
| 3 term quadratic, \((x + 80)(x - 60) = 0\), \(x = \ldots\) | M1 |
| \(x > 60\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(60 < x < 65\) | A1 | (4 marks) (8 marks) |
## Question 4:
### Part (a)
$2x + 2(x + 20) < 300$ | M1 A1 | Using $x - 20$ is A0 | (2 marks)
### Part (b)
$x(x + 20) > 4800$ | M1 A1 | Using $x - 20$ is A0 | (2 marks)
### Part (c)
$65$ (allow wrong inequality sign or $x = 65$) | B1ft |
3 term quadratic, $(x + 80)(x - 60) = 0$, $x = \ldots$ | M1 |
$x > 60$ | A1 |
($x < -80$ may be included but must be no other wrong solution to quadratic inequality such as $x > -80$)
$60 < x < 65$ | A1 | (4 marks) **(8 marks)**
---4. The width of a rectangular sports pitch is $x$ metres, $x > 0$. The length of the pitch is 20 m more than its width. Given that the perimeter of the pitch must be less than 300 m ,
\begin{enumerate}[label=(\alph*)]
\item form a linear inequality in $x$.
Given that the area of the pitch must be greater than $4800 \mathrm {~m} ^ { 2 }$,
\item form a quadratic inequality in $x$.
\item by solving your inequalities, find the set of possible values of $x$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [8]}}