| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Moderate -0.8 This is a straightforward two-part inequality question requiring basic algebraic manipulation (part a) and solving a quadratic inequality by factorization (part b). Both are standard C1 techniques with no conceptual challenges, making it easier than average but not trivial since part (b) requires rearranging, factorizing, and correctly interpreting the solution regions. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(5x > 20\) | M1 | Reducing to form \(px > q\) with one of \(p\) or \(q\) correct. Using \(px=q\) is M0 unless \(>\) appears later |
| \(x > 4\) | A1 | \(x > 4\) only |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x^2 - 4x - 12 = 0\) | ||
| \((x+2)(x-6)[=0]\) | M1 | Multiplying out and attempting to solve 3TQ with at least \(\pm 4x\) or \(\pm 12\) |
| \(x = 6,\ -2\) | A1 | For 6 and \(-2\) seen. Allow \(x > 6\), \(x > -2\) etc. Values may be on sketch |
| \(x < -2\ ,\ x > 6\) | M1, A1ft | 2nd M1 for choosing "outside region" for critical values. A1ft follows through 2 distinct critical values. Allow ",", "or" or blank between answers. Use of "and" is M1A0. Accept \((-\infty,-2)\cup(6,\infty)\) |
## Question 3:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $5x > 20$ | M1 | Reducing to form $px > q$ with one of $p$ or $q$ correct. Using $px=q$ is M0 unless $>$ appears later |
| $x > 4$ | A1 | $x > 4$ only |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x^2 - 4x - 12 = 0$ | | |
| $(x+2)(x-6)[=0]$ | M1 | Multiplying out and attempting to solve 3TQ with at least $\pm 4x$ or $\pm 12$ |
| $x = 6,\ -2$ | A1 | For 6 and $-2$ seen. Allow $x > 6$, $x > -2$ etc. Values may be on sketch |
| $x < -2\ ,\ x > 6$ | M1, A1ft | 2nd M1 for choosing "outside region" for critical values. A1ft follows through 2 distinct critical values. Allow ",", "or" or blank between answers. Use of "and" is M1A0. Accept $(-\infty,-2)\cup(6,\infty)$ |
---3. Find the set of values of $x$ for which
\begin{enumerate}[label=(\alph*)]
\item $4 x - 5 > 15 - x$
\item $x ( x - 4 ) > 12$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2012 Q3 [6]}}