| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Compound inequality with double bound |
| Difficulty | Moderate -0.8 Part (i) is a routine double inequality requiring simple algebraic manipulation (add 9, divide by 4). Part (ii) is a standard quadratic inequality requiring rearrangement to standard form, factorization, and sign analysis—all textbook procedures for C1. The 8 total marks reflect straightforward application of basic techniques with no problem-solving insight required, making this easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 < 4x - 9 < 5\) | M1 | 2 equations or inequalities both dealing with all 3 terms |
| \(10 < 4x < 14\) | M1 | |
| \(2.5 < x < 3.5\) | A1 | 3 marks; 2.5 and 3.5 seen oe |
| Answer | Marks | Guidance |
|---|---|---|
| \(y^2 \geq 4y + 5\) | B1 | |
| \(y^2 - 4y - 5 \geq 0\) | M1 | \(y^2 - 4y - 5 = 0\) soi; Correct method to solve quadratic |
| \((y-5)(y+1) \geq 0\) | A1 | |
| \(y \leq -1, y \geq 5\) | M1 | Correct method to solve inequality; -1, 5 (SR If both values obtained from trial and improvement, award B3) |
| \(y \leq -1, y \geq 5\) | A1 | 5 marks total |
## (i)
$1 < 4x - 9 < 5$ | M1 | 2 equations or inequalities both dealing with all 3 terms
$10 < 4x < 14$ | M1 |
$2.5 < x < 3.5$ | A1 | 3 marks; 2.5 and 3.5 seen oe
## (ii)
$y^2 \geq 4y + 5$ | B1 |
$y^2 - 4y - 5 \geq 0$ | M1 | $y^2 - 4y - 5 = 0$ soi; Correct method to solve quadratic
$(y-5)(y+1) \geq 0$ | A1 |
$y \leq -1, y \geq 5$ | M1 | Correct method to solve inequality; -1, 5 (SR If both values obtained from trial and improvement, award B3)
$y \leq -1, y \geq 5$ | A1 | 5 marks total
---Solve the inequalities
\begin{enumerate}[label=(\roman*)]
\item $1 < 4x - 9 < 5$, [3]
\item $y^2 \geq 4y + 5$. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2006 Q5 [8]}}