| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Moderate -0.8 This is a straightforward two-part question testing basic inequality manipulation and factorising a simple quadratic. Part (i) requires routine algebraic manipulation, and part (ii) involves factorising y(y+2) and determining sign regions—both are standard C1 exercises requiring recall of techniques rather than problem-solving, making this easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(8 < 3x - 2 < 11\) | M1 | 2 equations or inequalities both dealing with all 3 terms resulting in \(a < kx < b\) |
| \(10 < 3x < 13\) | A1 | 10 and 13 seen |
| \(\frac{10}{3} < x < \frac{13}{3}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(x(x+2) \geq 0\) | M1 | Correct method to solve a quadratic |
| \(0, -2\) | A1 | |
| Correct method to solve inequality | M1 | |
| \(x \geq 0,\ x \leq -2\) | A1 |
## Question 7(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $8 < 3x - 2 < 11$ | M1 | 2 equations or inequalities both dealing with all 3 terms resulting in $a < kx < b$ |
| $10 < 3x < 13$ | A1 | 10 and 13 seen |
| $\frac{10}{3} < x < \frac{13}{3}$ | A1 | |
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## Question 7(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $x(x+2) \geq 0$ | M1 | Correct method to solve a quadratic |
| $0, -2$ | A1 | |
| Correct method to solve inequality | M1 | |
| $x \geq 0,\ x \leq -2$ | A1 | |
---7 Solve the inequalities\\
(i) $8 < 3 x - 2 < 11$,\\
(ii) $y ^ { 2 } + 2 y \geqslant 0$.
\hfill \mbox{\textit{OCR C1 2008 Q7 [7]}}