| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Easy -1.2 This question involves two straightforward inequality problems: a linear inequality requiring simple algebraic manipulation, and a quadratic inequality requiring rearrangement and factorization/formula application. Both are routine C1 exercises with no problem-solving insight required, making them easier than average A-level questions. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(3x - 15 \leq 24\) | M1 | Attempt to simplify expression by multiplying out brackets |
| \(3x \leq 39\) | ||
| \(x \leq 13\) | A1 [2] | \(x \leq 13\) |
| or \(x-5 \leq 8\) | M1 | Attempt to simplify expression by dividing through by 3 |
| \(x \leq 13\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(5x^2 > 80\) | M1 | Attempt to rearrange inequality or equation to combine the constant terms |
| \(x^2 > 16\) | \(x > 4\) | |
| \(x > 4\) or \(x < -4\) | B1, A1 [3+2=5] | Fully correct, not wrapped, not 'and'. SR B1 for \(x \geq 4\), \(x \leq -4\) |
## Question 3:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $3x - 15 \leq 24$ | M1 | Attempt to simplify expression by multiplying out brackets |
| $3x \leq 39$ | | |
| $x \leq 13$ | A1 [2] | $x \leq 13$ |
| **or** $x-5 \leq 8$ | M1 | Attempt to simplify expression by dividing through by 3 |
| $x \leq 13$ | A1 | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $5x^2 > 80$ | M1 | Attempt to rearrange inequality or equation to combine the constant terms |
| $x^2 > 16$ | | $x > 4$ |
| $x > 4$ or $x < -4$ | B1, A1 [3+2=5] | Fully correct, not wrapped, not 'and'. **SR** B1 for $x \geq 4$, $x \leq -4$ |
---3 Solve the inequalities\\
(i) $3 ( x - 5 ) \leqslant 24$,\\
(ii) $5 x ^ { 2 } - 2 > 78$.
\hfill \mbox{\textit{OCR C1 2007 Q3 [5]}}