| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic inequality solving |
| Difficulty | Moderate -0.8 This is a straightforward multi-part question testing completing the square, identifying vertex coordinates, and solving a quadratic inequality—all standard C1 techniques with no problem-solving required. Each part follows directly from the previous, making it easier than average but not trivial since it requires correct execution of multiple routine procedures. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \((x+4)^2 - 16 + 15\) | B1 | \(a = 4\) |
| \(= (x+4)^2 - 1\) | M1, A1 (3) | \(15 -\) their \(a^2\); cao in required form |
| Answer | Marks | Guidance |
|---|---|---|
| \((-4, -1)\) | B1ft, B1ft (2) | Correct \(x\) coordinate; correct \(y\) coordinate |
| M1, A1 | Correct method to find roots; \(-5, -3\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(x^2 + 8x + 15 > 0\), \((x+5)(x+3) > 0\) | M1 | Correct method to solve quadratic inequality e.g. +ve quadratic graph |
| \(x < -5,\ x > -3\) | A1 (4) | (not wrapped, strict inequalities, no 'and') |
# Question 8:
**(i)**
$(x+4)^2 - 16 + 15$ | B1 | $a = 4$
$= (x+4)^2 - 1$ | M1, A1 (3) | $15 -$ their $a^2$; cao in required form
**(ii)**
$(-4, -1)$ | B1ft, B1ft (2) | Correct $x$ coordinate; correct $y$ coordinate
| M1, A1 | Correct method to find roots; $-5, -3$
**(iii)**
$x^2 + 8x + 15 > 0$, $(x+5)(x+3) > 0$ | M1 | Correct method to solve quadratic inequality e.g. +ve quadratic graph
$x < -5,\ x > -3$ | A1 (4) | (not wrapped, strict inequalities, no 'and')
---8 (i) Express $x ^ { 2 } + 8 x + 15$ in the form $( x + a ) ^ { 2 } - b$.\\
(ii) Hence state the coordinates of the vertex of the curve $y = x ^ { 2 } + 8 x + 15$.\\
(iii) Solve the inequality $x ^ { 2 } + 8 x + 15 > 0$.
\hfill \mbox{\textit{OCR C1 2007 Q8 [9]}}