| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2016 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Complete the square technique |
| Difficulty | Moderate -0.8 This is a straightforward two-part question testing basic completing the square (routine algebraic manipulation) followed by solving a simple quadratic inequality. Both parts are standard textbook exercises requiring only direct application of well-practiced techniques with no problem-solving insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \((x+3)^2 - 7\) | B1B1 [2] | For \(a = 3\), \(b = -7\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(1, -7\) seen | B1 | \(x > 1\) or \(x < -7\); Allow \(x \leqslant -7, x \geqslant 1\) oe |
| \(x > 1\), \(x < -7\) oe | B1 [2] |
## Question 1:
### Part (i):
$(x+3)^2 - 7$ | **B1B1** [2] | For $a = 3$, $b = -7$
### Part (ii):
$1, -7$ seen | **B1** | $x > 1$ or $x < -7$; Allow $x \leqslant -7, x \geqslant 1$ oe
$x > 1$, $x < -7$ oe | **B1** [2] |
---1 (i) Express $x ^ { 2 } + 6 x + 2$ in the form $( x + a ) ^ { 2 } + b$, where $a$ and $b$ are constants.\\
(ii) Hence, or otherwise, find the set of values of $x$ for which $x ^ { 2 } + 6 x + 2 > 9$.
\hfill \mbox{\textit{CAIE P1 2016 Q1 [4]}}