| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch modulus functions involving quadratic or other non-linear |
| Difficulty | Standard +0.3 This is a straightforward modulus sketch question requiring students to sketch a linear modulus function and a quadratic, then solve an inequality by finding intersection points. While it involves multiple steps (sketching, finding intersections, identifying regions), these are standard FP2 techniques with no novel insight required. The algebra is routine and the question structure is typical of textbook exercises, making it slightly easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| V shape drawn correctly | B1 | V shape |
| Parabola drawn correctly | B1 | Parabola |
| Positions correct | B1 | positions correct |
| Subtotal | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Put \(4 - x^2 = 2x - 3\) or \(4 - x^2 = -2x + 3\) | M1 | |
| Solve \(x^2 + 2x - 7 = 0\), to give \(x = \frac{-2 + \sqrt{4+28}}{2} = -1 + 2\sqrt{2}\) | M1 A1 | |
| Solve \(x^2 - 2x - 1 = 0\), to give \(x = \frac{2 - \sqrt{4+4}}{2} = 1 - \sqrt{2}\) | M1 A1 | |
| So \(1 - \sqrt{2} < x < 2\sqrt{2} - 1\) | B1 | |
| Subtotal | (6) | |
| Total | (9) |
## Question 2:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| V shape drawn correctly | B1 | V shape |
| Parabola drawn correctly | B1 | Parabola |
| Positions correct | B1 | positions correct |
| **Subtotal** | **(3)** | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Put $4 - x^2 = 2x - 3$ or $4 - x^2 = -2x + 3$ | M1 | |
| Solve $x^2 + 2x - 7 = 0$, to give $x = \frac{-2 + \sqrt{4+28}}{2} = -1 + 2\sqrt{2}$ | M1 A1 | |
| Solve $x^2 - 2x - 1 = 0$, to give $x = \frac{2 - \sqrt{4+4}}{2} = 1 - \sqrt{2}$ | M1 A1 | |
| So $1 - \sqrt{2} < x < 2\sqrt{2} - 1$ | B1 | |
| **Subtotal** | **(6)** | |
| **Total** | **(9)** | |
---2. (a) Sketch, on the same axes,
\begin{enumerate}[label=(\roman*)]
\item $y = | 2 x - 3 |$
\item $y = 4 - x ^ { 2 }$\\
(b) Find the set of values of $x$ for which
$$4 - x ^ { 2 } > | 2 x - 3 |$$
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 2013 Q2 [9]}}