| Exam Board | Edexcel |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Solve quadratic inequality |
| Difficulty | Moderate -0.8 This is a straightforward P1 question combining basic sketching (linear and quadratic functions), shading regions, and solving a quadratic inequality. Part (a) requires routine intercept finding, part (b) is simple shading, and part (c) involves factorising and reading from the graph or using standard inequality methods. All techniques are standard with no problem-solving insight required, making it easier than average. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02i Represent inequalities: graphically on coordinate plane1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks |
|---|---|
| 5(a) | Straight line, positive gradient positive |
| Answer | Marks |
|---|---|
| with intersection shown at (cid:11)−2(cid:15) (cid:19)(cid:12) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | Finite region between line and curve shaded | B1 |
| Answer | Marks |
|---|---|
| (c) | (x2 – x − (cid:25) (cid:31) x + 2 ) (cid:159) x2 – 2x − (cid:27) (cid:31) (cid:19) |
| (x − (cid:23)(cid:12)(cid:11) x + 2) < 0 (cid:159) Line and curve intersect at x = 4 and x (cid:32) −2 | M1 A1 |
| −2 (cid:31) x < 4 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Scheme | Marks |
Question 5:
--- 5(a) ---
5(a) | Straight line, positive gradient positive
intercept
Curve ‘U’ shape anywhere
Correct y intercepts 2, (cid:16)6
Correct x-intercepts of (cid:16)2 and 3
with intersection shown at (cid:11)−2(cid:15) (cid:19)(cid:12) | B1
B1
B1
B1
(4)
(b) | Finite region between line and curve shaded | B1
(1)
(c) | (x2 – x − (cid:25) (cid:31) x + 2 ) (cid:159) x2 – 2x − (cid:27) (cid:31) (cid:19)
(x − (cid:23)(cid:12)(cid:11) x + 2) < 0 (cid:159) Line and curve intersect at x = 4 and x (cid:32) −2 | M1 A1
−2 (cid:31) x < 4 | A1
(3)
(8 marks)
Notes:
(a) As scheme.
(b) As scheme.
(c)
M1: For a valid attempt to solve the equation x2 – 2x − (cid:27) = 0
A1: For x = 4 and x(cid:32)(cid:16)2
A1: −2 (cid:31) x < 4
x
Question | Scheme | Marks\begin{enumerate}[label=(\alph*)]
\item On the same axes, sketch the graphs of $y = x + 2$ and $y = x^2 - x - 6$ showing the coordinates of all points at which each graph crosses the coordinate axes. [4]
\item On your sketch, show, by shading, the region $R$ defined by the inequalities
$$y < x + 2 \text{ and } y > x^2 - x - 6$$ [1]
\item Hence, or otherwise, find the set of values of $x$ for which $x^2 - 2x - 8 < 0$ [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel P1 2018 Q5 [8]}}