| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal translation of factored polynomial |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing factorisation, curve sketching, and substitution. Part (a) requires basic factorisation (common factor then perfect square), part (b) is routine sketching using the factorised form, and part (c) involves substituting a point and solving a cubic that's already been factorised in part (a). All techniques are standard with no novel insight required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| 13(a) | x3(cid:14)10x2 (cid:14)25x(cid:32) x(x2 (cid:14)10x(cid:14)25) | M1 |
| (cid:32) x(x(cid:14)5)2 | A1 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | A cubic | M1 |
| Answer | Marks |
|---|---|
| A1ft | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| (c) | Curve has been translated a to the left | M1 |
| a = (cid:16)2 | A1ft | 3.2a |
| a = 3 | A1ft | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Scheme | Marks |
Question 13:
--- 13(a) ---
13(a) | x3(cid:14)10x2 (cid:14)25x(cid:32) x(x2 (cid:14)10x(cid:14)25) | M1 | 1.1b
(cid:32) x(x(cid:14)5)2 | A1 | 1.1b
(2)
(b) | A cubic | M1 | 1.1b
with
correct
orientation
Curve
passes
through the
origin (0, 0)
and touches
at ((cid:16)5, 0)
(see note
below for ft)
A1ft | 1.1b
(2)
(c) | Curve has been translated a to the left | M1 | 3.1a
a = (cid:16)2 | A1ft | 3.2a
a = 3 | A1ft | 1.1b
(3)
(7 marks)
Notes:
(a)
M1: Takes out factor x
A1: Correct factorisation – allow x(x + 5)(x + 5)
(b)
M1: Correct shape
A1ft: Curve passes through the origin (0, 0) and touches at ((cid:16)5, 0) – allow follow through
from incorrect factorisation
(c)
M1: May be implied by one of the correct answers for a or by a statement
A1ft: ft from their cubic as long as it meets the x-axis only twice
A1ft: ft from their cubic as long as it meets the x-axis only twice
A cubic
with
correct
orientation
Curve
passes
through the
origin (0, 0)
and touches
at ((cid:16)5, 0)
(see note
below for ft)
Question | Scheme | Marks | AOs\begin{enumerate}[label=(\alph*)]
\item Factorise completely $x^3 + 10x^2 + 25x$
[2]
\item Sketch the curve with equation
$$y = x^3 + 10x^2 + 25x$$
showing the coordinates of the points at which the curve cuts or touches the $x$-axis.
[2]
\end{enumerate}
The point with coordinates $(-3, 0)$ lies on the curve with equation
$$y = (x + a)^3 + 10(x + a)^2 + 25(x + a)$$
where $a$ is a constant.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the two possible values of $a$.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q13 [7]}}