| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal translation of factored polynomial |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic factorisation, curve sketching of a cubic, and recognition of horizontal translation. All parts are routine: factorising x³-4x requires only taking out common factor x, sketching requires plotting the three roots, and part (c) simply translates the graph right by 1 unit. No problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Roots: \(x,\ (x-2)(x+2)\) | B1, M1 A1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Shape | B1 | |
| Through origin | B1 (dep.) | |
| \(-2\) and \(2\) shown | B1 | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Curve translated \(+1\) parallel to \(x\)-axis | B1 ft | |
| Intercepts \(-1,\ 1\) and \(3\) (B1 ft for one value) | B1 ft B1 | 3 marks |
## Question 7:
Roots: $x,\ (x-2)(x+2)$ | B1, M1 A1 | **3 marks**
**First graph:**
Shape | B1 |
Through origin | B1 (dep.) |
$-2$ and $2$ shown | B1 | **3 marks**
**Second graph (translated):**
Curve translated $+1$ parallel to $x$-axis | B1 ft |
Intercepts $-1,\ 1$ and $3$ (B1 ft for one value) | B1 ft B1 | **3 marks**
**Total: 9 marks**
---7. (a) Factorise completely $x ^ { 3 } - 4 x$. \\
(3) \\
(b) Sketch the curve with equation $y = x ^ { 3 } - 4 x$, showing the coordinates of the points where the curve crosses the $x$-axis. \\
(3) \\
(c) On a separate diagram, sketch the curve with equation \(y = ( x - 1 ) ^ { 3 } - 4 ( x - 1 ) ,\) \\
showing the coordinates of the points where the curve crosses the $x$-axis. \\
(3) \\
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\hfill \mbox{\textit{Edexcel C1 Q7 [9]}}