| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Expand from factored form |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic algebraic expansion and standard curve sketching from factored form. The expansion is routine, and the sketch only requires identifying roots (already given in factored form) and the y-intercept, with no calculus needed. Simpler than average A-level questions. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((x^2 - 4x + 4)(x+1)\) | M1 | Attempt to multiply a 3 term quadratic by a linear factor, or expand all 3 brackets with an \(x^3\) term |
| Expansion with at most 1 incorrect term | A1 | |
| \(= x^3 - 3x^2 + 4\) | A1 | 3 Correct simplified answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| +ve cubic with 2 or 3 roots | B1 | |
| Intercept of curve labelled \((0, 4)\) or indicated on \(y\)-axis | B1 | |
| \((-1, 0)\) and turning point at \((2, 0)\) labelled or indicated on \(x\)-axis and no other \(x\) intercepts | B1 | 3 |
# Question 4:
## Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(x^2 - 4x + 4)(x+1)$ | M1 | Attempt to multiply a 3 term quadratic by a linear factor, or expand all 3 brackets with an $x^3$ term |
| Expansion with at most 1 incorrect term | A1 | |
| $= x^3 - 3x^2 + 4$ | A1 | **3** Correct simplified answer |
## Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| +ve cubic with 2 or 3 roots | B1 | |
| Intercept of curve labelled $(0, 4)$ or indicated on $y$-axis | B1 | |
| $(-1, 0)$ and turning point at $(2, 0)$ labelled or indicated on $x$-axis and no other $x$ intercepts | B1 | **3** |
---4 (i) Expand $( x - 2 ) ^ { 2 } ( x + 1 )$, simplifying your answer.\\
(ii) Sketch the curve $y = ( x - 2 ) ^ { 2 } ( x + 1 )$, indicating the coordinates of all intercepts with the axes.
\hfill \mbox{\textit{OCR C1 2010 Q4 [6]}}