| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Single transformation application |
| Difficulty | Easy -1.2 This is a straightforward C1 transformations question requiring basic recall: sketching a simple cubic, applying a horizontal translation (standard textbook exercise), and identifying a vertical stretch. All three parts are routine with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| [Negative cubic through \((0,0)\)] | M1 | Negative cubic through \((0,0)\) (may have max and min); Must be continuous. Allow slight curve towards or away from \(y\)-axis at one end, but not both. |
| [Correct shape with rotational symmetry] | A1 | 2 marks; Must have reasonable rotational symmetry. Cannot be a finite "plot". Allow negative gradient at origin. Correct curvature at both ends. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(y = -(x-3)^3\) | M1 | \(\pm(x-3)^3\) seen |
| or \(y = (3-x)^3\) | A1 | 2 marks; Must have "\(y =\)" for A mark; SR \(y = -(x-3)^2\) B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Stretch | B1 | Allow "factor" for "scale factor" |
| scale factor \(5\) parallel to \(y\)-axis | B1 | 2 marks (total 6); o.e. e.g. scale factor \(\frac{1}{\sqrt[3]{5}}\) parallel to \(x\)-axis; For "parallel to the \(y\)-axis" allow "vertically", "in the \(y\) direction". Do not accept "in/on/across/up/along the \(y\) axis" |
# Question 5:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| [Negative cubic through $(0,0)$] | M1 | Negative cubic through $(0,0)$ (may have max and min); Must be continuous. Allow slight curve towards or away from $y$-axis at one end, but not both. |
| [Correct shape with rotational symmetry] | A1 | **2 marks**; Must have reasonable rotational symmetry. Cannot be a finite "plot". Allow negative gradient at origin. Correct curvature at both ends. |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $y = -(x-3)^3$ | M1 | $\pm(x-3)^3$ seen |
| or $y = (3-x)^3$ | A1 | **2 marks**; Must have "$y =$" for A mark; **SR** $y = -(x-3)^2$ **B1** |
## Part (iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Stretch | B1 | Allow "factor" for "scale factor" |
| scale factor $5$ parallel to $y$-axis | B1 | **2 marks** (total **6**); o.e. e.g. scale factor $\frac{1}{\sqrt[3]{5}}$ parallel to $x$-axis; For "parallel to the $y$-axis" allow "vertically", "in the $y$ direction". **Do not accept** "in/on/across/up/along the $y$ axis" |
---5 (i) Sketch the curve $y = - x ^ { 3 }$.\\
(ii) The curve $y = - x ^ { 3 }$ is translated by 3 units in the positive $x$-direction. Find the equation of the curve after it has been translated.\\
(iii) Describe a transformation that transforms the curve $y = - x ^ { 3 }$ to the curve $y = - 5 x ^ { 3 }$.
\hfill \mbox{\textit{OCR C1 2011 Q5 [6]}}