| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify/describe sequence of transformations between two given equations |
| Difficulty | Standard +0.3 This is a straightforward C3 transformations question requiring identification of horizontal stretch and vertical translation, sketching an absolute value transformation (reflecting negative portions), and solving simultaneous equations using substitution. All techniques are standard for this module with no novel problem-solving required. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Refer to stretch and translation | M1 | in either order; allow here informal terms |
| State stretch, factor \(\frac{1}{k}\), in \(x\) direction | A1 | or equiv; now with correct terminology |
| State translation in negative \(y\) direction by \(a\) | A1 | 3 |
| [SC: If M0 but one transformation completely correct – B1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Show attempt to reflect negative part in \(x\)-axis | M1 | ignoring curvature |
| Show correct sketch | A1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempt method with \(x = 0\) to find value of \(a\) | M1 | other than (or in addition to) value \(-12\) and nothing else |
| Obtain \(a = 14\) | A1 | |
| Attempt to solve for \(k\) | M1 | using any numerical \(a\) with sound process |
| Obtain \(k = 3\) | A1 | 4 |
# Question 7:
## Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Refer to stretch and translation | M1 | in either order; allow here informal terms |
| State stretch, factor $\frac{1}{k}$, in $x$ direction | A1 | or equiv; now with correct terminology |
| State translation in negative $y$ direction by $a$ | A1 | **3** | or equiv; now with correct terminology |
| [SC: If M0 but one transformation completely correct – B1] | | |
## Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Show attempt to reflect negative part in $x$-axis | M1 | ignoring curvature |
| Show correct sketch | A1 | **2** | with correct curvature, no pronounced 'rounding' at $x$-axis and no obvious maximum point |
## Part (iii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt method with $x = 0$ to find value of $a$ | M1 | other than (or in addition to) value $-12$ and nothing else |
| Obtain $a = 14$ | A1 | |
| Attempt to solve for $k$ | M1 | using any numerical $a$ with sound process |
| Obtain $k = 3$ | A1 | **4** | |
---7\\
\includegraphics[max width=\textwidth, alt={}, center]{c940af95-e291-402a-856c-9090d13163d5-3_419_700_1809_721}
The diagram shows the curve $y = \mathrm { e } ^ { k x } - a$, where $k$ and $a$ are constants.\\
(i) Give details of the pair of transformations which transforms the curve $y = \mathrm { e } ^ { x }$ to the curve $y = \mathrm { e } ^ { k x } - a$.\\
(ii) Sketch the curve $y = \left| \mathrm { e } ^ { k x } - a \right|$.\\
(iii) Given that the curve $y = \left| \mathrm { e } ^ { k x } - a \right|$ passes through the points $( 0,13 )$ and $( \ln 3,13 )$, find the values of $k$ and $a$.
\hfill \mbox{\textit{OCR C3 2009 Q7 [9]}}