CAIE P1 2020 March — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFunction Transformations
TypeAlgebraic to algebraic transformation description
DifficultyEasy -1.2 This is a straightforward recall question on function transformations requiring students to identify two standard transformations: a horizontal stretch by scale factor 2 (from the 1/2x) and a vertical translation up by 1 unit. It tests basic knowledge with no problem-solving or novel insight required, making it easier than average.
Spec1.02w Graph transformations: simple transformations of f(x)
2 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 1 + \mathrm { f } \left( \frac { 1 } { 2 } x \right)\).
Describe fully the two single transformations which have been combined to give the resulting transformation.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
[Stretch] [factor 2, \(x\) direction (or \(y\)-axis invariant)]\*B1, DB1
[Translation or Shift] [1 unit in \(y\) direction] or [Translation/Shift] \(\begin{pmatrix} 0 \\ 1 \end{pmatrix}\)B1B1 Accept transformations in either order. Allow \((0, 1)\) for the vector
Total: 4 
**Question 2:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| [Stretch] [factor 2, $x$ direction (or $y$-axis invariant)] | \*B1, DB1 | |
| [Translation or Shift] [1 unit in $y$ direction] **or** [Translation/Shift] $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ | B1B1 | Accept transformations in either order. Allow $(0, 1)$ for the vector |
| **Total: 4** | | |
2 The graph of $y = \mathrm { f } ( x )$ is transformed to the graph of $y = 1 + \mathrm { f } \left( \frac { 1 } { 2 } x \right)$.\\
Describe fully the two single transformations which have been combined to give the resulting transformation.\\

\hfill \mbox{\textit{CAIE P1 2020 Q2 [4]}}
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