CAIE P1 2024 June — Question 2 6 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicFunction Transformations
TypeDescribe transformation from graph
DifficultyModerate -0.8 This is a straightforward function transformation question requiring students to identify transformations from a graph (horizontal translation and vertical stretch) and then write the composite function. It involves standard A-level techniques with no problem-solving complexity—students follow a mechanical process of identifying and applying transformations in the correct order.
Spec1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations
\includegraphics{figure_2} The diagram shows two curves. One curve has equation \(y = \sin x\) and the other curve has equation \(y = \text{f}(x)\).
  1. In order to transform the curve \(y = \sin x\) to the curve \(y = \text{f}(x)\), the curve \(y = \sin x\) is first reflected in the \(x\)-axis. Describe fully a sequence of two further transformations which are required. [4]
  2. Find f\((x)\) in terms of \(\sin x\). [2]
Question 2:
AnswerMarks Guidance
2(a){Stretch}{factor 3}{ in y-direction} B2,1,0
 0 
{Translation} 
2
AnswerMarks Guidance
 B2,1,0 Accept shift.
Alternative Method for Question 2(a)
 0 
 
{Translation}  2
 
AnswerMarks Guidance
 3(B2,1,0) 2 out of 3 scores B1.
Accept shift.
AnswerMarks
{Stretch}{factor 3}{ in y-direction}(B2,1,0)
4
AnswerMarks Guidance
2(b) fx {3sinx}{2}
 B1 B1 No marks awarded if extra terms seen.
2
AnswerMarks Guidance
QuestionAnswer Marks 
Question 2:
--- 2(a) ---
2(a) | {Stretch}{factor 3}{ in y-direction} | B2,1,0 | 2 out of 3 scores B1.
 0 
{Translation} 
2
  | B2,1,0 | Accept shift.
Alternative Method for Question 2(a)
 0 
 
{Translation}  2
 
 3 | (B2,1,0) | 2 out of 3 scores B1.
Accept shift.
{Stretch}{factor 3}{ in y-direction} | (B2,1,0)
4
--- 2(b) ---
2(b) |  fx {3sinx}{2}
  | B1 B1 | No marks awarded if extra terms seen.
2
Question | Answer | Marks | Guidance
\includegraphics{figure_2}

The diagram shows two curves. One curve has equation $y = \sin x$ and the other curve has equation $y = \text{f}(x)$.

\begin{enumerate}[label=(\alph*)]
\item In order to transform the curve $y = \sin x$ to the curve $y = \text{f}(x)$, the curve $y = \sin x$ is first reflected in the $x$-axis.

Describe fully a sequence of two further transformations which are required. [4]

\item Find f$(x)$ in terms of $\sin x$. [2]
\end{enumerate}

\hfill \mbox{\textit{CAIE P1 2024 Q2 [6]}}
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Q1 5 Q2 6 Q3 5 Q4 3 Q5 6 Q6 7 Q7 8 Q8 8 Q9 6 Q10 8 Q11 13