CAIE P1 2021 June — Question 4 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeRead parameters from graph of transformed trig function
DifficultyModerate -0.8 This is a straightforward graph reading exercise requiring identification of three parameters from a transformed tan graph. Students need to identify the vertical shift (c) from the asymptote positions, the period gives standard tan so a affects amplitude/reflection, and b is the horizontal shift. While it requires understanding of transformations, it's primarily pattern recognition with no calculation or problem-solving, making it easier than average.
Spec1.05f Trigonometric function graphs: symmetries and periodicities1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2

4 \includegraphics[max width=\textwidth, alt={}, center]{80a20f05-61db-42d9-b4ba-53eea2290b2d-05_677_1591_260_278} The diagram shows part of the graph of \(y = a \tan ( x - b ) + c\).
Given that \(0 < b < \pi\), state the values of the constants \(a , b\) and \(c\).

Question 4:
AnswerMarks Guidance
AnswerMarks Guidance
\(a = 2\)B1
\(b = \dfrac{\pi}{4}\)B1 or \(\dfrac{2\pi}{8}\)
\(c = 1\)B1
3
## Question 4:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $a = 2$ | B1 | |
| $b = \dfrac{\pi}{4}$ | B1 | or $\dfrac{2\pi}{8}$ |
| $c = 1$ | B1 | |
| | **3** | |
4\\
\includegraphics[max width=\textwidth, alt={}, center]{80a20f05-61db-42d9-b4ba-53eea2290b2d-05_677_1591_260_278}

The diagram shows part of the graph of $y = a \tan ( x - b ) + c$.\\
Given that $0 < b < \pi$, state the values of the constants $a , b$ and $c$.\\

\hfill \mbox{\textit{CAIE P1 2021 Q4 [3]}}