CAIE P3 2004 June — Question 1 3 marks

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2004
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrig Graphs & Exact Values
TypeSketch single reciprocal or inverse trig graph
DifficultyModerate -0.8 This is a straightforward recall question requiring knowledge of the secant graph's basic shape, asymptotes at x = π/2 and 3π/2, and key values. It's easier than average as it tests only graph sketching without transformations, intersections, or problem-solving elements.
Spec1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs
1 Sketch the graph of \(y = \sec x\), for \(0 \leqslant x \leqslant 2 \pi\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Correct sketch for \(0 \leq x < \frac{1}{2}\pi\)B1
Correct sketch for \(\frac{1}{2}\pi < x < \frac{3}{2}\pi\) or \(\frac{3}{2}\pi < x \leq 2\pi\)B1
Completely correct sketchB1 Total: 3
[SR: for a graph with \(y = 0\) when \(x = 0, \pi, 2\pi\) but otherwise correct shape, award B1.] 
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct sketch for $0 \leq x < \frac{1}{2}\pi$ | B1 | |
| Correct sketch for $\frac{1}{2}\pi < x < \frac{3}{2}\pi$ or $\frac{3}{2}\pi < x \leq 2\pi$ | B1 | |
| Completely correct sketch | B1 | **Total: 3** |
| [SR: for a graph with $y = 0$ when $x = 0, \pi, 2\pi$ but otherwise correct shape, award B1.] | | |

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1 Sketch the graph of $y = \sec x$, for $0 \leqslant x \leqslant 2 \pi$.

\hfill \mbox{\textit{CAIE P3 2004 Q1 [3]}}
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