Challenging +1.2 This requires recognizing that sinh ΞΈ + cosh ΞΈ = e^ΞΈ (a standard hyperbolic identity), then sketching an exponential spiral in polar coordinates. While the identity recall and polar sketching are A-level appropriate, this is a Further Maths topic with a straightforward application of a known result, making it moderately above average difficulty but not requiring deep problem-solving.
Completes a fully correct sketch with the spiral beginning and
Answer
Marks
Guidance
ending on the initial line (not at the pole.)
1.1b
A1
Total
3
Q
Marking instructions
AO
Question 11:
11 | Selects an approach to sketch the polar graph of
ππ = sinhππ+
e.g. by evaluating for at least 3 values of PI
coshππ
or
ππ ππ
by finding .
ππ
sinhππ+coshππ = e | 3.1a | M1 | ππ
sinhππ+coshππ = e
Draws a spiral. | 1.1a | M1
Completes a fully correct sketch with the spiral beginning and
ending on the initial line (not at the pole.) | 1.1b | A1
Total | 3
Q | Marking instructions | AO | Marks | Typical solution
Sketch the polar graph of
$$r = \sinh \theta + \cosh \theta$$
for $0 \leq \theta \leq 2\pi$
\includegraphics{figure_11}
[3 marks]
\hfill \mbox{\textit{AQA Further AS Paper 1 2020 Q11 [3]}}