Mathematics AA: GRAPHS Topical Past Paper Questions

[Maximum mark: 26] The following question explores features of composed trigonometric functions, such as $ \sin(\sin x) $, $ \sin(\sin(\sin x)) $. Suppose $ S_n(x) $ denotes the function $ \sin x $ composed within itself $ n-1 $ times, defined for $ n \geq 1 $, $ n \in \mathbb{Z}…

[Maximum mark: 8] Consider the curve $ y=\frac{x-4}{ax^{2}+bx+c} $, where a, b and c are non-zero constants. The curve has a local minimum point at (2, 1) and a vertical asymptote with equation x = 1. Find the values of a, b and c.

[Maximum mark:20] The function $f$ is defined by $f(x) = \cos^{2}x - 3\sin^{2}x$, $0 \leq x \leq \pi$. (a) Find the roots of the equation $ f(x)=0 $. [5] (b) (i) Find $ f'(x) $. (ii) Hence find the coordinates of the points on the graph of $ y = f(x) $ where $ f'(x) = 0 $. [7] (c…