Mathematics AA: ALGEBRA-FUNCTIONS - ROOTS 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:7] Consider the function $ f(x)=11\sqrt{x}-2x-11 $, where $ 0 \leq x \leq 20 $. (a) Find the value of (i) $ f(0) $; (ii) $ f(20) $. (b) Find the two roots of $f(x)=0$. (c) Sketch the graph of $y=f(x)$ on the following grid.

[Maximum mark: 19] Consider the function defined by $ f(x) = \frac{x^2 - 14x + 24}{2x + 6} $, where $ x \in \mathbb{R} $, $ x \neq -3 $. (a) State the equation of the vertical asymptote on the graph of $ f $. [1] (b) Find the coordinates of the points where the graph of $ f $ cro…