Mathematics AA: DIFFERENTIATION 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:16] In this question all values of x and t are in radians. Consider the function $ f(x) = 6\cos(\pi x) $. (a) (i) Write down the amplitude of the graph of $f$. (ii) Find the period of $f$. [3] Consider a second function $ g(x) = -8 \sin(\pi x) $. The sum of these fu…

[Maximum mark: 14] The solid shown in the following diagram is comprised of a cylinder and two hemispheres. The cylinder has height h cm and radius x cm. The hemispheres fit exactly onto either end of the cylinder. The volume of the cylinder is $45\ cm^{3}$. (a) Show that the tot…