Maths Core WMA01/WMA02: DIFFERENTIATION Topical Past Paper Questions

A scientist is studying a population of lizards on an island. The number of lizards, N, in the population, t years after the start of the study, is modelled by the equation $$ N=\frac{1800}{2+3\mathrm{e}^{-0.2t}}\qquad t\in\mathbb{R},t\geqslant0 $$ Use the model to answer parts (…

Figure 2 Figure 2 shows a sketch of part of the curve y = f(x), where $$ \mathrm{f}(x)=\frac{6x+2}{3x^{2}+5},\qquad x\in\mathbb{R} $$ (a) Find f'(x), writing your answer as a single fraction in its simplest form. (3) The curve has two turning points, a maximum at point A and a mi…

Figure 3 The curve C shown in Figure 3 has parametric equations $$ x=3\cos t,\qquad y=9\sin2t,\qquad0\leqslant t\leqslant2\pi $$ The curve C meets the x-axis at the origin and at the points A and B, as shown in Figure 3. (a) Write down the coordinates of A and B. (2) (b) Find the…