Mathematics Pure WMA11: Differentiation Topical Past Paper Questions

Figure 2 The curve C, shown in Figure 2 has equation $$ x^{2}\tan y+\frac{32y^{2}}{\pi^{2}}=11\quad0 (2) (b) Use algebraic differentiation to find the exact value of $ \frac{dy}{dx} $ at P. (5) (c) Hence, showing your working, find the value of (the gradient of the tangent to C a…

The curve C has parametric equations $$ x=\frac{3+2t}{1-t}\quad 佔 \quad y=1-t^{2}\quad 佔 \quad t\neq1 $$ The point $P$, where $t=2$, lies on $C$. (a) Use parametric differentiation to find the equation of the normal to C at P. Give your answer in the form $ ax + by + c = 0 $ wher…

The current, x amps, at time t seconds after a switch is closed in a particular electric circuit is modelled by the equation $$ \frac{\mathrm{d}x}{\mathrm{d}t}=k-3x $$ where k is a constant. Initially there is zero current in the circuit. (a) Solve the differential equation to fi…