Mathematics Pure WMA11: Algebra and Functions Topical Past Paper Questions

Figure 1 The curve C, shown in Figure 1, has parametric equations $$ x=\frac{4t-5}{2t+1}\quad 丼 \quad y=2t^{2}-4t+4\quad 丼 \quad t\geqslant0 $$ The point P lies on C and has parameter t = 3 (a) Find the coordinates of $P$. (2) (b) Find $ \frac{dy}{dx} $ in terms of t, writing the…

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…

Figure 3 The curve C, shown in Figure 3, has equation $$ y=\frac{x^{-\frac{1}{4}}}{\sqrt{1+x}\left(\arctan\sqrt{x}\right)} $$ The region R, shown shaded in Figure 3, is bounded by C, the line with equation x = 3, the x-axis and the line with equation $ x = \frac{1}{3} $ The regio…