Further Pure Math 9-1 4PM1: Calculus Topical Past Paper Questions

Figure 3 Figure 3 shows part of the curve C with equation $ y = 3\sqrt{4 - x} $ and part of the line l with equation $ px + qy + r = 0 $ where p and r are integers and q is prime. The curve C cuts the y-axis at the point A The line $l$ is the tangent to $C$ at $A$ (a) Find the va…

A curve C has equation $$ y=\frac{5x-2}{3x+2}\quad x\neq-\frac{2}{3} $$ (a) Find the coordinates of the point where C intersects the (i) x-axis (ii) y-axis (b) Write down an equation of the asymptote to C that is (i) parallel to the x-axis (ii) parallel to the y-axis (c) Sketch C…

Figure 2 Figure 2 shows part of the curve $S$ with equation $y = \left(\cos 3\theta + \sqrt{3} \sin 3\theta\right)^{\frac{1}{2}}$ where $m \leqslant \theta \leqslant n$ The curve S meets the x-axis at the point with coordinates $ (m, 0) $ and at the point with coordinates $ (n, 0…