Applications of Differentiation

2018 CJC Promo Q10 (b) During the performance, a drone is positioned at the center of the circular stage, $O$, and a performer is standing at the circumference of the

2018 EJC Promo Q6 A curve $D$ has parametric equations $x=atheta -asin theta $, $y=a-acos theta $, where $a>0$ and $0<theta <pi $. (i) Show that $frac{text{d}y}{text{d}x}=cot frac{theta }{2}$. [3]

2014 CJC P1 Q2 The diagram shows a sphere with fixed radius $a$ which is inscribed in a cone with radius $r$ and height $h$. Show that ${{r}^{2}}=frac{{{a}^{2}}h}{h-2a}$ and find

SH1 NJC Revision Package Vol 2 Q3 (b) A rectangular piece of paper is $24$ cm long and $12$ cm wide. The upper right-hand corner is folded down to reach

2019 HCI P1 Q11 A container is made up of a cylinder and an inverted right circular cone as shown in the diagram below. The height and the diameter of

2022 HCI P1 Q9 A curve $C$ is given by the equation ${{text{e}}^{{{x}^{2}}}}y=ln {{x}^{2}}$, where $xne 0$. (i) Show that $2xln {{x}^{2}}+{{text{e}}^{{{x}^{2}}}}frac{text{d}y}{text{d}x}=frac{2}{x}$. [2] (ii) Find the equation of the tangent

2022 HCI P1 Q11 (b) Sam tests his kite at an open area, and he wants to fly his kite at a fixed vertical height of $30$m above the horizontal

2019 RI P1 Q2 Two variables $u$ and $v$ are connected by the equation $frac{1}{u}+frac{1}{v}=frac{1}{20}$. Given that $u$ and $v$ both vary with time $t$, find an equation connecting $frac{text{d}u}{text{d}t}$,

2021 TMJC P1 Q6 The folium of Descartes is a curve given by the equation ${{x}^{3}}-9xy+{{y}^{3}}=0$. (i) Find the equation of the tangent to the curve at the point $left(