2022 DHS Promo Q5 A curve $C$ has equation $frac{1-{{x}^{2}}{{y}^{2}}}{3{{y}^{2}}+{{x}^{2}}}=frac{1}{2}$. (a) Show that $frac{text{d}y}{text{d}x}=frac{-x-2x{{y}^{2}}}{yleft( 3+2{{x}^{2}} right)}$. [3] (b) Find the equations of the tangents to the curve that are parallel
2021 ASRJC Promo Q4 A curve $C$ has equation ${{y}^{3}}-2x{{y}^{2}}+3{{x}^{2}}-3=0$ (i) Find $frac{text{d}y}{text{d}x}$ in terms of $x$ and $y$. [2] (ii) Find the equation of the normal to the curve
2022 NJC P2 Q6 Every weekday morning, Jo arrives at the bus stop nearest to her home to catch bus $156$ to Bishan MRT station. The waiting time for bus
2022 MI P2 Q11 In this question you should, where applicable, state clearly all the distributions that you use, together with the values of the appropriate parameters. The time spent
2022 DHS P2 Q10 In this question you should state the parameters of any distributions that you use.A fruit stall vendor sells rock melons and watermelons. The masses (in grams)
2022 ACJC P2 Q11 (a) (i) It is known that the probability of a customer using e-payment at a hawker stall is $0.25$. A group of customers is chosen at
2012 MJC P2 Q12 (a) The random variable $X$ is the number of successes in $n$ independent trials of an experiment in which the probability of a success at a
2015 SAJC P1 Q7 A curve $C$ has parametric equations $x=3-{{cos }^{3}}theta ,text{ }y=4+sin theta ,$ where $0le theta le pi $. (i) Sketch $C$, showing clearly the coordinates of
2021 DHS Promo Q8 (i) Using integration by parts, show that $int{frac{1}{{{x}^{2}}}ln xtext{d}x}=-frac{1}{x}ln x-frac{1}{x}+beta $, where $beta $ is an arbitrary constant. [2] The graph of the curve $C$ with
2019 TJC Promo Q7 A napkin-holder is formed by boring a cylindrical hole, of length $2h$, through a wooden sphere of radius $a$, where $a$ is a fixed constant. The