Timothy Gan

2022 ASRJC P1 Q11

2022 ASRJC P1 Q11 The cylindrical tank in a research laboratory has a cross-sectional area of $4$ m$^{2}$. To cool the tank, water is pumped in and out of the

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2022 ACJC P1 Q11

2022 ACJC P1 Q11 With the proliferation of online social network, sociologists recognised a phenomenon called social diffusion which is the spreading of a piece of information through the population.

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2022 VJC P1 Q11

2022 VJC P1 Q11 A tank contains $500$ litres of water in which $100$ g of a poisonous chemical called Prokrastenate is dissolved. A solution containing $0.1$ g of Prokrastenate

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2022 DHS P1 Q10

2022 DHS P1 Q10 An object is moving from rest in a gas chamber and $t$ seconds later, its velocity $v$ metres per second satisfies the differential equation $frac{text{d}v}{text{d}t}=5-0.2{{v}^{2}}$ It

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2023 CJC P2 Q3

2023 CJC P2 Q3 Following the popularity of the action role-playing game, Ginseng Impact, three years ago, developers have developed a strategy game, Ginseng Impactful. The number of people who

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2023 NJC P1 Q3

2023 NJC P1 Q3 It is given that $y={{left( 1+{{tan }^{-1}}x right)}^{2}}$. (a) Prove that ${{left( 1+{{x}^{2}} right)}^{2}}frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}+2xleft( 1+{{x}^{2}} right)frac{text{d}y}{text{d}x}=2$. [3] (b) Obtain an equation relating $frac{{{text{d}}^{3}}y}{text{d}{{x}^{3}}}$, $frac{{{text{d}}^{2}}y}{text{d}{{x}^{2}}}$ and $frac{text{d}y}{text{d}x}$.

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