H2 Math Student Only

2023 TJC P1 Q10 Water is being pumped from reservoir into a filtration device at a constant rate of $8$ gallons per hour. The filtration device processes the water and

2015 NJC P1 Q10 The population (in thousands) of fish present in a lake at time $t$ years is denoted by $x$. It is found that the growth rate of

2013 MJC P1 Q7 A tank contains $2$ m $^{3}$of water initially. Water flows into the tank at a constant rate of $4$ m$^{3}$s$^{-1}$and flows out at a rate which

2013 JJC P2 Q2 A researcher is investigating the spread of a certain disease in a town with a population of $3000$ people. The researcher suggests that $I$, the number

2023 RI P1 Q6 Alice bakes a large pie and removes it from the oven at $1$pm. The temperature reading of the pie using a food thermometer is $200{}^circ text{C}$

2023 EJC P2 Q3 The variables $x$ and $y$ are related by the differential equation $pi frac{text{d}y}{text{d}x}+yleft( 3-pi tan x right)=0$. (a) Using the substitution $y=zsec x$, show that $frac{text{d}z}{text{d}x}=frac{-3x}{pi

2023 ACJC P1 Q5 (i) Find $frac{text{d}}{text{d}x}{{text{e}}^{-{{x}^{2}}}}$. Hence find $int{{{x}^{3}}{{text{e}}^{-{{x}^{2}}}}}text{d}x$. [3] (ii) By using the substitution $z={{text{e}}^{-{{x}^{2}}}}y$, find the general solution of $frac{text{d}y}{text{d}x}-2xy={{x}^{3}}$, expressing $y$ in teams of $x$. [4]

2023 YIJC P1 Q7 (a) (i) It is given that $frac{text{d}y}{text{d}x}={{left( 4x-y+2 right)}^{2}}$. Using the substitution $v=4x-y$, show that the differential equation can be transformed to $frac{text{d}v}{text{d}x}=text{f}left( v right)$, where