 # Timothy Gan ### 2022 NJC Promo Q4

2022 NJC Promo Q4 (a) Find $int{frac{x+1}{4+3{{x}^{2}}}text{d}x}$.  (b) The region bounded by the curve ${{left( y-1 right)}^{2}}=x$ and the line $x=1$ is rotated through $2pi$ radians about the ### 2022 NJC P2 Q5

2022 NJC P2 Q5 The random variable $W$ has the distribution $text{B}left( n,p right)$ and a mode $m$. By considering the inequality $text{P}left( W=m right)ge text{P}left( W=m+1 right)$, show that ### 2022 CJC P2 Q10

2022 CJC P2 Q10 The random variable $X$ has distribution $text{B}left( n,p right)$. It is given that the mean of $X$ is $4.5$ and the variance of $X$ is $3.15$. ### 2022 EJC P2 Q7

2022 EJC P2 Q7 In a carnival lucky dip game, a game master places n consolation tickets, $m$ blank tickets, and one golden ticket into a box. A contestant taking ### 2022 DHS Promo Q6

2022 DHS Promo Q6 (a) Find $int{frac{1-3x}{1+9{{x}^{2}}}},text{d}x$.  (b) Use the substitution $x=2sin theta$, where $theta$ is acute, to find $int{frac{{{left( x-1 right)}^{2}}}{sqrt{4-{{x}^{2}}}}text{d}x}$.  Suggested Video Solutions Suggested ### 2022 NJC Promo Q6

2022 NJC Promo Q6 (i) Use the substitution $x=mtan t$ to find $int{frac{1}{sqrt{{{m}^{2}}+{{x}^{2}}}}text{d}x}$, where $m$ is a positive constant and $0le t<frac{pi }{2}$.  (ii) Find $int{frac{x}{sqrt{{{m}^{2}}+{{x}^{2}}}}text{d}x}$.  (iii) Hence, 