2022 NJC Promo Q4 (a) Find $int{frac{x+1}{4+3{{x}^{2}}}text{d}x}$. [4] (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 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 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 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 MI P2 Q7 A bag contains three red balls, $n-1$ blue balls and $n$ white ball, where $nge 3$. The balls are identical except for their colour. Two balls
2022 DHS Promo Q6 (a) Find $int{frac{1-3x}{1+9{{x}^{2}}}},text{d}x$. [3] (b) Use the substitution $x=2sin theta $, where $theta $ is acute, to find $int{frac{{{left( x-1 right)}^{2}}}{sqrt{4-{{x}^{2}}}}text{d}x}$. [5] Suggested Video Solutions Suggested
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 $0le t<frac{pi }{2}$. [4] (ii) Find $int{frac{x}{sqrt{{{m}^{2}}+{{x}^{2}}}}text{d}x}$. [2] (iii) Hence,
2018 TJC Promo Q5 (b) Without using a graphing calculator, show that $int_{0}^{1}{frac{{{x}^{3}}}{1+{{x}^{2}}}}text{ d}x=kleft( 1-ln 2 right)$, where $k$ is a real number to be determined. [3] Hence find $int_{0}^{1}{{{x}^{2}}{{tan
2022 HCI Promo Q8 (a) Find $int{3t{{tan }^{-1}}left( 3t right)text{d}t}$. [4] (b) Using the substitution $u={{x}^{2}}+1$, show that $int_{0}^{sqrt{7}}{{{x}^{3}}{{left( {{x}^{2}}+1 right)}^{frac{1}{3}}}text{d}x}$ can be expressed as $frac{1}{2}int_{a}^{b}{{{u}^{frac{4}{3}}}-{{u}^{frac{1}{3}}}}text{ d}u$, where $a$ and
2022 EJC Promo Q6 (a) Find $int{x{{text{e}}^{3{{x}^{2}}+1}}}text{d}x$. [1] (b) Find $int{{{sin }^{2}}left( 5x right)},text{d}x$. [3] (c) Find $int{frac{x}{4{{x}^{2}}-4x+17}},text{d}x$. [5] Suggested Video Solutions Suggested Handwritten Solutions (a) (b) (c) (a) (b)