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ACJC Complex Numbers Tutorial Q13 On an Argand diagram, the points $P$ and $Q$ represent the complex numbers $p$ and $q$ respectively where $p=cos theta +mathbf{i}sin theta $, $0<theta <frac{pi
2012 NJC P2 Q7 [Modified] (a) Find the number of ways in which the letters of the word NATIONAL can be arranged if (i) there are no restrictions, [1] (ii)
2008 JJC P2 Q9 In a game played by two people $A$ and $B$, each player is given three cards with three different animal pictures printed on them. The players
2021 SAJC Promo Q5 (a) (i) Show that $frac{text{d}}{text{d}x}left( {{3}^{2x}} right)={{9}^{x}}ln 9$. (ii) Hence, differentiate ${{tan }^{-1}}left( {{3}^{2x}} right)$, $x>0$ with respect to $x$. (b) Given that ${{y}^{2y}}={{e}^{3x+2e}}$, where $y>{{e}^{-1}}$,
2024 EJC Permutation And Combination Tutorial Tutorial Q7 A six digit number is to be formed from the digits $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$ and $9$. For
2015 VJC P2 Q7 A game is to be played between two players, $A$ and $B$. A bag contains $5$ balls each with $A$’s name and $8$ balls each with
2009 SAJC P2 Q3 [Modified] Given that ${{u}_{r}}=frac{1}{{{r}^{3}}}$, (i) Show that ${{u}_{r-1}}-{{u}_{r+1}}=frac{6{{r}^{2}}+2}{{{left( {{r}^{2}}-1 right)}^{3}}}$. (ii) Hence find $sumlimits_{r=2}^{n}{frac{3{{r}^{2}}+1}{{{left( {{r}^{2}}-1 right)}^{3}}}}$ in terms of $n$. (iii) Use your answer to part
2016 NJC P2 Q1 (a) Kenny took a loan of $$9600$ from a friend, and arranged to pay his loan fully in a period of exactly $48$ months. To fulfil
2016 JJC P2 Q6 The table below shows the number of male and female students studying Chemistry, Physics and Biology at a private school. One of the students is chosen
2017 IJC BT2 Q7 The discrete random variable $X$ has probability function $text{P}left( X=x right)=left{ begin{matrix}kleft( frac{5}{2}-x right),,,,x=0,2, \kleft( x-2 right),,,,,,,,,,,x=3, \0,text{otherwise,} \end{matrix} right.$ where $k$ is a positive constant.