Timothy Gan

2023 DHS Promo Q7

2023 DHS Promo Q7 (a) It is given that $sumlimits_{r=1}^{n}{{{r}^{2}}=frac{1}{6}nleft( n+1 right)left( 2n+1 right)}$. (i) Find $sumlimits_{r=1}^{n}{left( {{2}^{r+1}}+3r-{{r}^{2}} right)}$ in the form $Aleft( {{2}^{n}}-1 right)+text{f}left( n right)$, where $A$ is

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2021 TMJC P1 Q9

2021 TMJC P1 Q9 The line $l$ passes through the point $A$ with coordinates $left( 1,-2,3 right)$ and is parallel to the vector $left( begin{matrix} 4 \ 0 \ -1

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2022 MI P2 Q4

2022 MI P2 Q4 The equations of the plane ${{pi }_{1}}$ and the line $l$ are $mathbf{r}cdot left( begin{matrix} 1 \ 0 \ 1 \ end{matrix} right)=1$ and $frac{x}{2}=y+1$, $z=2$

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2021 YIJC P2 Q4

2021 YIJC P2 Q4 The line $l$ has equation $frac{x+1}{2}=frac{y-a}{b}=frac{z-4}{3}$. The plane$~p$ has equation $x+y-z-11=0$. (i) If $l$ and $~p$ do not intersect, what can be said about the values

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2021 YIJC P2 Q3

2021 YIJC P2 Q3 Do not use a calculator in answering this question. (a) The complex number $z$ is given by $z=frac{{{left( 1-mathbf{i} right)}^{3}}}{sqrt{2}{{left( a+mathbf{i} right)}^{2}}}$, where $a<0$. (i) Given

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2021 NYJC P1 Q9

2021 NYJC P1 Q9 The complex numbers $z$ and $w$ where $wne 0$ satisfy the relation $2z=left| w right|+1$. (i) It is given that $a$ is a real number and

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2021 ASRJC P2 Q1

2021 ASRJC P2 Q1 The complex numbers $z$ and $w$ have moduli $k$ and $3{{k}^{2}}$ respectively and arguments $alpha $ and $4alpha $ respectively, where $k$ is a positive constant

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2021 ACJC P1 Q9

2021 ACJC P1 Q9 (a) (i) Show that the cubic polynomial ${{x}^{3}}+p{{x}^{2}}+{{p}^{2}}x+q$ can be reduced to ${{y}^{3}}+left( frac{2{{p}^{2}}}{3} right)y+alpha $ by the substitution $x=y-frac{p}{3}$, where $alpha $ is to be

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2021 SAJC P1 Q7

2021 SAJC P1 Q7 (a) It is given that $z=1+sqrt{3},mathbf{i}$ is a root of the equation $3{{z}^{3}}+a{{z}^{2}}+bz-8=0$, where $a$ and $b$ are real numbers. Find the exact values of $a$

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2021 ASRJC P1 Q1

2021 ASRJC P1 Q1 Do not use a calculator in answering this question. It is given that $text{f}left( z right)={{z}^{4}}+2sqrt{2}{{z}^{3}}+{{z}^{2}}+8sqrt{2}z-12$. One of the roots of the equation $text{f}left( z right)=0$

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