2009 NJC P1 Q7
Timothy Gan
27th April 2024
2009 NJC P1 Q7 In a triangle $ABC$, $AB=3$ cm and $AC=2$ cm. If angle $BAC$ is increasing at a constant rate of $0.1$ radians per second, find the rate
SAJC Functions Tutorial Q11
Timothy Gan
27th April 2024
SAJC Functions Tutorial Q11 The functions $text{f}$ and $text{g}$ are defined as follows $text{f}:xmapsto sin x$, $xin mathbb{R}$, $-pi le xle 2pi $.$text{g}:xmapsto cos x$, $xin mathbb{R}$, $0le xle 2pi
2006 MJC Promo
Timothy Gan
26th April 2024
2006 MJC Promo The function $text{f}$ is defined by $text{f}:xmapsto ln left( {{x}^{2}}-x-2 right)$, $c<x<d$, where $c<d<0$. (a) Find the values of $c$ and $d$ such that the range of
2022 HCI J1 BT Q1
Timothy Gan
26th April 2024
2022 HCI J1 BT Q1 A piecewise function is given as $text{f}left( x right)=left{ begin{matrix}3-xtext{ for }1le xle 3, \sqrt{4-{{left( x-5 right)}^{2}}}text{ for }3<xle 5 \end{matrix} right.$ And that $text{f}left(
2010 ACJC CT2
Timothy Gan
25th April 2024
2010 ACJC CT2 (a) Given the functions $text{f}:xmapsto 3{{x}^{3}}-4{{x}^{2}}-1$, $xge 1$,$text{g}:xmapsto {{text{e}}^{2-0.25{{x}^{2}}}}$, $xge -3$. (i) Explain why the functions ${{text{f}}^{-1}}$ and $text{gf}$ exist, [2] (ii) Find the exact value of
2022 TJC Promo Q12
Timothy Gan
25th April 2024
2022 TJC Promo Q12 As part of a structure for a marble race, a plane $p$ is placed at an angle $theta $ to the horizontal ground. The ground is
ACJC Parametric Equations Tutorial 4 Q7
Timothy Gan
16th April 2024
ACJC Parametric Equations Tutorial 4 Q7 The pirate ship Shark is chasing down a ship Arica loaded with treasure. On a rectangular grid in units of kilometres at time $t=0$,
2012 NJC P1 Q2
Timothy Gan
16th April 2024
2012 NJC P1 Q2 Relative to the origin $O$, the position vectors of the points $A$, $B$ and $P$ are $-mathbf{i}-3mathbf{j}+2mathbf{k}$, $5mathbf{i}+2mathbf{k}$ and $left( 1+2lambda right)mathbf{i}+left( lambda -2 right)mathbf{j}+2mathbf{k}$ respectively,
2018 EJC Promo Q5
Timothy Gan
16th April 2024
2018 EJC Promo Q5 (a) Given that $mathbf{u}$ and $mathbf{v}$ are non-zero vectors such that $mathbf{u}times mathbf{v}=left( mathbf{u}-mathbf{v} right)times left( mathbf{u}+mathbf{v} right)$, what can be deduced about $mathbf{u}$ and $mathbf{v}$?
RI Differentiation Tutorial Q11
Timothy Gan
16th April 2024
RI Parametric Equations Tutorial Q11 The parametric equations of a curve are $x=at$, $y=a{{t}^{2}}$ where $a$ is a positive constant. The points $Pleft( ap,,,a{{p}^{2}} right)$ and $Qleft( aq,,,a{{q}^{2}} right)$ lie