These Ten-Year-Series (TYS) worked solutions with video explanations for 2015 A Level H2 Mathematics Paper 2 Question 3 are suggested by Mr Gan. For any comments or suggestions please contact
2021 NYJC P1 Q5 (b) The function $text{g}$ is given by $text{g}:xmapsto ln left( frac{{{e}^{x}}+5}{{{e}^{x}}-1} right)$, for $xin mathbb{R}$, $x>0$. (i) Find ${{text{g}}^{-1}}left( x right)$ and states its domain. The
2020 ACJC Promo Q7 The functions $text{f}$ and $text{g}$ are defined as follows: $text{f}:xmapsto 7{{left( x-a right)}^{2}}-1$, $xin mathbb{R}$, $x<3$ $text{g}:xmapsto 1+b-{{e}^{-x}}$, $xge 0$, where $a$ and $b$ are real
NYJC Basic Graphing Techniques Assignment Q2 The curve $y=text{f}left( x right)$ for $0le x<3$ is shown below. It is given that $text{f}$ is an odd function, $text{f}left( -x right)=-text{f}left( x
2022 NJC Promo Q8 The function $text{f}$ is defined by $text{f}left( x right)=left{ begin{matrix}x-4,,,,,text{for},,,,,xle 1 \cos x,,,,,text{for},,,,,1<xle pi \end{matrix} right.$ (i) Show that $text{f}$ has an inverse. [3] (ii) Find
2021 NJC Promo Q5 It is given that $text{f}left( x right)=left{ begin{matrix}{{left( x-2 right)}^{2}},0le x<2 \2x-4,2le xle 4 \end{matrix} right.$ and that $text{f}left( x right)=text{f}left( x+4 right)$ for all real
2021 ACJC Promo Q7 The functions $text{f}$ and $text{g}$ are defined by $text{f}:xmapsto frac{1}{left| 1-{{x}^{2}} right|}$, $xin mathbb{R}$, $-2le x<-1$,$text{g}:xmapsto -{{left( x-2 right)}^{2}}+k$, $xin mathbb{R}$, $xge 0$ where $k$ is
2021 NYJC Promo Q4 The function $text{f}$ is defined by $text{f}left( x right)=frac{1}{{{x}^{2}}+1}$, $xin mathbb{R}$, $xge k$. (i) State the minimum value of $k$ for which the function ${{text{f}}^{-1}}$ exists.
2022 YIJC Promo Q9 The function $text{f}$ is defined by $text{f}:xmapsto {{x}^{2}}-4x-5$, for $xin mathbb{R}$, $xle 2$. (a) Find ${{text{f}}^{-1}}left( x right)$ and state the domain of ${{text{f}}^{-1}}$. [3] (b)
2022 HCI P1 Q6 The function $text{f}$ is defined by $text{f}:xmapsto left{ begin{matrix}5+ln x,,,,,,,text{for},,0<x<1, \-{{x}^{2}}+6x,,,,text{for }1le xle a, \end{matrix} right.$ where $a$ is a constant. (i) Given that $text{f}$ has