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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 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(
In the ever-evolving landscape of education, where academic success is often measured by performance in exams, the need for effective test preparation has never been more critical. Students face a
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
2018 PJC BT2 P2 Q8 Tomatoes are sold in boxes of $16$. On average, $15%$ of them are damaged. (i) State, in context, two assumptions needed for the number of
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
2017 ACJC P2 Q6 Alex and his friend stand randomly in a queue with $3$ other people. The random variable $X$ is the number of people standing between Alex and
2020 YIJC P2 Q8 A manufacturing company produces surgical masks. The surgical masks are randomly packed into boxes of $50$. On average, $15%$ of the surgical masks are defective. The
2017 HCI P2 Q6 A biased tetrahedral ($4$-sided) die has its faces numbered ‘$-1$’, ‘$0$’, ‘$2$’ and ‘$3$’. It is thrown onto a table and the random variable $X$ denotes
These Ten-Year-Series (TYS) worked solutions with video explanations for 1995 A Level H2 Mathematics Paper 2 Question Q6 are suggested by Mr Gan. For any comments or suggestions please contact