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2010 JJC P1 Q10 (i) By sketching the graphs of $y=3{{text{e}}^{x}}$ and $y=x+3$ or otherwise, solve the inequality $3{{text{e}}^{x}}>x+3$. [3] Hence find $int_{-2}^{2}{left| 3{{text{e}}^{x}}-x-3 right|text{d}x}$ , giving your answer in
2023 ASRJC Promo Q9 (i) State a sequence of three transformations which transform the graph with equation ${{x}^{2}}+{{y}^{2}}=1$ to the graph with equation $frac{{{(x+1)}^{2}}}{4}+frac{{{y}^{2}}}{9}=1$. [3] (ii) Sketch, on the same
2023 RI Promo Q2 Do not use a calculator in answering this question. Solve the inequality ${{x}^{2}}+6x+5le frac{x+5}{3x+1}$. [4] Hence solve (a) ${{x}^{4}}+6{{x}^{2}}+5le frac{{{x}^{2}}+5}{3{{x}^{2}}+1}$, [2] (b) ${{left( ln x right)}^{2}}+6ln
2023 ACJC Promo Q2 (i) Sketch the graph of $y=left| b+frac{a}{x+b} right|$, where $0<a<b$, stating the equations of any asymptotes and the coordinates of the points that cross the axes.
2023 VJC Promo Q3 Given that $ain mathbb{R}$ and $a>1$, use an algebraic method to solve the inequality $frac{ax-a+2}{left( x-a right)left( 1-x right)}le 1$. [5] Hence find the set of
2023 DHS Promo Q2 Given that $x<0$, solve the inequality $frac{2}{x}<left| x right|-a$, where $a$ is constant such that $a>3$. [4] Suggested Video and Handwritten Solutions Written by Did You Enjoy
2022 NYJC Promo Q1 (i) Solve the inequality $ln left( x+1 right)le frac{4}{x}$. [3] (ii) Hence solve the inequality $cos x+1le {{text{e}}^{4sec x}}$ for $0<x<pi $. [3] Suggested Video Solutions
2022 TJC Promo Q2 Solve the inequality $frac{x-2k}{{{x}^{2}}-k}le 0$ in terms of $k$ given that (i) $k$ is a real constant greater than $1$. [3] (ii) $k$ is a negative
2022 ASRJC Promo Q2 Using an algebraic method, solve $frac{{{x}^{2}}+2x+3}{{{x}^{2}}+x-2}ge 1$. [4] Suggested Video and Handwritten Solutions Continue reading
2022 VJC Promo Q2 (i) Show that ${{x}^{2}}+2x+2$ is always positive for all real values of $x$. [1] (ii) Without using a calculator, solve the inequality $frac{x-12}{{{x}^{2}}+3x-10}>1$. [3] Suggested Video