Inequalities

Timothy Gan

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2022 NYJC Promo Q1

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

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2022 TJC Promo Q2

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

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2022 ASRJC Promo Q2

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

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2022 VJC Promo Q2

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

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2022 RI Promo Q2

2022 RI Promo Q2 Without using a calculator, solve the inequality $3x+1le frac{{{x}^{2}}+2}{x}$. [5] Suggested Video and Handwritten Solutions Continue reading

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2022 YIJC Promo Q2

2022 YIJC Promo Q2 (a) Using an algebraic method, solve the inequality $2x-1le frac{5}{x-2}$. [3] (b) Hence, solve (i) $2{{text{e}}^{x}}-1le frac{5}{{{text{e}}^{x}}-2}$, [2] (ii) $2x+1ge frac{5}{x+2}$. [2] Suggested Video Solutions Suggested Handwritten

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2020 HCI C1CT2 Q1

2020 HCI C1CT2 Q1 (i) Without using a calculator, solve the inequality $frac{x}{1-16{{x}^{4}}}le frac{x}{4{{x}^{2}}+1}$. [4] Hence solve the following inequalities, (ii) $frac{left| x right|}{1-16{{x}^{4}}}le frac{left| x right|}{4{{x}^{2}}+1}$, [2] (iii) $frac{sin

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2022 RI P1 Q1

2022 RI P1 Q1 (i) On the same axes, sketch the graphs of $y=frac{x}{x-a}$ and $y=2left| x-a right|+1$, where $a$ is a positive constant. [3] (ii) Hence solve the inequality

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2009 AJC Promo Q4

2009 AJC Promo Q4 Solve the inequality $2<left| 2-ax right|le 4$, where $a$ is a positive constant. Hence, solve the inequality $2<left| 2left( 1+a right)-ax right|le 4$. Suggested Video and Handwritten

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TJC Inequalities Tutorial Q10

TJC Inequalities Tutorial Q10 (i) A wooden artwork is designed to take the form of a right pyramid with square base of sides $2x$m and fixed volume $frac{4}{3}$m$^{3}$. All its

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