# Inequalities

###### 5 Essential Questions

Here is where we provide free online Revision materials for your H2 Math. We have compiled 5 essential questions from each topic for you and broken down the core concepts with video explanations. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses.

• Q1
• Q2
• Q3
• Q4
• Q5
##### 2019 NJC P1 Q2

Without using a calculator

(i)

Solve the inequality $\frac{2{{x}^{2}}+5x+9}{x-7}\le x-4$.

[4]

(i) Solve the inequality $\frac{2{{x}^{2}}+5x+9}{x-7}\le x-4$.

[4]

(ii)

Hence, solve the inequality $\frac{2+5{{e}^{x}}+9{{e}^{2x}}}{7{{e}^{x}}-1}\ge 4{{e}^{x}}-1$.

[2]

(ii) Hence, solve the inequality $\frac{2+5{{e}^{x}}+9{{e}^{2x}}}{7{{e}^{x}}-1}\ge 4{{e}^{x}}-1$.

[2]

• (i)
• (ii)
• (i)
• (ii)

##### 2013 CJC Promo Q8

(a)

(i)

Without using a calculator, solve the inequality $\frac{x+6}{{{x}^{2}}-3x-4}\le \frac{1}{4-x}$.

[3]

(i) Without using a calculator, solve the inequality $\frac{x+6}{{{x}^{2}}-3x-4}\le \frac{1}{4-x}$.

[3]

(ii)

Hence, deduce the range of values of $x$ that satisfies

$\frac{\left| x \right|+6}{{{x}^{2}}-3\left| x \right|-4}\le \frac{1}{4-\left| x \right|}$.

[2]

(ii) Hence, deduce the range of values of $x$ that satisfies

$\frac{\left| x \right|+6}{{{x}^{2}}-3\left| x \right|-4}\le \frac{1}{4-\left| x \right|}$.

[2]

(b)

Solve the inequality $\ln \left( x+6 \right)\le -\frac{x}{3}$.

[3]

(b) Solve the inequality $\ln \left( x+6 \right)\le -\frac{x}{3}$.

[3]

• (a) (i)
• (a)(ii)
• (b)
• (a) (i)
• (a) (ii)
• (b)

##### 2020 CJC Promo Q1

Without using a calculator, solve

$x<\frac{3}{x-2}$.

[3]

Hence solve

${{\text{e}}^{-x}}<\frac{3}{{{\text{e}}^{-x}}-2}$.

[2]

##### 2019 TJC Promo Q1

(i)

Sketch the curve with equation $y=\left| \frac{\alpha x}{x+1} \right|$, where $\alpha$ is a positive constant, stating the equations of the asymptotes. On the same diagram, sketch the line with equation $y=\alpha x-2$.

[3]

(i) Sketch the curve with equation $y=\left| \frac{\alpha x}{x+1} \right|$, where $\alpha$ is a positive constant, stating the equations of the asymptotes. On the same diagram, sketch the line with equation $y=\alpha x-2$.

[3]

(ii)

Solve the inequality $\left| \frac{\alpha x}{x+1} \right|\ge \alpha x-2$, giving your answers in term of $\alpha$.

[3]

(ii) Solve the inequality $\left| \frac{\alpha x}{x+1} \right|\ge \alpha x-2$, giving your answers in term of $\alpha$.

[3]

• (i)
• (ii)
• -
• (i)
• (ii)
• -

##### 2013 ACJC P1 Q1

Do not use a graphic calculator in answering this question.
By considering the cases $x<0$ and $x\ge 0$, find the range of values of $x$ that satisfy the inequality

$\left( 10-x \right)\left( 10-\left| x \right| \right)>11$,

[5]