A-Level H2 Math | 5 Essential Questions

In mathematics, the inequality relation is one of the fundamental building blocks for inequalities. It deals with the mathematical comparison of two elements, and it serves as a key to understanding why numbers behave the way they do. Inequalities allow us to describe sets of numbers and the relationship between those numbers.

This free online revision course is specially designed for students to revise important topics from A Level H2 Maths. The course content is presented in an easy to study format with 5 essential questions, core concepts and explanation videos for each question. Please download the worksheet and try the questions yourself! Have fun learning with us, consider joining our tuition classes or online courses. 
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]

Suggested Handwritten and Video Solutions
Inequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources

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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]

Suggested Handwritten and Video Solutions
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free Resources

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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]

Suggested Handwritten and Video Solutions

Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources

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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]

Suggested Handwritten and Video Solutions
Inequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free Resources
Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources

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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

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

giving your answers in exact form.

[5]

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Inequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free ResourcesInequalities A-Level (H2 Math) Inequalities Free Resources

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