Proportion

Summary and Exam Tips for Proportion

Proportion is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This topic focuses on understanding the concepts of direct and inverse variation and how to express these relationships using algebra. In direct proportion, two quantities increase or decrease at the same rate, represented as $x \propto y$ or $x = ky$, where $k$ is a constant. For example, if $z$ is directly proportional to $m$, and $z = 20$ when $m = 4$, then $z = 5m$ when $m = 7$.

In inverse proportion, one quantity increases as the other decreases, expressed as $b \propto \frac{1}{e}$ or $b = \frac{k}{e}$. For instance, if $b = 6$ when $e = 2$, then $b = 1$ when $e = 12$. Understanding these relationships allows students to solve various problems, such as calculating electric current inversely proportional to resistance or determining water temperature inversely proportional to depth. Practice questions and past paper examples reinforce these concepts, ensuring students can apply algebraic expressions to solve proportion-related problems effectively.

Exam Tips

• Understand Key Concepts: Ensure you grasp the difference between direct and inverse proportion. Remember, direct proportion means both quantities change at the same rate, while inverse proportion means one increases as the other decreases.

• Use Algebraic Expressions: Practice writing and solving equations for both direct ($x = ky$) and inverse ($x = \frac{k}{y}$) proportions. This will help you tackle exam questions efficiently.

• Solve Step-by-Step: Break down problems into steps: identify the relationship, substitute known values, solve for the constant, and find the unknown. This methodical approach will help you avoid mistakes.

• Practice with Past Papers: Familiarize yourself with the types of questions asked in past exams. This will boost your confidence and improve your problem-solving speed.

• Check Units and Values: Always double-check your calculations and ensure that your final answers make sense in the context of the problem.