y proportional to x².y=3 when x = 0.5 x inversely proportional to w.x=2 when w= 0.2 Find y when w=2

Описание: y is proportional to x² y=3 when x = 0.5

x is inversely proportional to w x=2 when w= 0.2

Find the value of y when w=2
gcse maths direct and inverse proportion problems old previous years question papers calculator paper higher tier edexcel 2023
This video walks through a full solution to a multistep algebraic problem where y is directly proportional to x squared and x is inversely proportional to w. Given the values y = 3 when x = 0.5 and x = 2 when w = 0.2, we are required to find the value of y when w = 2. This type of compound variation problem builds foundational algebraic understanding and appears across all major math syllabi globally in core topics like functional relationships, modeling, and proportional reasoning.

In the CBSE mathematics curriculum, this type of reasoning is embedded in chapters covering linear equations, algebraic expressions, and real-world modeling tasks. While not always labeled directly, these compound relationships are routinely tested in application-based questions, internal assessments, and skill-based sections. In ICSE mathematics, similar tasks are given as part of direct and inverse proportion, often integrated into word problems and algebraic simplifications.

The IGCSE Extended Math syllabus includes such problems in Paper 2 and Paper 4 under variation and algebraic modeling. In GCSE assessments by Edexcel and AQA, these linked variation problems are part of non-calculator and calculator papers alike, especially in topics related to formula-based interpretation and application. In the IB Middle Years Programme and Diploma Programme mathematics tracks, both Applications and Interpretation and Analysis and Approaches include questions that expect learners to apply variation principles to multi-step functions.

This exact concept is also tested in Advanced Placement courses such as Algebra 2 and Precalculus under mathematical modeling and function-based reasoning. Learners following the South African CAPS curriculum in grades preparing for external exams regularly encounter variation tasks in problem-solving sections of the paper. Similar expectations are set in the Australian NESA framework, particularly under Stage 5 algebra, and the New Zealand NCEA curriculum emphasizes variation in early algebra modules.

During this lesson, you will see how to handle two mathematical relationships: first y ∝ x², then x ∝ 1/w. We calculate the constant of proportionality for both equations and combine them logically to reach the final answer. Each step is explained clearly using algebraic reasoning that is consistent with the requirements of modern global math assessments. These types of problems test more than just calculations; they demand logical sequencing, pattern recognition, and understanding the underlying structure of variable relationships.

This form of layered algebraic logic appears in math competitions and standardised tests such as the SAT Math Subject Test, ACT Math, NTSE, SOF Olympiads, and school entrance assessments across different countries. Schools that follow international syllabi use questions of this type in internal examinations and formative tasks to train students in compound functional relationships.

Students preparing for ICSE or CBSE school tests, IGCSE math papers, IB examinations, AP mathematics units, or national math contests will benefit from seeing this entire solution. Whether the question appears in a test or during coursework, mastering this approach helps build flexible thinking and algebraic fluency. The method shown here aligns with current curricular goals across all major educational systems, enhancing learners’ ability to perform well under structured assessment formats.

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