Simple Equations and Variations - Mathematics (Senior Secondary)

This course builds essential algebraic skills required for all scientific and technical fields. It is divided into two parts: the manipulation of equations and the study of variation. You will first learn to confidently rearrange and solve formulae, then master the principles of direct, inverse, joint, and partial variation to model relationships between quantities. The ability to manipulate equations and understand variation is fundamental to problem-solving in science and engineering. These skills are not abstract - they are the tools used to model physical laws, analyse data, and create predictive financial models. Proficiency here is a direct prerequisite for physics, chemistry, economics, and higher mathematics. By the end of of this course, you will be able to change the subject of any formula, regardless of its complexity. You will also be able to identify the type of variation in a given problem, formulate an equation to model it, and use that equation to find unknown values. This course is designed for students building their core algebraic foundation. It is essential for anyone planning to study science, engineering, or economics at a higher level. A basic understanding of linear equations is assumed.

Enrolment valid for 12 months

Course Chapters

1. Change Of Subject of Formula Involving Roots, Bracket, Powers
Changing the subject of a formula by rearranging equations that include roots, powers and brackets to isolate the desired variable.
1. Introduction
1
This chapter outlines the two main topics of the course. It introduces the concepts of algebraic manipulation and variation, explaining why they are critical skills for problem-solving. Key learning objectives include understanding the course structure and recognising the importance of rearranging formulae and modelling relationships between variables.
Concept Overviews
1 Lesson
2. Working With Formulae
2
1
This chapter focuses on the essential skill of manipulating algebraic equations. It covers the systematic process for changing the subject of a formula and substituting values correctly. Key learning objectives include isolating any variable in a formula and performing substitutions accurately, even with complex expressions.
Concept Overviews
2 Lessons
Problem Walkthroughs
1 Lesson
2. Subject of Formula and Substitution
In this chapter you will further learn how to substitute for a given variable after making it the subject of the Formula.
3. Variations
In this chapter, you will learn different types of variation like:- Direct, Inverse, Joint and Partial variation.
3. Variations
2
3
This chapter provides a comprehensive introduction to the concept of variation. It defines and analyses the four primary types of variation used to model relationships between variables and applies them to real-world problems. Key learning objectives include identifying and describing direct, inverse, joint, and partial variation, and translating word problems into mathematical equations to solve for unknown values.
Concept Overviews
2 Lessons
Problem Walkthroughs
3 Lessons
4. Applications of Variation
Learning how different types of variation:-direct, inverse, joint, and partial are used to solve everyday problems and practical questions.
4. Conclusion and Next Steps
2
This concluding chapter reviews the core algebraic skills covered in the course. It solidifies the understanding of manipulating equations and modelling variation. Key outcomes include a review of the methods for changing the subject of a formula and solving variation problems, in preparation for the next level of algebra.
Concept Overviews
2 Lessons