Introduction to Quadratic Equations - Mathematics (Senior Secondary)

This course provides a focused introduction to quadratic equations, a cornerstone of algebra. We will move beyond linear equations to explore expressions with a squared term, covering the essential skills needed for the first term curriculum. The course focuses on the factorisation method for solving quadratics and the process of forming equations from their roots. Quadratic equations are essential tools in a vast range of fields. They are used in physics to model projectile motion, in engineering to design parabolic structures like satellite dishes, and in finance to optimise profit. Mastering these introductory concepts is a non-negotiable step for anyone advancing in mathematics or the physical sciences. By the end of this course, you will be able to factorise any simple quadratic expression and use this method to find the roots of an equation. You will also learn to construct a quadratic equation if you are given its roots, providing a solid foundation before moving on to more advanced methods in later terms. This course is designed for students who have a solid foundation in linear equations and algebraic factorisation. It is a critical course for all students on the science track and serves as the gateway to the study of more complex polynomials and functions.

Enrolment valid for 12 months

Course Chapters

1. Introduction
1
This chapter introduces the concept of a quadratic equation. It defines its standard form and explains why it represents a significant step forward from linear equations. Key learning objectives include identifying a quadratic equation and understanding the new types of problems that can be solved.
Concept Overviews
1 Lesson
2. Solving Quadratic Equations by Factorisation
3
1
This chapter focuses on the algebraic method of solving quadratic equations by factorisation. It builds on existing knowledge of integers to develop a systematic approach to finding roots. Key learning objectives include factorising quadratic expressions and mastering the use of the null factor law to solve quadratic equations.
Concept Overviews
3 Lessons
Problem Walkthroughs
1 Lesson
3. Forming and Graphing Equations
3
1
This chapter explores the relationship between the roots of a quadratic equation and its algebraic and graphical forms. It covers how to construct equations and visualise them as parabolas. Key learning objectives include forming a quadratic equation from its given roots and drawing a quadratic graph to obtain its roots visually.
Concept Overviews
3 Lessons
Problem Walkthroughs
1 Lesson
4. Conclusion and Next Steps
2
This concluding chapter summarises the key concepts of quadratic equations, reinforcing the understanding of algebraic and graphical methods. It prepares the student for more advanced topics. Key outcomes include a review of the methods for solving, forming, and graphing quadratic equations, and an understanding of how this knowledge fits into the broader study of functions.
Concept Overviews
2 Lessons