Introduction to Solving Equations

Solving Equations I – AQA GCSE (8300): Higher Tier

In this course, Professor Kieth Ball (University of Warwick) explores solving equations, covering Topics A17-A18 in the AQA GCSE (9-1) Mathematics (8300) Specification for Higher Tier. In the first mini-lecture, we give an introduction to solving equations and think about what it means to ‘solve’ and equation. In the second mini-lecture, we discuss how to solve linear equations and how to approximate solutions to linear equations using a graph (Topic A17). In the third mini-lecture, we consider how to solve quadratic equations by factorising and by using the special properties of zero (Topic A18). In the fourth mini-lecture, we learn how to solve quadratic equations by completing the square (Topic A18). In the fifth mini-lecture, we learn how to solve quadratic equations using the quadratic formula (Topic A18). The sixth mini-lecture shows how to derive the quadratic formula by competing the square on the general quadratic equation, ax² + bx + c = 0 — this is extension content that is not required for exams. In the seventh mini-lecture, we learn how to approximate solutions to quadratic equations by graphing (Topic A18).

Introduction to Solving Equations

In this mini-lecture, we give an introduction to solving equations. In particular, we think about: (i) the types of everyday problems that require solving equations; (ii) what is means to ‘solve’ and equation, such as x + 5 = 7, that is what number can we substitute in for x to make the equation true; and (iii) how to solve equations systematically using inverse operations.