Introduction to Graphs

Graphs I – AQA GCSE (8300): Higher Tier

In this course, Professor Keith Ball (University of Warwick) gives an introduction to graphs, covering topics A8-A10 in the AQA GCSE (9-1) Mathematics (8300) Specification for Higher Tier. In the first mini-lecture, we provide motivation for why studying graphs is useful and give an overview of what we will learn in the course. In the second mini-lecture, we explore the coordinate plane, discuss how to identify points on a graph, and introduce the four quadrants that make up the coordinate plane (Topic A8). In the third mini-lecture, we explore straight-line graphs and compare lines with various steepnesses (Topic A9). In the fourth mini-lecture, we explore the equation of a straight line (y = mx + c) and relate the numbers m and c to properties of the graph, where we see that m is the gradient and c is the y-intercept (Topic A10). In the fifth mini-lecture, we consider equations of lines written in forms other than y = mx + c, such as the equations of horizontal and vertical lines (Topics A9, A10). In the sixth mini-lecture, we explore how to find equations of lines given various properties, such as a point on the line and the gradient or two points on the line (Topic A9). Finally, in the seventh mini-lecture, we discuss parallel and perpendicular lines and see how to find lines that are parallel or perpendicular to a given line (Topic A9).

Introduction to Graphs

In this mini-lecture, we provide motivation for why studying graphs is useful and give an overview of what we will learn in this course. In particular, we consider: (i) a table of height versus age values; and (ii) the graph of these numbers, which helps us better understand the relationship between the two quantities (height and age).