The Gradient – R14, R15

Ratio, Proportion, and Rates of Change IV – AQA GCSE (8300): Higher Tier

In this course, Dr Thomas Woolley (Cardiff University) explores how changes in sets of numbers are related, covering Topics R14-R16 in the AQA GCSE (9-1) Mathematics (8500) Specification for Higher Tier. In the first mini-lecture, we introduce the concept of the gradient and learn how to calculate the gradient of straight-line graphs (Topics R14, R15). In the second mini-lecture, we learn how to calculate or estimate the gradients of piece-wise graphs and curves (Topic R15). In the third mini-lecture, we explore how to calculate average rates of change (Topic R15). In the fourth mini-lecture, we introduce growth and decay problems, in which populations grow or decay at a constant proportion of the original population, and we use a systematic iterative approach called a bisection search (Topic R16). In the fifth mini-lecture, we continue our discussion of growth and decay problems but focus on examples involving multiple scale factors (Topic R16).

The Gradient – R14, R15

In this mini-lecture, we discuss Topic R14 by introducing the concept of the gradient. In particular, we consider: (i) how y changes with respect to x on the curve of a graph; (ii) define the gradient as the change in y divided by the change in x; (iii) how to identify a gradient as large, small, or negative; and (iv) examples of how to calculate and interpret the gradient of straight-line graphs.