The Gradient – 7.04b

Ratio, Proportion, and Rates of Change IV – OCR GCSE (J560): Higher Tier

In this course, Dr Thomas Woolley (Cardiff University) explores how changes in sets of numbers are related, covering Topics 7.04b, 5.03a, and 6.03e in the OCR GCSE (9-1) Mathematics (J560) 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 (Topic 7.04b). In the second mini-lecture, we learn how to calculate or estimate the gradients of piece-wise graphs and curves (Topic 7.04b). In the third mini-lecture, we explore how to calculate average rates of change (Topic 7.04b). 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 (Topics 5.03a, 6.03e). In the fifth mini-lecture, we continue our discussion of growth and decay problems but focus on examples involving multiple scale factors (Topic 5.03a).

The Gradient – 7.04b

In this mini-lecture, we discuss Topic 7.04b 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.