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This topic covers the gradient of a straight line and of a curve (via a tangent), and interpreting gradients on real-life graphs as rates of change such as speed. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
Gradient is the change in y divided by the change in x between two points. On a curve, draw a tangent and find its gradient. In context, the gradient carries units and a meaning — on a distance-time graph it is speed.
Before you start
You will want linear graphs and coordinates at your fingertips first. From here the path runs to differentiation.
What you learn
A gradient measures a rate of change. Between two points, the gradient of the chord gives an average rate; at a single point, the gradient of the tangent gives the instantaneous rate. The rate at a single point is the gradient of the tangent there. On a distance–time graph the gradient is the speed. The course works through average rate of change, instantaneous rate of change and rates in real graphs. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Gradients & Rates of Change as one of the Algebra topics in our GCSE course library, at Higher tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Nearby topics in the same strand are Inequalities, Linear Equations, Linear Graphs, Quadratic Equations and Quadratic Inequalities. For unlimited practice, the Algebra revision engine builds new questions on demand and records your accuracy.
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